JP2010086473A - Static analysis device, method and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To easily analyze a behavior of a structure when a load of a constant ratio is input at a plurality of places of the structure to displace the structure by a prescribed amount, even in a proof stress degradation area. <P>SOLUTION: The static analysis device uses an analysis object model obtained by adding a loading spring group composed of a plurality of loading springs each arranged between a plurality of loading points of a structure model and dummy nodes for displacement input for a structure model representing a structure of an analysis target, calculates stress and displacement of the analysis object model when a specified quantity of displacement is given to the dummy nodes after setting an initial value of spring stiffness in individual loading springs, calculates a load that is input at an individual loading point through an individual loading spring, and searches a balancing point by repeating the modification of the spring stiffness of slave springs except a master spring connected to a loading point of a displacement control target in the loading spring group so that the ratio of magnitude of a load input to the individual loading point coincides with a prescribed ratio. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a static analysis apparatus, method, and program, and more particularly, to a static analysis apparatus that calculates stress and displacement at each location of a structure when the modeled structure is displaced, and the static analysis apparatus. The present invention relates to an applicable static analysis method and a static analysis program for causing a computer to function as the static analysis device.

When a structure receives a load, displacement (deformation) occurs. However, when a relationship between load and displacement in an arbitrary structure (an example of the relationship is shown in FIG. 10C) is obtained, the following (1) Incremental equilibrium equations are often used.
K · Δu = Δf (1)
In Equation (1), K is a structure stiffness matrix, Δu is a displacement increment, and Δf is a load increment. If the load increment Δf is known, the displacement increment Δu at the balance point can be obtained from the equation (1). If the displacement increment Δu is known, the load increment Δf at the balance point can be obtained from the equation (1). it can. Then, by performing each of the above calculations (static analysis) for a plurality of balance points, the relationship between the load and displacement in the structure to be analyzed can be grasped. In addition, the method of searching for a balance point by determining the load increment or the displacement increment as described above is referred to as a load control method and a displacement control method, respectively.

  By the way, a load is input to each floor at the time of an earthquake, and the load input to each floor has a magnitude (approximately constant ratio) according to the weight and height of each floor. For this reason, in order to accurately grasp the behavior of a structure such as a building (such as the relationship between load and displacement) during an earthquake, etc., loads are input at a fixed ratio to multiple locations (multiple loading points) of the structure. It is necessary to perform the above-mentioned static analysis under the condition that it is (multi-point loading: see also FIGS. 10A and 10B as an example). On the other hand, although the load control method described above can perform static analysis under multi-point loading conditions, it is an algorithm that determines the load increment and searches for a point that satisfies it. After reaching the maximum proof stress value, there is a defect that analysis cannot be performed in the proof strength reduction region (see FIG. 10C) in which the load (proof strength of the structure) decreases with increasing displacement. Further, although the above-described displacement control method can be applied to the analysis in the proof stress reduction region, there is a problem that the analysis under the multipoint loading condition is difficult. In the case of multi-point loading, the deformation state of the structure in which the load input to multiple loading points is a constant ratio changes as the structure becomes non-linear. This is because it is difficult to determine the displacement increment.

In addition, the arc length method is known as a method that enables analysis in a proof stress reduction region under multi-point loading conditions. In the arc length method, as shown in the following equation (2), the load increment Δf in the above equation (1) is divided into the load parameter λ and the load mode fref, and the load increment is known and the displacement increment and the load parameter are obtained. It is a technique.
K · Δu = λfref (2)
However, since the number of unknowns is larger than the number of equations in equation (2) alone, the arc length method further adds an equation that gives a constraint condition (an example is shown in equation (3) below) and solves it using simultaneous equations. Will be asked.
S (Δu, λ) = 0 (3)
The above constraint conditions include various conditions such as a condition that restricts (limits) the vector length of a path from a known balance point to an unknown next balance point (path along which the relationship between load and displacement follows). Proposed.

