JP2008008855A - Time history response analysis method, device, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform time history response analysis with high-accuracy in which the frequency dependence and nonlinear strain dependence are each taken into account for a first object, having a relation between external force vibrating the object and the behavior of the object exhibiting frequency dependence and nonlinear strain dependence or a second object influenced by the behavior of the first object. <P>SOLUTION: Dynamic rigidity, when strain level γ of the ground is at each value, is calculated (102), and a set of impulse response values, when the strain level γ of the ground is at each value, are calculated by converting the calculated dynamic rigidly into respective time region (104 to 112). The strain level γ, when the analysis object time t is at each time, is calculated; and after the set of impulse response values corresponding to the calculated strain level γ are calculated for each time (114 to 124), the time history response analysis that calculates the displacement, the velocity, and the acceleration of the analysis object at each time is performed (126 to 138), while sequentially using the set of impulse response values calculated for each time. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a time history response analysis method, apparatus, and program, and in particular, a first object in which the relationship between an external force that vibrates an object and the behavior of the object exhibits frequency dependence and nonlinear distortion dependence, or the first Time history response analysis method suitable for time history response analysis of the second object affected by the behavior of the object, time history response analysis device to which the time history response analysis method can be applied, and computer for the time history response analysis device Related to a time history response analysis program.

  Viscoelastic bodies used in the ground during earthquakes, damping dampers, etc. have non-linear relationships between the external force (reaction force) and behavior (displacement) (dynamic characteristics) and frequency dependence (also called frequency dependence). It is known that each exhibits a strain dependency (characteristic that a reaction force of an object changes nonlinearly with respect to a change in the strain of the object: also referred to as strain amplitude dependency). When analyzing and evaluating the behavior of this type of object, simply performing a linear response analysis (frequency response analysis) in the frequency domain or a non-linear response analysis (time history response analysis) in the time domain It is difficult to accurately analyze the behavior of the object by evaluating the influence of the frequency dependence of the dynamic characteristics and the influence of the nonlinear strain dependence.

  For such a problem, a method of performing a response analysis by replacing an object to be analyzed with a simple physical model is known. For example, Non-Patent Document 1 discloses a generalization that is a kind of the above physical model. A technique is disclosed in which the frequency dependence is expressed by the Maxwell element, and the nonlinear distortion dependence is expressed by changing the coefficient of the generalized Maxwell element. When the object to be analyzed is replaced with a simple physical model such as a generalized Maxwell element, nonlinear response analysis is performed on the replaced physical model in the time domain, thereby affecting the influence of frequency dependence and nonlinear distortion dependence. The behavior of an object can be analyzed in consideration of the influence of sex.

In connection with the above, the inventor of the present application described the dynamic characteristics of the ground (specifically, the relationship between the seismic motion and the ground behavior, the frequency at which the values of the real part and the imaginary part change according to the change in the frequency of vibration As a conversion method that can convert the dynamic stiffness of the ground to the impulse response expressed in the time domain with high accuracy even when the frequency dependence of the ground dynamic stiffness (also referred to as ground impedance) expressed by a complex function of the region is strong. In addition to the time-delay component that is both displacement-dependent and velocity-dependent, a form having an acceleration-dependent simultaneous component is set as a general solution of the reaction force F (t) using the impulse response, and the set reaction force F (t ) And the equation of the dynamic stiffness S (ω) of the ground expressed by using the simultaneous component and the time delay component of the impulse response from this general solution, N (at each frequency of ω _{0 to} ω _n = N + 1) Dynamic stiffness data D (ω _i ) of ground A conversion method is proposed in which simultaneous equations having a coefficient matrix of 2N × 2N are set up and each component of the impulse response is obtained by solving the simultaneous equations (see Patent Document 1).

In addition, when the technique described in Patent Document 1 is applied, the inventor of the present application converts the dynamic characteristics of the analysis target object in the frequency domain even when the dynamic characteristics of the analysis target object shows frequency dependence. Focusing on the fact that the impulse response (impulse response reflecting the frequency dependence) that accurately represents the dynamic characteristics of the object in the time domain can be obtained, the impulse response proposed in Patent Document 1 By using the mathematical expression that defines the reaction force F (t) and transforming the dynamic characteristics of the object to be analyzed so that the nonlinear distortion dependence can be expressed and used for time history response analysis, the motion of the object to be analyzed A technique that enables time history response analysis in consideration of frequency dependence and nonlinear distortion dependence in the dynamic characteristics has also been proposed (see also Patent Document 2).
Mika Kaneko and Yutaka Nakamura, “Building a mechanical model of viscoelastic dampers with amplitude and frequency dependence”, Architectural Institute of Japan, Vol. 44B, March 1998, p. 263-270 JP 2006-010604 A JP 2006-071366 A

  If the technique described in Non-Patent Document 1 or the technique described in Patent Document 2 is applied, the relationship between the external force that vibrates the object and the behavior of the object exhibits frequency dependence and nonlinear distortion dependence. Time history response analysis can be performed in consideration of frequency dependence and nonlinear distortion dependence. However, these technologies are based on the premise that the frequency-dependent characteristics of the object do not change even if the distortion level of the object changes (the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain). In fact, the relationship between the external force that vibrates the object and the behavior of the object shows frequency dependence and nonlinear distortion dependence. Along with the change, the frequency-dependent characteristic of the object itself changes. Therefore, even if the behavior of the object as described above is analyzed using these techniques, it is difficult to accurately evaluate the influence of the frequency dependence and the nonlinear distortion dependence of the dynamic characteristics of the object. There was room for improvement.

  The present invention has been made in consideration of the above facts, and the relationship between the external force that vibrates the object and the behavior of the object exhibits frequency dependence and nonlinear distortion dependence, or the behavior of the first object. Time history response analysis method, time history response analysis apparatus, and time history response analysis capable of performing highly accurate time history response analysis in consideration of frequency dependence and nonlinear distortion dependence for the second object affected The purpose is to get a program.

  In order to achieve the above object, the time history response analysis method according to the first aspect of the present invention provides an external force that vibrates the first object and the first force when the strain level of the first object is a plurality of different values. Each of the dynamic stiffnesses representing the relationship with the behavior of one object in the frequency domain is obtained, and the dynamic stiffness when the strain level is each value is converted into the time domain, so that when the strain level is each value, An impulse response that represents the relationship of the first object in the time domain is obtained, and an impulse response corresponding to a distortion level of the first object at the analysis target time t is used to determine the first object at the analysis target time t. By analyzing the behavior or the behavior of the second object affected by the behavior of the first object while repeating the analysis target time t in increments of Δt, the first object or the second object Time history response solution It is carried out.