In addition, as another technique that enables analysis in a proof stress region under multi-point loading conditions, Non-Patent Document 1 expands the displacement control method and includes a diagonal term component of a stiffness matrix of a displacement component that is desired to be displaced. A method for performing analysis by setting a very large value and converting the stiffness matrix according to the load distribution ratio is described.
Fukuzo Sudo, Akira Wada, “Nonlinear analysis method including unstable region of structures subjected to multiple loads”, Japan Steel Structure Association 11th Annual Meeting, Proceedings of Matrix Analysis, June 1977 , P. 217-222

  However, the arc length method described above has a problem that it is difficult to set the control parameter, and if an appropriate value is not set as the initial value of the control parameter, the route is traced in the reverse direction (unloading direction). The desired solution may not be obtained. Further, in the analysis for the purpose of grasping the behavior of a structure such as a building during an earthquake or the like, as shown in FIG. As an input condition, a load is input so that loading and unloading is repeated on the structure, and a condition (repetitive loading condition) that also defines the displacement of the structure in the process of loading and unloading is repeated. The analysis is performed according to the repeated loading conditions. On the other hand, since the displacement increment is unknown in the arc length method, there is a problem that the displacement cannot be analyzed by changing the displacement amount of the structure in accordance with a preset repeated loading condition.

  In the technique described in Non-Patent Document 1 described above, the displacement amount of the structure can be specified. However, the displacement amount is corrected when the stiffness matrix is converted, and the displacement of the structure is changed according to the corrected displacement amount. Since the displacement is controlled, the accuracy of the displacement control is low, and similarly to the arc length method, there is a problem that the displacement amount of the structure cannot be repeatedly analyzed according to the loading condition.

  The present invention has been made in consideration of the above facts, and analyzes the behavior of a structure when a predetermined amount of load is input to a plurality of locations of the structure and the structure is displaced by a predetermined amount. However, it is an object to obtain a static analysis device, a static analysis method, and a static analysis program that can be easily and accurately performed.

  In order to achieve the above object, a static analysis device according to the invention described in claim 1 includes a structure model representing a structure to be analyzed, and a loading point provided at a plurality of locations of the structure model. For an analysis target model including a spring element group consisting of a plurality of spring elements respectively arranged between different loading points and a displacement input dummy node, the initial stiffness of each spring element of the spring element group is determined. Setting means for setting each value, first calculation means for calculating stress and displacement at each location of the model to be analyzed when a predetermined amount of displacement is applied to the dummy nodes, and calculation by the first calculation means A second computing means for computing the magnitude of a load input to each loading point of the structure model via the individual spring elements based on the stress and displacement at each location; and the second computing means. Calculated by If the deviation between the ratio of the magnitude of the load input to each individual loading point and the predetermined ratio is equal to or greater than the allowable value, the specific spring elements other than the specific spring elements are selected so that they match. And control means for correcting the spring stiffness set in the spring element and causing the calculation by the first calculation means and the second calculation means to be performed again.

  According to the first aspect of the present invention, as the analysis target model, a structure model representing a structure to be analyzed, a loading point different from among loading points provided at a plurality of locations of the structure model, and a dummy for displacement input A model including a spring element group composed of a plurality of spring elements each arranged between the nodes is used. In the first aspect of the present invention, the individual spring elements of the spring element group in the analysis target model may be connected to the same (single) dummy node, respectively. As described, the same number of dummy nodes as the spring elements may be provided, and the individual spring elements may be connected to different dummy nodes.

  In the first aspect of the invention, the initial value of the spring stiffness is set for each spring element of the spring element group by the setting means for the analysis target model, and the first calculation means is a dummy node. The stress and displacement of each part of the model to be analyzed when a predetermined amount of displacement is applied to are calculated. As described above, the individual spring elements of the spring element group are respectively arranged between different loading points and dummy nodes, so that by giving a predetermined amount of displacement to the dummy nodes as described above, Loads are respectively input to a plurality of loading points of the structure model via the spring elements. Further, the magnitude of the displacement applied to each loading point of the structure model depends on the spring stiffness of the spring element connected to each loading point, but the spring of the spring element connected to the specific loading point. By setting the rigidity to a value that is sufficiently larger than the rigidity of the entire structure model (for example, a value that is sufficiently more rigid than the rigidity of the entire structure model as described in claim 3), The magnitude of the displacement at the point where the point is provided can be made approximately equal to the magnitude of the displacement given to the dummy node.