  According to the first aspect of the present invention, the dynamic stiffness expressing the relationship between the external force that vibrates the first object and the behavior of the first object in the frequency domain when the strain level of the first object is different from each other. Each is obtained, and the dynamic stiffness when the strain level of the first object is each value is converted into the time domain, whereby the relationship between the external force and the behavior of the first object when the strain level of the first object is each value. Are respectively obtained in the time domain. In this way, the dynamic stiffness of the first object is obtained, and the impulse response is obtained from the obtained dynamic stiffness by performing each of the cases when the strain level of the first object is different from each other. Impulse responses that express the relationship between the external force that vibrates the object and the behavior of the object in the time domain can be obtained for each time when the strain level of the first object is each value.

  The invention described in claim 1 uses the impulse response corresponding to the distortion level of the first object at the analysis target time t to determine the behavior of the first object at the analysis target time t or the influence of the behavior of the first object. By analyzing the behavior of the received second object while changing the analysis target time t in increments of Δt, the time history response analysis of the first object or the second object is performed. As the first object, an object in which the relationship between the external force that vibrates the object and the behavior of the object exhibits frequency dependency and nonlinear strain dependency, such as a ground or a viscoelastic body at the time of an earthquake, can be applied. In addition, examples of the second object affected by the behavior of the first object include a building constructed on the ground as the first object. The present invention can be applied to the case where the time history response analysis is performed for any of the first object and the second object. Further, analyzing the behavior of the first object or the second object at the analysis target time t is performed, for example, by calculating the reaction force, displacement, velocity, and acceleration of the first object or the second object at the analysis target time t. be able to.

  Thus, according to the first aspect of the present invention, the impulse response when the distortion level of the first object is each value is obtained in advance, and the time history response analysis of the first object or the second object is performed at each time. Since the behavior of the first object or the second object at each time is sequentially analyzed while appropriately switching the impulse response used for the calculation in accordance with the distortion level of the one object, the first object is changed along with the change in the distortion level of the first object. The change in the frequency dependence characteristic of the first object and the change in the behavior of the first object can be reflected in the behavior analysis at each time by switching the impulse response. Therefore, according to the first aspect of the present invention, the relationship between the external force that vibrates the object and the behavior of the object is affected by the first object exhibiting frequency dependence and nonlinear distortion dependence or the behavior of the first object. Time history response analysis can be performed with high accuracy for the second object in consideration of frequency dependence and nonlinear distortion dependence.

  According to the first aspect of the present invention, the first calculation means calculates the dynamic stiffness when the strain level of the first object has a plurality of values, and the second calculation means calculates the calculated dynamic stiffness as time. Since the impulse response is calculated by converting each to the region, the distortion level for which the corresponding impulse response is calculated is discretely distributed with respect to the change of the distortion level, and the first object at the analysis target time t. May be a value for which the corresponding impulse response is not calculated. In consideration of the above, for example, as described in claim 2, when the distortion level of the first object at the analysis target time t is a distortion level whose corresponding impulse response is an unknown distortion level, the corresponding impulse response is a known distortion level. It is preferable that an impulse response corresponding to the distortion level of the first object at the analysis target time t is obtained by interpolation calculation from the impulse response at the level. As a result, even when the distortion level of the first object at the analysis target time t is a value for which the corresponding impulse response is unknown (not calculated), the accuracy of the time history response analysis at the analysis target time t and its vicinity. Can be prevented from significantly decreasing.

  In the time history response analysis, the behavior of the object at the analysis target time t is calculated and analyzed in consideration of the behavior (for example, displacement, velocity, etc.) of the object at the time before the analysis target time t. If it changes every moment, the impulse response corresponding to the distortion level of the object at which time is used as the impulse response that multiplies the displacement or velocity of the object at the time before the analysis target time t as a coefficient. It becomes a problem. Here, in the invention described in claim 1, the impulse response at the time t-tj (where j is a natural number and tj = Δt · j) prior to the analysis target time t is, for example, as described in claim 3. In addition, a first impulse response corresponding to the strain level of the first object at time t-tj, a second impulse response corresponding to the strain level of the first object at analysis target time t, and after time t-tj and Calculation (for example, average) from the third impulse response corresponding to the distortion level of the first object at any time after the analysis target time t, and a plurality of impulse responses corresponding to the distortion levels of the first object at different times Any one of the fourth impulse responses obtained by calculation of the value and the interpolated value) can be used, and any one of the first to fourth impulse responses can be used at the analysis target time t. Behavior of first object or the second object can be analyzed.

  As long as the inventor of the present application has analyzed and analyzed, the time history response analysis is performed when any of the first to fourth impulse responses is used as the impulse response at the time t-tj before the analysis target time t. It has been confirmed that there is no significant difference in accuracy, and any one of the first to fourth impulse responses may be used. Depending on the type and conditions of the object to be analyzed, the accuracy of the time history response analysis may vary depending on which of the first to fourth impulse responses is used. Whichever of the impulse responses is used, the calculation amount itself is substantially the same. In this case, the impulse response that provides the highest accuracy among the first to fourth impulse responses may be selectively used.

  In the invention described in claim 1, the time history response analysis of the first object or the second object is more specifically described in claim 4, in which the first object is analyzed when the analysis target time t is each time. After calculating the strain level in advance, assuming the displacement / velocity / acceleration of the first object or the second object at the analysis target time t, an impulse response corresponding to the strain level of the first object calculated at the analysis target time t is calculated in advance. The displacement / velocity / acceleration of the first object or the second object at the analysis target time t is used to calculate whether the external force applied to the first object or the second object is balanced with the reaction force of the first object or the second object. If it is determined that the external force and the reaction force are not balanced, the assumed displacement / velocity / acceleration of the first object or the second object is corrected until it is determined that the external force and the reaction force are balanced. Displacement of one object or second object The process of repeating the calculation of the velocity and acceleration can be realized by sequentially performed while changing the analysis target time t by Delta] t.

  In the invention according to claim 4, the distortion level of the first object when the analysis target time t is each time is calculated in advance, and the assumed displacement of the first object or the second object at a certain analysis target time t. Regardless of whether the velocity / acceleration is corrected or not, the displacement / velocity / acceleration of the first object or the second object is calculated using an impulse response corresponding to the distortion level of the first object calculated at that time in advance. Therefore, although the accuracy of the time history response analysis may be somewhat lowered, the processing time can be shortened. In addition, when the relationship between the external force and the behavior of the object is frequency-dependent and nonlinear distortion-dependent (first object) and the object to be analyzed in the time history response analysis are different (the object to be analyzed is Even in the case of the second object, it is possible to perform a time history response analysis of the second object in consideration of the influence of the frequency dependency and nonlinear distortion dependency of the first object.

  In the first aspect of the invention, when the object to be analyzed in the time history response analysis is the first object, the time history response analysis of the first object is more specifically analyzed as described in claim 5. Assuming the displacement / velocity / acceleration of the first object at the target time t, the distortion level of the first object corresponding to the assumed displacement of the first object is calculated, and analysis is performed using the impulse response corresponding to the calculated distortion level. The displacement / velocity / acceleration of the first object at the target time t is calculated, it is determined whether or not the external force applied to the first object and the reaction force of the first object are balanced, and it is determined that the external force and the reaction force are not balanced. In this case, the assumed first object displacement / velocity / acceleration is corrected, the first object strain level is calculated, and the first object displacement / velocity / acceleration is calculated until it is determined that the external force and the reaction force are balanced. Repeat the process to analyze While the time t is varied by Δt it can be implemented by performing in sequence.

  In the invention according to claim 5, the object to be analyzed in the time history response analysis is different from the object (first object) in which the relationship between the external force and the behavior of the object exhibits frequency dependence and nonlinear distortion dependence. Although it is difficult to apply in some cases, it is corrected when the assumed displacement / velocity / acceleration of the first object is corrected by determining that the external force applied to the first object and the reaction force of the first object are not balanced. The distortion level of the first object is corrected (recalculated) in accordance with the displacement of the first object, and the displacement, velocity, and acceleration of the first object at the analysis target time t using the impulse response corresponding to the corrected distortion level. Therefore, the accuracy of the time history response analysis can be improved as compared with the invention according to claim 4.

  According to a sixth aspect of the present invention, there is provided the time history response analyzing apparatus according to the present invention, wherein the relationship between the external force that vibrates the first object and the behavior of the first object when the distortion level of the first object is a plurality of different values. First dynamic means for calculating the dynamic stiffness expressed in the frequency domain, respectively, and converting the dynamic stiffness when the strain level is each value into the time domain, so that the strain level when the strain level is each value. Second calculation means for calculating an impulse response representing the relationship of the first object in the time domain, and an impulse response corresponding to the distortion level of the first object at the analysis target time t, and the analysis target time t Analyzing the behavior of the first object or the behavior of the second object affected by the behavior of the first object is repeated while changing the analysis target time t in increments of Δt. Or of the second object Therefore, the relationship between the external force that vibrates the object and the behavior of the object is frequency-dependent and non-linear strain-dependent, as in the first aspect of the invention. The time history response analysis can be performed with high accuracy in consideration of the frequency dependence and the nonlinear distortion dependence on the first object exhibiting the property or the second object affected by the behavior of the first object.

  According to a seventh aspect of the present invention, there is provided a time history response analysis program that causes a computer to cause an external force to vibrate the first object and a behavior of the first object when the first object has a plurality of different strain levels. First dynamic means for calculating the dynamic stiffness representing the relationship with the frequency domain, respectively, by converting the dynamic stiffness when the strain level is each value into the time domain, so that the strain level is each value Second analysis means for calculating an impulse response representing the relationship of the first object in a time domain, and an impulse response corresponding to a distortion level of the first object at an analysis target time t. By repeating the analysis of the behavior of the first object at the time t or the behavior of the second object affected by the behavior of the first object while changing the analysis target time t in increments of Δt, First To function as an analysis means for performing a time history analysis of the object or the second object.

  The time history response analysis program according to the invention as set forth in claim 7 is a program for causing a computer to function as the first calculation means, the second calculation means and the analysis means, and therefore the computer according to claim 7. By executing the time history response analysis program according to the above, the computer functions as the time history response analysis device according to claim 6, and vibrates the object as in the inventions according to claims 1 and 6. Frequency dependence and nonlinear strain dependence for a first object whose relationship between the external force to be applied and the behavior of the object exhibits frequency dependence and nonlinear strain dependence or a second object affected by the behavior of the first object It is possible to perform time history response analysis considering each of the above with high accuracy.

  As described above, the present invention calculates the dynamic stiffness when the strain level of the first object has a plurality of different values, and converts each of the dynamic stiffness into the time domain. The analysis object is to calculate the impulse response at the time of each value and analyze the behavior of the first object or the second object at the analysis object time t using the impulse response corresponding to the distortion level of the object at the analysis object time t. Since the time history response analysis of the object is performed by repeating time t while changing by Δt, the relationship between the external force that vibrates the object and the behavior of the object shows frequency dependence and nonlinear distortion dependence. An excellent effect that a time history response analysis can be performed with high accuracy in consideration of frequency dependence and nonlinear distortion dependence for one object or a second object affected by the behavior of the first object. Have .

  Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 shows a personal computer (PC) 10 to which the present invention can be applied. The PC 10 is configured by connecting a CPU 10A, a ROM 10B, a RAM 10C, and an input / output port 10D to each other via a bus 10E including a data bus, a control bus, an address bus, and the like. The input / output port 10D is a CD 12 for reading out information from a display 12, a keyboard 14, a mouse 16, a printer 18, a hard disk drive (HDD) 20, and a CD-ROM 22 as various input / output devices. -ROM drives 24 are connected to each other.

  A time history response analysis program for performing a time history response analysis process described later is installed in the HDD 20 of the PC 10. This time history response analysis program corresponds to the time history response analysis program according to the present invention. There are several methods for installing (transferring) the time history response analysis program to the PC 10. For example, the time history response analysis program is recorded on the CD-ROM 22 together with the setup program, and the CD-ROM 22 is stored in the CD-ROM. If set in the drive 24 and instructs the CPU 10A to execute the setup program, the time history response analysis program is sequentially read from the CD-ROM 22, and the read time history response analysis program is sequentially written to the HDD 20. Thus, the time history response analysis program is installed. The PC 10 functions as a time history response analysis apparatus according to the present invention by the CPU 10A executing the time history response analysis program.

  The computer according to claim 7 is not limited to the PC 10, and may be, for example, a workstation or a general-purpose large computer.

  Next, as an operation of the present embodiment, the execution of the time history response analysis program is instructed via the keyboard 14 or the mouse 16 by the operator who desires to execute the time history response analysis, and is executed by the CPU 10A of the PC 10. The time history response analysis process will be described with reference to the flowchart of FIG. In the following, the relationship between the external force (reaction force) and the behavior (displacement) (dynamic characteristics) shows frequency dependency (frequency dependency) and nonlinear strain dependency (strain amplitude dependency). An example in which the ground is applied as an object, and a building (corresponding to the second object) that is constructed on the ground and is affected by the behavior of the ground during an earthquake is applied as an object to be analyzed in the time history response analysis Explained. The ground on which the building to be analyzed is constructed is hereinafter referred to as the ground to be analyzed.