  According to the first aspect of the present invention, based on the stress and displacement of each part of the model to be analyzed calculated by the first calculation means, it is input to each loading point of the structure model via each spring element. The magnitude of the load is calculated by the second calculation means. When the deviation between the ratio of the magnitude of the load input to each loading point calculated by the second calculation means and the predetermined ratio is equal to or greater than the allowable value, the control means The spring stiffness set for the spring elements other than the specific spring element among the spring elements is corrected, and the calculation by the first calculation means and the second calculation means is performed again.

  As a result, the spring stiffness of the spring elements other than the specific spring element is repeatedly corrected until the deviation between the ratio of the magnitude of the load input to each loading point of the structure model and the predetermined ratio becomes less than the allowable value. Therefore, the behavior of the structure will be analyzed when a certain amount of load is input to multiple locations of the structure and the structure is displaced by a predetermined amount (loads input to individual loading points). When the deviation between the ratio of the magnitude and the predetermined ratio is determined to be less than the allowable value by the control means, the stress and displacement of each part of the analysis target model calculated by the first calculation means become the above behavior. Equivalent to). In addition, since the invention according to claim 1 performs the calculation with the displacement (increment) as a known amount in the same manner as the displacement control method, the behavior of the structure can be analyzed even when the structure is in the proof stress reduction region. As in the long method, a solution cannot be obtained when an appropriate value is not set as a control parameter. In addition, the accuracy of analysis can be improved by making the magnitude of displacement at a location where a specific loading point is provided in the structure model approximately match the magnitude of displacement given to the dummy node. it can. Therefore, according to the first aspect of the present invention, the analysis of the behavior of the structure when the structure is displaced by a predetermined amount by inputting a constant ratio load to a plurality of locations of the structure is a proof stress reduction region. Can be carried out easily and with high accuracy.

  In the first aspect of the invention, the analysis target model includes, for example, as described in the second aspect, the individual spring elements of the spring element group are spring reaction forces between different loading points and dummy nodes. It can be set as the structure arrange | positioned so that the direction of may correspond to the input direction of the load to a loading point.

Further, in the invention according to claim 1 or 2, as described in claim 3, for example, as the specific spring element (spring element not subject to correction of spring stiffness), the structure model provided with the loading point is used. A spring element disposed between a specific loading point and a dummy node provided at a location to be controlled for displacement among a plurality of locations can be applied, and the setting means sets an initial value of spring stiffness for the specific spring element. As a value sufficiently stiffer than the rigidity of the entire structure model (for example, a value within a range of 10 to 10 ⁵ times the rigidity of the entire structure model, preferably a value of about 10 ⁴ times the rigidity of the entire structure model) It is preferable to configure so as to set. As a result, the spring rigidity of the specific spring element is sufficiently larger than the rigidity of the entire structure model, so that the location subject to displacement control (the specific loading point to which the specific spring element is connected is provided in the structure model. The size of the displacement at the location) is approximately equal to the size of the displacement given to the dummy node, and the structure when the desired displacement is given to the location subject to displacement control of the structure model It becomes possible to analyze the behavior of.

  Further, in the invention according to any one of claims 1 to 3, the first calculation means sets an initial value of rigidity to the nonlinear element constituting the analysis target model, as described in claim 4, for example. After calculating the stress and displacement at each location of the model to be analyzed when a predetermined amount of displacement is applied to the dummy node, the residual force of the structure model is calculated based on the calculated stress and displacement at each location. If the calculated residual force exceeds the allowable value, correct the stiffness set for the nonlinear element and recalculate the stress and displacement at each location in the model to be analyzed when a predetermined amount of displacement is applied to the dummy node. It is preferable to repeat the process until the residual force becomes less than the allowable value. Thereby, even when the structure represented by the structure model includes a nonlinear element, the behavior of the structure can be analyzed with high accuracy.