In step 100, calculation condition data for calculating the dynamic stiffness of the ground to be analyzed is acquired. As the calculation condition data, for example, as shown in FIG. 3A, the structure of the ground to be analyzed, the layer thickness H of each layer, the propagation velocity Vs of the seismic wave, the Poisson's ratio ν, the density ρ, the attenuation rate h, Data on the shape and size of the foundation of the building to be analyzed and, as shown in FIG. 3 (B), the strain level γ-shear stiffness reduction rate G / G ₀ characteristics, strain level γ-damping rate of the ground to be analyzed h characteristics and the like. In addition, in FIG. 3A, as an example of the ground to be analyzed, the dynamic characteristics of only the surface ground are frequency dependence (frequency dependence) and non-linear strain dependence (strain amplitude dependence) as an example of the ground to be analyzed. ) Is shown. For this reason, in FIG. 3A, the surface velocity of the ground layer Vs and the damping rate h are shown for convenience when the ground strain level γ ≦ 0.001%, and the shear stiffness reduction rate of the upper layer is shown. G / G ₀ and the attenuation rate h change as shown in FIG. 3B with respect to the change in the strain level γ of the ground to be analyzed.

  Of the data acquired in step 100, various data relating to the ground to be analyzed can be obtained by, for example, boring the ground to be analyzed and performing a predetermined test on the sample obtained by this boring. it can. In addition, the above calculation condition data is not limited to using data obtained by performing a predetermined test on a sample as it is, for example, an analysis target for aftershocks after a relatively strong earthquake has occurred. When you want to analyze the behavior of the ground or the building built on it, assuming that the characteristics of the ground subject to analysis change due to a relatively strong earthquake, for the data obtained by a predetermined test, Data obtained by changing the value corresponding to the characteristic change may be used as the calculation condition data. In step 100, the calculation condition data is acquired by allowing the operator to input the calculation condition data through the keyboard 14 or by reading the calculation condition data from a recording medium (for example, a CD-ROM) in which the calculation condition data is recorded in advance. Is temporarily stored in the memory (RAM 10C) or HDD 20.

In the next step 102, the calculation condition data acquired in step 100 is read from the memory or the HDD 20, and the dynamic stiffness of the analysis target ground when the strain level γ of the analysis target ground is each value is calculated from the read calculation condition data. Calculate each one. Specifically, for example, among parameters used for calculating the dynamic stiffness of the ground, parameters that do not depend on changes in the ground strain level γ (for example, Poisson's ratio ν and density ρ) are set in the read calculation condition data. For parameters that change depending on changes in the ground strain level γ (for example, seismic wave propagation velocity Vs, attenuation rate h, etc.), the γ-shear stiffness reduction included in the read calculation condition data A value when the ground strain level γ is a predetermined value is derived from the rate G / G ₀ characteristic or γ-h characteristic and used. Based on these parameters, the dynamic stiffness of the ground to be analyzed when the ground strain level γ is a predetermined value is calculated by applying a calculation method such as the thin layer element method, and the dynamic dynamics obtained by the calculation are calculated. Rigidity data is temporarily stored in the memory or HDD 20. By performing the above process using m different values (γ ₁ , γ ₂ , ..., γ _m ) as the ground strain level γ, the external force (earthquake) that vibrates the ground and the behavior of the ground Dynamic stiffness data representing the relationship in the frequency domain can be obtained for each of m different strain levels γ.

  For example, in FIG. 4, the values of 0.001%, 0.002%, 0.005%, 0.01%, 0.02%, 0.05%, 0.1%, 0.2%, 0.5%, and 1.0% are used as the strain level for calculating the dynamic stiffness. (M = 10), the dynamic stiffness of the ground to be analyzed shown in FIGS. 3 (A) and 3 (B) is calculated over the frequency range of 0 to 10 (Hz) as the horizontal component / rotational component. , Divided into real part / imaginary part. The dynamic stiffness data is not limited to being obtained by calculation, but can be obtained by performing an experiment. Steps 100 and 102 described above correspond to the first calculation means according to the present invention.

In step 104, 1 is substituted for the variable i, and in the next step 106, among the data of the dynamic rigidity of the ground to be analyzed at each strain level obtained by the calculation in step 102, the analysis target at the strain level γ _i is obtained. Data on the dynamic stiffness of the ground is read from the memory or HDD 20. Then, from the read dynamic stiffness data, N representing the value of dynamic stiffness at N types of frequencies (N types of angular frequencies ω ₁ ,..., Ω _N ) within a preset frequency range to be calculated. Each of the complex data D (ω ₁ ),..., D (ω _N ) is extracted, and the extracted complex data is stored in the memory or the HDD 20.

  The complex data extracted in step 106 is used for the calculation of an impulse response that represents the relationship between the external force (reaction force) and the behavior (displacement) of the object in the time domain. By this calculation, time t = 0 and time t = Impulse response data representing the impulse response of the ground at each time of Δt · j (j = 1, 2, ..., n) can be obtained. The number of impulse response data obtained depends on the number of complex data used in the calculation. The maximum value n of j is the number of complex data −1 (= N−1), and the time range of the impulse response of the ground represented by the obtained impulse response data also depends on the number of complex data used in the calculation. (For example, when the number of complex data is 21 and Δt = 0.05 seconds, tn = Δt · jmax = 0.05 × 20 = 1 second, which represents the impulse response of the ground in the time range from time t = 0 to 1 second. 21 Impulse response Therefore, the number of complex data extracted from the dynamic stiffness of the ground (number of types of frequencies for extracting complex data) is also the length of the time range for calculating the impulse response of the ground. It can be determined in advance.

Here, the dynamic stiffness S (γ, ω) of an object in which the relationship between the external force (reaction force) and the behavior (displacement) shows frequency dependency and nonlinear strain dependency is expressed by the following equation (1). Thus, it is represented by the sum of the real part S ₁ (γ, ω) and the imaginary part S ₂ (γ, ω).
S (γ, ω) = S ₁ (γ, ω) + i · S ₂ (γ, ω) (1)
Also, the simultaneous component of the impulse response (rigidity term) depending on the displacement of the object is k ₀ (γ), the simultaneous component of the impulse response (attenuation term) depending on the velocity of the object is c ₀ (γ), and the acceleration of the object. The simultaneous component of the dependent impulse response (mass term) is m ₀ (γ), the time delay component in Δt increments of the impulse response depending on the displacement of the object is k _j (γ), and the impulse response is dependent on the velocity of the object Δt The time delay component of the step is c _j (γ) (where j is a natural number, t _j = Δt · j), the displacement of the object in the time domain is u (t), the velocity is u '(t), and the acceleration is u “(t), the reaction force F (γ, t) corresponding to the strain level γ is expressed by the following equation (2).

In addition, the simultaneous component (k ₀ (γ), c ₀ (γ), m ₀ (γ)) and the time delay component (k ₁ (γ), k ₂ (γ),. k _N-1 (γ), c ₁ (γ), c ₂ (γ),..., c _N-2 (γ)), the dynamic stiffness S (γ, ω) is expressed by the following equation (3): It is represented by

Based on the above equations (2) and (3), impulse response is obtained by converting _N complex data D (ω ₁ ), ..., D (ω _N ) extracted from dynamic stiffness data into the time domain. Having a coefficient matrix of 2N × 2N for calculating the values (k ₀ (γ) to k _N-1 (γ), c ₀ (γ) to c _N-2 (γ), m ₀ (γ)) Simultaneous equations (equations (4) and (5)) are derived.

The HDD 20 of the PC 10 according to the present embodiment stores the above simultaneous equations (formulas (4) and (5)) for obtaining the impulse response from the dynamic stiffness data in advance. Are obtained from the HDD 20, and the N complex data D (ω ₁ ),..., D (ω _N ) extracted in step 106 are substituted into the read simultaneous equations, and a solution of the simultaneous equations is obtained. Then, impulse response data representing the impulse response of the ground to be analyzed at the strain level γ _i is calculated in increments of Δt set in advance. By this calculation, a simultaneous component (k ₀ (γ), c ₀ (γ), m ₀ (γ)) of the impulse response is obtained as impulse response data representing the impulse response of the ground, and a time delay component of the impulse response is obtained. (K ₁ (γ), k ₂ (γ), ..., k _N-1 (γ), c ₁ (γ), c ₂ (γ), ..., c _N-2 (γ)) are obtained in increments of Δt. It is done. The obtained impulse response data is temporarily stored in the memory or the HDD 20.

  In the next step 110, it is determined whether or not the variable i matches the constant m, that is, whether or not impulse response data has been calculated for all strain levels for which dynamic stiffness has been calculated in step 102. If the determination is negative, the routine proceeds to step 112, where the variable i is incremented by 1, and the routine returns to step 106. Thus, steps 106 to 112 are repeated until the determination in step 110 is affirmed, and impulse response data is calculated for each of the m types of strain levels for which dynamic stiffness has been calculated in step 102. As an example, FIG. 5 shows 21 types of frequencies (0.1 (Hz), 0.5 (Hz), 0.5 Hz), which are different from the dynamic stiffness data shown in FIG. 4 as complex data in the frequency range 0 to 10 (Hz). 1.0 (Hz), 1.5 (Hz), 2.0 (Hz),..., 10.0 (Hz)), and using the extracted complex data, Δt is 0.1 seconds and the number of time delay components to be calculated ( The result of calculating the impulse response data under the condition that n ′) is 4, the horizontal component / rotation component, the stiffness term (term depending on the displacement of the object) k / damping term (term depending on the velocity of the object) c / Mass terms (terms depending on the acceleration of the object) m are shown separately.

  For reference, in FIG. 6, among the impulse response data at each distortion level shown in FIG. 5, the impulse response data at the distortion level γ = 0.01 (%), 1 (%) is reconverted into the frequency domain. The dynamic stiffness is reproduced for each, and the result of comparing the reproduced dynamic stiffness (reproduced value) with the original dynamic stiffness (data point) corresponding to the same strain level is used as the horizontal component and rotational component. Separately shown. In FIG. 6, “Real” means the real part of the dynamic stiffness and “Imag” means the imaginary part of the dynamic stiffness. As is clear from FIG. 6, the reproduced dynamic stiffness is in good agreement with the original dynamic stiffness regardless of the magnitude of the strain level γ, horizontal component / rotational component, real part / imaginary part, It can be understood from steps 100 to 112 described above that an impulse response that accurately represents the dynamic characteristics of the ground to be analyzed in the time domain can be obtained for each strain level. Steps 104 to 112 described above correspond to the second calculation means according to the present invention.

  In the next step 114 to step 124, based on the impulse response data obtained by the above process, the strain level γ of the ground to be analyzed at each time to be analyzed in the time history response analysis described later is calculated. The impulse response value used for the calculation of the time history response analysis is determined. That is, at step 114, time t is initialized to zero. In the next step 116, data representing an external force applied to the ground to be analyzed at time t is captured, and the displacement u (t) of the ground to be analyzed at time t is estimated based on the external force represented by the captured data. The external force at the analysis target time t corresponds to the earthquake motion applied to the analysis target ground at the analysis target time t, and is performed by extracting the data of the ground motion applied to the ground at the analysis target time t from the assumed earthquake motion data. Can do. In step 118, based on the displacement u (t) of the ground to be analyzed at the time to be analyzed t estimated in step 116, the strain level γ of the ground to be analyzed at the time to be analyzed t is calculated.

In the next step 120, a set of impulse response values corresponding to the distortion level γ calculated in step 118 (simultaneous components k ₀ , c ₀ , m ₀ and time delay components k ₁ , k ₂ ,..., K _N−1 , c ₁ , c ₂ ,..., c _N−2 ), and the acquired set of impulse response values is written in the memory or HDD 20 in association with time t. As described above, in the time history response analysis processing according to the present embodiment, the dynamic stiffness and the impulse response value are calculated for m types of strain levels that are discretely distributed with respect to the strain level change. For this reason, the impulse response value set is acquired in step 120 if the strain level γ calculated in step 118 is a value obtained by calculating the dynamic stiffness and the impulse response value. Alternatively, when the strain level γ calculated in step 118 is a value corresponding to the strain level γ subjected to the calculation of the dynamic stiffness and the impulse response value, A plurality of sets of impulse response data corresponding to the preceding and following distortion levels γ are read from the memory or HDD 20, respectively, and a set of impulse response values corresponding to the distortion levels γ calculated in step 118 based on the read sets of impulse response data. Is obtained by interpolation.

Here, regarding the simultaneous components k ₀ , c ₀ , m _{0 in} the set of impulse response values, it is only necessary to acquire (read or interpolate) the impulse response value corresponding to the distortion level γ at time t. The time delay components k _j , c _j , (where j = 1, 2,..., N−2orN−1) in the set of response values are the time before time t in the time history response analysis process described later. While this is a value that takes into account the effect of the behavior of the ground subject to analysis at t-tj (where j is a natural number and tj = Δt · j), the strain level γ of the ground subject to analysis during an earthquake is sometimes Since it changes every moment, there is room for selection as to which value corresponding to the strain level γ of the ground at any point in time is used as the time delay components k _j and c _j of the impulse response value used in the calculation of the time history response analysis. There is.

As options for the time delay components k _j and c _j of the impulse response value used in the calculation of time history response analysis, for example, a time delay corresponding to the strain level γ of the ground to be analyzed at time t−tj before time t A case using components (k _j = k _j (t−tj), c _j = c _j (t−tj)) (referred to as case 1; corresponding to the first impulse response according to claim 3), time t A case using a time delay component (k _j = k _j (t), c _j = c _j (t)) corresponding to the strain level γ of the ground to be analyzed in (referred to as case 3). 2), a time delay component corresponding to the average value of case 1 and case 3 (k _j = k _j (t−t _j ) + k _j (t) / 2, c _j = c _j (t− _{tj) + c j (t)} / 2) is referred to as a case (case 2 using: fourth impulse response according to claim 3 Or equivalent), and the like.