  By the way, in the invention according to any one of claims 1 to 4, the magnitude of displacement at each location of the structure model is input to each of a plurality of loading points of the structure model via individual spring elements. As described above, if the spring stiffness of the spring element connected to a specific loading point is set to a value sufficiently larger than the stiffness of the entire structure model, as described above, The magnitude of the displacement at the location where the specific loading point is provided can be made approximately equal to the magnitude of the displacement given to the dummy node. However, when the individual spring elements of the spring element group are respectively connected to the same (single) dummy node, the position of the end of the individual spring element connected to the dummy node (to the loading point) Therefore, if there is a loading point that shows a larger displacement than the specific loading point among the multiple loading points of the structure model, the loading point The sign of the stress that occurs in the connected spring element is different from the sign of the stress that occurs in the other spring element (one spring element becomes tension and the other spring element becomes compression), so a correct solution cannot be obtained. A possibility arises.

  This problem can be solved by providing a specific loading point (loading point connected to a specific spring element whose spring stiffness is not corrected) at the location where the displacement is maximum in the structure model. If you want to perform an analysis while controlling the displacement of the part other than the part where the maximum is, or if the part of the structure model where the displacement is maximum is unknown, It is not applicable when the part to be moved.

  In consideration of the above, in the invention according to any one of claims 1 to 4, for example, as described in claim 5, the analysis target model is provided with the same number of dummy nodes as the spring elements. The individual spring elements are respectively arranged between different loading points and different dummy nodes, and the first calculation means is the same as the specific loading point provided at the location of the displacement control target of the structure model. Each part of the model to be analyzed when a predetermined amount of displacement is applied to a specific dummy node connected to a specific spring element, and a displacement that is proportional to and greater than a predetermined amount is applied to a dummy node other than the specific dummy node It is preferable to be configured to calculate the stress and displacement.

  In the present invention, the displacement (magnitude) given to the spring element other than the specific spring element via the dummy node is a convenience for inputting a load to the loading point connected to the spring element. The displacement given to the corresponding loading point of the structure model via a spring element other than the spring element changes in accordance with the spring stiffness of the spring element other than the specific spring element. With the above configuration, a displacement that roughly matches the displacement given to the specific dummy node is given to the location of the displacement control target of the structure model via the specific spring element, while the spring elements other than the specific spring element Since the spring stiffness is adjusted by the control means so that the deviation between the ratio of the magnitude of the load input to the loading point and the predetermined ratio is less than the allowable value, dummy nodes other than the specific dummy nodes as described above Giving a displacement larger than a specific dummy node does not adversely affect the analysis.

  And even when a specific loading point is not provided at a location where the displacement is maximum in the structure model by giving a larger displacement than the specific dummy node to the dummy nodes other than the specific dummy node as described above. Since the signs of the stresses generated in the individual spring elements can be made uniform, it is possible to prevent inconveniences such as failure to obtain a correct solution.

  In the invention according to claim 5, the ratio between the magnitude of displacement given to the specific dummy node by the first computing means and the magnitude of displacement given to the dummy nodes other than the specific dummy node by the first computing means is, for example, According to a sixth aspect of the present invention, the initial value of the spring stiffness is set for each spring element of the spring element group by the setting means, and the individual spring elements are calculated by the second calculation means. Thus, it is possible to set so that the directions of loads inputted to the individual loading points of the structure model are all the same.