Although details will be described later, as a result of analysis conducted by the inventor of the present application, the time history response analysis accuracy is improved when any of cases 1 to 3 is used as the time delay components k _j and c _j of the impulse response value. It has been confirmed that there is no significant difference, and any of case 1 to case 3 may be used as the time delay components k _j and c _j of the impulse response value. Depending on the type of object to be analyzed, conditions, etc., the accuracy of time history response analysis may vary depending on which of Case 1 to Case 3 is used as the time delay components k _j , c _j of the impulse response value. However, the amount of calculation itself is substantially the same regardless of which of Case 1 to Case 3 is used as the time delay components k _j and c _j of the impulse response value. Any case where the highest accuracy can be obtained may be selectively used as the time delay components k _j and c _j of the impulse response value.

  In the next step 122, it is determined whether or not the time t has reached an analysis end time tmax in a time history response analysis described later. If the determination is negative, the process proceeds to step 124, and Δt is added to time t to update time t, and the process returns to step 116. Thereby, steps 116 to 124 are repeated until the determination in step 122 is affirmed, and the impulse level corresponding to the strain level γ and the strain level γ of the ground to be analyzed at each time interval from time t = 0 to time Δt. A value is calculated.

In the next step 128 and after, time history response analysis is performed on the building as the object to be analyzed. That is, in step 126, the analysis target time t is initialized to zero. In the next step 128, data representing an external force applied to the analysis target building at the analysis target time t is captured, and based on the external force represented by the acquired data, the displacement u _s of the ground portion of the analysis target building at the analysis target time t. (t), velocity u _s '(t), acceleration u _s "(t), displacement u _b (t) of the foundation of the analysis target building, velocity u _b ' (t), acceleration u _b " (t) Are estimated. In the next step 130, among the impulse response value sets obtained at the respective times in the previous steps 114 to 124, the impulse response value set at the analysis target time t (simultaneous components k ₀ (t), c ₀ (t), m ₀ (t) and time delay components k ₁ (t), k ₂ (t), ..., k _N-1 (t), c ₁ (t), c ₂ (t), ..., c Take in _N-2 (t). Note that “(t)” attached to each impulse response value represents an impulse response value used for calculation at the analysis target time t.

In step 132, the above-mentioned displacement u _s (t), velocity u _s ' (t), acceleration u _s "(t) of the building to be analyzed assumed in step 128, and displacement u _b (t) of the base portion. , Velocity u _b ′ (t), acceleration u _b ″ (t), set of impulse response values taken in step 130, and other constants are substituted into the following equations (6) to (8), and the Newmark β method The behavior of the building to be analyzed at the time to be analyzed t is calculated by the equation (6) (the equation of motion of the seismic response analysis for the ground-building coupled system).

In the above formula, the subscript s represents the ground part of the building to be analyzed, the subscript b represents the base part, M represents the mass matrix of each part, C represents the attenuation matrix of each part, and K represents the rigidity of each part. In the matrix, y ₀ "(t) represents the input ground motion.

In the next step 134, it is determined whether or not the external force applied to the analysis target building at the analysis target time t is balanced with the reaction force of the analysis target building as a result of the calculation in step 132. In the equation of motion of equation (6), the first term on the right side represents the external force applied to the building to be analyzed at the time to be analyzed t, and the other terms in equation (6) represent the analysis target at the time to be analyzed t. It represents the reaction force of the building. The determination in step 134 is whether the deviation between the value of the first term on the right side of equation (6) and the value of the other term in equation (6) (the error in the balance between the external force and the reaction force) is within an allowable range. It is done by judging. If the determination in step 134 is negative, the process returns to step 128. In step 128, the displacement u _s (t) and velocity u _s ′ (t) of the ground portion of the building to be analyzed at the time t to be analyzed previously assumed. Then, after correcting the acceleration u _s "(t), the displacement u _b (t) of the base portion, the velocity u _b '(t), and the acceleration u _b " (t), the processing after step 130 is performed. Since the above-described steps 128 to 134 are repeated until the determination in step 134 is affirmed, the displacement u _s (t), the speed u _s ′ (t), the acceleration of the ground portion of the building to be analyzed at the analysis target time t. u _s "(t), foundation displacement u _b (t), velocity u _b '(t), acceleration u _b " (t) are within the allowable range of deviation of reaction force with respect to external force at analysis target time t Will converge to the value

The determination in step 134 is affirmed, and the displacement u _s (t), velocity u _s ′ (t), acceleration u of the ground portion of the building to be analyzed in which the deviation of the reaction force with respect to the external force at the analysis time t is within the allowable range. _{When s} "(t), foundation displacement u _b (t), velocity u _b '(t), acceleration u _b " (t) are obtained, the process proceeds to step 136, and the above time history response analysis (at each time) Displacement u _s (t), velocity u _s '(t), acceleration u _s "(t), foundation displacement u _b (t), velocity u _b ' (t), acceleration It is determined whether the calculation of u _b "(t)) has been performed until the analysis end time tmax of the time history response analysis (the analysis target time t has reached the analysis end time tmax). If the determination is negative, the process proceeds to step 138, Δt is added to the analysis target time t to update the analysis target time t, and the process returns to step 128.

Thus, steps 128 to 138 are repeated until the determination at step 136 is affirmed, and for each time in increments of time Δt from the analysis target time t, a time is set using a set of impulse response values calculated in advance for each time. History response analysis (displacement u _s (t), velocity u _s ' (t), acceleration us _s "(t), displacement u _b (t) of foundation at each time of analysis , Speed u _b ′ (t) and acceleration u _b ″ (t) are calculated sequentially. When the determination at step 136 is affirmed, the time history response analysis process is terminated. Steps 114 to 138 described above correspond to the analyzing means according to the present invention.

  As described above, in the time history response analysis processing according to the present embodiment, a set of impulse response values when the ground strain level γ is each value is calculated, and the ground time when the analysis target time t is each time is calculated. Calculate the distortion level γ, calculate the impulse response value set corresponding to the calculated distortion level γ for each time, and then use the impulse response value set calculated for each time in turn to analyze Since the time history response analysis is performed to calculate the displacement, velocity and acceleration of the building, the frequency-dependent characteristics of the ground change with the change of the ground strain level γ, and the behavior of the ground with the change of the frequency-dependent characteristics Can be reflected in the analysis of each time by switching the impulse response. Therefore, the time history response analysis of the building can be performed with high accuracy in consideration of the influence of the ground frequency dependency and nonlinear distortion dependency.

  In the above description, the relationship between the external force that vibrates the object and the behavior of the object is influenced by the behavior of the first object (that is, the ground) that exhibits frequency dependence and nonlinear distortion dependence. However, the present invention is not limited to this, and the relationship between the external force that vibrates the object and the behavior of the object shows frequency dependence and nonlinear distortion dependence. It is also possible to apply when performing time history response analysis for one object (for example, ground or viscoelastic body). In this case, as in the time history response analysis process shown in FIG. 2, prior to the execution of the time history response analysis, the distortion level of the object at each time to be analyzed is calculated, and the impulse response value corresponding to the calculated distortion level ( (Impulse response value used for time history response analysis) may be obtained in advance at each time, but the present invention is not limited to this, and the impulse response value used for calculation of time history response analysis is the time history response. You may make it obtain | require at the time of execution of analysis.

  Specifically, for example, as shown in FIG. 7, when a set of impulse response values when the distortion level γ of the object is each value is calculated (steps 104 to 114), a time history response analysis is performed in the next step 126 and thereafter. And the displacement / velocity / acceleration of the object to be analyzed at the analysis object time t is assumed (step 128), and the distortion level γ of the object to be analyzed at the analysis object time t is calculated from the assumed displacement of the object (step 128). 129), a set of impulse response values corresponding to the calculated distortion level γ is acquired (step 131), and the analysis target time is calculated using the assumed displacement / velocity / acceleration of the object to be analyzed and the set of acquired impulse response values. The behavior of the object to be analyzed at t is calculated (step 132). In this aspect, when it is determined that the external force and the reaction force are not balanced as a result of the calculation in step 132 (when the determination in step 134 is negative), in step 128 the analysis target object is analyzed at the analysis target time t. The displacement / velocity / acceleration is corrected, and based on the corrected displacement of the object to be analyzed, the recalculation of the strain level γ of the object to be analyzed at the time to be analyzed t (step 129), the impulse corresponding to the strain level γ Since the response value set is reacquired (step 131), the processing time may increase, but the accuracy of the time history response analysis can be further improved.

In the above description, the time delay corresponding to the strain level γ of the ground to be analyzed at time t−tj before time t is used as the time delay components k _j and c _j of the impulse response value used for the calculation of time history response analysis. Case 1 using components (k _j = k _j (t−tj), c _j = c _j (t−tj)), time delay component corresponding to the strain level γ of the ground to be analyzed at time t (k _j = Case 3 using k _j (t), c _j = c _j (t)), time delay component corresponding to the average value of case 1 and case 3 (k _j = k _j (t−tj) + k _j (t ) / 2, c _j = c _j (t−t _j ) + c _j (t) / 2) has been described as an example, but the present invention is not limited to this, and the time t Time delay component (k _j = k _j (t−tx) corresponding to the strain level γ of the ground to be analyzed at an arbitrary time before time tx (where 0 <tx <tj) ), c _j = c _j (t−tx)) (this case corresponds to the third impulse response according to claim 3), case 1 and case 3 In place of the time delay component corresponding to the average value (case 2), the strain level γ of the ground to be analyzed at different times (any time between time t and time t-tj before time t) A case of using a time delay component obtained by calculating an average value, an interpolated value, a weighted average value, etc., from a plurality of impulse responses corresponding to (this case corresponds to the fourth impulse response according to claim 3). May be applicable).

Next, the results of analysis studies conducted by the present inventors will be described. In this analysis study, the model shown in FIG. 3A was used as the ground to be analyzed, the surface layer was divided into 10 parts, and the lower part was used as a viscous boundary of the substrate physical properties. In addition, the Ramberg-Osgood model (hereinafter referred to as the R-O model) is used as the surface ground history characteristics, and the strain level γ at which the shear stiffness reduction rate G / G ₀ = 0.5 is set to 0.1%, and the damping rate hmax is set to 26%. By doing so, the γ-G / G ₀ characteristic and the γ-h characteristic almost corresponding to FIG. 3B were obtained. After obtaining impulse response values for each strain level by applying the present invention to the above ground model, an earthquake using Kobe phase level 2 notification wave (time increment 0.005 seconds, duration 30 seconds) as input seismic motion Response analysis was performed.

Of the impulse response values used in this seismic response analysis, the temporal change in the simultaneous component k ₀ of the horizontal component and the time delay components k ₂ and k ₄ is shown in FIG. FIG. 8B shows changes with time of the component c ₀ and the time delay components c ₂ and c ₄ , respectively. As is clear from FIG. 8, the impulse response value used for the calculation of the seismic response analysis also fluctuates greatly with time as the ground strain level γ fluctuates with time due to the input of earthquake motion. I can understand that. FIG. 8 also shows the time-dependent changes in the case where Case 1 to Case 3 are applied as the time delay components of the impulse response values for the time delay components k ₂ , k ₄ , c ₂ , and c ₄ of the impulse response values. However, the time delay component of the impulse response value used for the calculation of the seismic response analysis may be slightly different for each case where the impulse response value changes suddenly with the sudden change of the strain level γ. I can confirm.

  Moreover, this inventor performed the earthquake response analysis using the case 1-case 3 as a time delay component of an impulse response value with respect to the building built on the ground model shown to FIG. 3 (A), respectively. The building to be analyzed was a linear structure with a base of 30m x 30m and a reinforced concrete structure with 5 stories, and the mass system Sway-Rocking model (hereinafter referred to as SR model) shown in Fig. 9A was used as the analysis model. The specifications of the analysis model are shown in Table 1 below.

In addition, the internal attenuation of the building is a strain energy proportional type and h = 3%, the seismic motion shown in FIG. 9B is used as the input seismic motion, and the Sway-Rocking spring on the foundation bottom of the building changes depending on the strain level of the surface It was supposed to be.

  FIG. 10 shows the maximum response acceleration and the maximum response shear force for each case obtained by this earthquake response analysis. The maximum response acceleration in the base portion is caused by a difference of about 4% between Case 1 and Case 3, but the differences in other parts are all 1% or less, and Case 1 and Case 3 are substantially the same as a whole. . Further, the response values of case 2 are all between the response value of case 1 and the response value of case 3. Although not shown, the maximum response value generation times are almost the same in all cases, the maximum acceleration in the base portion is around 8.6 to 9.0 seconds, and the maximum response values in other parts are all around 12.6 seconds. . From these results, under the conditions of the earthquake response analysis performed by the present inventor, even if any of Case 1 to Case 3 is used as the time delay component of the impulse response used for the calculation of the time history response analysis, the analysis accuracy is improved. It can be understood that there is no big difference.

  In addition, based on the result of the seismic response analysis using the case 2 as the time delay component of the impulse response in the above seismic response analysis, as the load deformation relation of the dynamic stiffness (horizontal component) of the ground, FIG. 11A shows a chart plotting the relationship between the displacement and the reaction force of the foundation. FIG. 11B shows a chart plotted as a comparative example based on the result of performing a seismic response analysis under the same conditions by applying a known SHAKE (equivalent linear analysis method). As shown in FIG. 3B, the ground has a characteristic that rigidity (for example, shear rigidity G) decreases as the strain level γ increases. The stiffness of the ground appears as the inclination in the major axis direction of the locus drawing the ellipse shape on the chart of FIG. 11, but in the conventional method shown in FIG. 11B, the size of the ellipse drawn by the locus changes. There is no clear change in the inclination in the major axis direction. On the other hand, in the method of the present invention shown in FIG. 11A, when the size of the ellipse drawn by the trajectory is small (when the displacement is small and the strain level γ is also small), the inclination in the major axis direction is large and the size of the ellipse is large. When the height is large (when the displacement is large and the strain level γ is large), it can be confirmed that the inclination in the major axis direction is small. From this result, it can be understood that the method of the present invention can realize high-accuracy analysis reflecting the characteristics of the ground with higher accuracy than the conventional method.

It is a block diagram which shows schematic structure of PC concerning this embodiment. It is a flowchart which shows the content of a time history response analysis process. (A) is a conceptual diagram showing an example of the configuration of the ground to be analyzed, and (B) is a diagram showing an example of G-γ characteristics and h-γ characteristics. It is an image figure which shows an example of the calculation result of the dynamic rigidity for every strain level. It is an image figure which shows an example of the impulse response of the dynamic rigidity for every strain level. It is a diagram which shows the result of having compared the dynamic stiffness reproduced from the impulse response with the original dynamic stiffness. It is a flowchart which shows the other example of a time history response analysis process. It is a diagram which shows a time-dependent change of the impulse response value used for the earthquake response analysis of the ground in the analysis examination by this inventor. (A) is a conceptual diagram showing a building model, and (B) is a diagram showing an input seismic motion, which was used for the earthquake response analysis of the building in the analysis examination by the present inventor. FIGS. 4A and 4B are diagrams respectively showing the maximum response acceleration and the (B) respectively showing the maximum response shear force obtained for the cases 1 to 3 by the seismic response analysis of the building in the analysis examination by the inventor of the present application. It is a diagram which shows each the load deformation relationship of the dynamic rigidity (horizontal component) of the ground obtained by applying this invention system and a conventional system and performing an earthquake response analysis.

Explanation of symbols

10 PC
12 Display 14 Keyboard 16 Mouse 20 HDD

Claims (7)

When the strain level of the first object is a plurality of different values, dynamic stiffness representing the relationship between the external force that vibrates the first object and the behavior of the first object in the frequency domain is obtained.
By converting the dynamic stiffness when the strain level is each value to the time domain, respectively, the impulse response representing the relationship of the first object in the time domain when the strain level is each value is obtained, respectively.
Using the impulse response corresponding to the strain level of the first object at the analysis target time t, the behavior of the first object at the analysis target time t or the second object affected by the behavior of the first object A time history response analysis method for performing time history response analysis of the first object or the second object by repeating behavior analysis while changing the analysis target time t in increments of Δt.   When the distortion level of the first object at the analysis target time t is a distortion level whose corresponding impulse response is an unknown distortion level, from the impulse response when the corresponding impulse response is a known distortion level, the analysis target time t 2. The time history response analysis method according to claim 1, wherein an impulse response corresponding to the distortion level of the first object is obtained by interpolation calculation.   A first impulse corresponding to a distortion level of the first object at time t-tj as an impulse response at time t-tj (where j is a natural number, tj = Δt · j) prior to the analysis target time t. Response, second impulse response corresponding to the distortion level of the first object at the analysis object time t, distortion of the first object at any time after the time t-tj and after the analysis object time t The analysis target using any one of a third impulse response corresponding to a level and a fourth impulse response obtained by calculation from a plurality of impulse responses corresponding to distortion levels of the first object at different times The time history response analysis method according to claim 1, wherein the behavior of the first object or the second object at time t is analyzed. After calculating in advance the distortion level of the first object when the analysis target time t is each time,
Assuming the displacement / velocity / acceleration of the first object or the second object at the analysis target time t, the analysis target is calculated using an impulse response corresponding to the strain level of the first object calculated at the analysis target time t. The displacement / velocity / acceleration of the first object or the second object at time t is calculated, and the external force applied to the first object or the second object balances the reaction force of the first object or the second object. If it is determined that the external force and the reaction force are not balanced, the hypothetical first object or the second object is determined until it is determined that the external force and the reaction force are balanced. The first object is obtained by sequentially performing the process of correcting the displacement / velocity / acceleration and calculating the displacement / velocity / acceleration of the first object or the second object while changing the analysis target time t by Δt. Time history analysis method according to claim 1, characterized in that the time history analysis of the second object.   Assuming the displacement / velocity / acceleration of the first object at the analysis target time t, the strain level of the first object corresponding to the assumed displacement of the first object is calculated, and the impulse response corresponding to the calculated strain level Is used to calculate the displacement / velocity / acceleration of the first object at the analysis target time t, determine whether the external force applied to the first object and the reaction force of the first object are balanced, and the external force and If it is determined that the reaction force is not balanced, the assumed correction of the displacement / velocity / acceleration of the first object and the distortion of the first object until it is determined that the external force and the reaction force are balanced. The time history response analysis of the first object is performed by sequentially performing the calculation of the level and the calculation of the displacement / velocity / acceleration of the first object while changing the analysis target time t by Δt. To Time history response analysis method of Motomeko 1, wherein the. A first calculation for calculating dynamic rigidity representing a relationship between an external force that vibrates the first object and a behavior of the first object in a frequency domain when the strain level of the first object is different from each other. Means,
By converting dynamic stiffness when the strain level is each value into the time domain, respectively, impulse responses representing the relationship of the first object in the time domain when the strain level is each value are calculated. Two computing means;
Using the impulse response corresponding to the strain level of the first object at the analysis target time t, the behavior of the first object at the analysis target time t or the second object affected by the behavior of the first object Analysis means for performing time history response analysis of the first object or the second object by repeating the behavior analysis while changing the analysis target time t in increments of Δt;
Time history response analysis device including Computer
A first calculation for calculating dynamic rigidity representing a relationship between an external force that vibrates the first object and a behavior of the first object in a frequency domain when the strain level of the first object is different from each other. means,
By converting dynamic stiffness when the strain level is each value into the time domain, respectively, impulse responses representing the relationship of the first object in the time domain when the strain level is each value are calculated. 2 computing means,
And a second affected by the behavior of the first object or the behavior of the first object using the impulse response corresponding to the strain level of the first object at the analysis time t. Analyzing the behavior of the object by repeating the analysis target time t in increments of Δt, thereby functioning as a time history response analysis of the time history response analysis of the first object or the second object. program.

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