  Further, in the invention according to any one of claims 1 to 6, for example, as described in claim 7, there are a plurality of values and an order of giving the plurality of values as the magnitude of the displacement given to the dummy nodes. The calculation by the first calculation means and the second calculation means and the processing by the control means are set in advance and are configured to be repeated while sequentially switching the magnitude of the displacement given to the dummy nodes according to a plurality of values and their order. Also good. As a result, the magnitude of the external force received by the structure to be analyzed and its time-series change can be defined by the multiple values representing the magnitude of displacement given to the dummy nodes and the order in which the multiple values are given. It is possible to analyze with high accuracy the behavior at each stage when the external structure receives the external force (stress and displacement at each location of the structure when the displacement applied to the dummy node is each value) .

  Further, in the invention described in claim 7, for example, as described in claim 8, the structure to be analyzed is a building, and a plurality of values representing the magnitude of displacement given to the dummy nodes and the plurality of values are given. The order may be set so as to simulate the earthquake motion received by the building. In this case, the behavior of each structure when the building as the structure to be analyzed is subjected to earthquake motions defined by multiple values representing the magnitude of displacement given to the dummy nodes and the order in which multiple values are given is enhanced. It can be analyzed with accuracy.

  According to a ninth aspect of the present invention, there is provided a static analysis method comprising: a computer, a structure model representing a structure to be analyzed; and different loading points among loading points provided at a plurality of locations of the structure model. Initial value of spring stiffness is set for each spring element of the spring element group for the analysis target model including a spring element group composed of a plurality of spring elements respectively arranged between the input and the displacement input dummy node. Then, the stress and displacement at each location of the model to be analyzed when a predetermined amount of displacement is applied to the dummy node are calculated, and the individual spring elements are inserted based on the calculated stress and displacement at each location. The magnitude of the load inputted to each loading point of the structure model is calculated, and the deviation between the calculated ratio of the magnitude of the load inputted to each loading point and the predetermined ratio has an allowable value. Beyond In addition, the spring stiffness set to the spring elements other than the specific spring element among the individual spring elements is corrected so that they match, and the stress and displacement at each location of the analysis target model are calculated, and the structure model The process of calculating the magnitude of the load input to each individual loading point is repeated until the deviation between the ratio of the magnitude of the load input to each individual loading point and a predetermined ratio falls within an allowable value. Therefore, as in the first aspect of the invention, the analysis of the behavior of the structure when a predetermined amount of load is input to a plurality of locations of the structure and the structure is displaced by a predetermined amount Can be carried out easily and with high accuracy.

  The static analysis program according to the invention described in claim 10 is a computer program comprising: a structure model representing a structure to be analyzed; and loading points different from each other among loading points provided at a plurality of locations of the structure model. And a spring element group composed of a plurality of spring elements respectively arranged between the displacement input dummy nodes, and an initial value of spring stiffness for each spring element of the spring element group. Setting means for setting each, first computing means for computing stress and displacement at each location of the model to be analyzed when a predetermined amount of displacement is applied to the dummy node, and each location computed by the first computing means A second computing means for computing the magnitude of the load inputted to each loading point of the structure model via the individual spring elements, and the second computing means based on the stress and displacement of When the deviation between the calculated ratio of the magnitude of the load inputted to each individual loading point and the predetermined ratio exceeds an allowable value, the specific springs of the individual spring elements are matched so that they match. The spring stiffness set for the spring elements other than the elements is corrected and functions as control means for causing the calculation by the first calculation means and the second calculation means to be performed again.

  The static analysis program according to the invention described in claim 10 is a program for causing a computer to function as the setting means, the first calculation means, the second calculation means, and the control means. By executing the static analysis program according to the present invention, the computer functions as the static analysis device according to claim 1, and, like the invention according to claim 1, the computer is fixed at a plurality of locations. The analysis of the behavior of the structure when the ratio load is input and the structure is displaced by a predetermined amount can be easily and highly accurately performed even in the proof stress reduction region.

  Since the static analysis program according to the invention described in claim 11 causes the computer to function as the static analysis device according to any one of claims 1 to 8, the computer relates to the invention according to claim 11. By executing the static analysis program, the computer functions as the static analysis device according to any one of claims 1 to 8, and according to any one of claims 1 to 8. Similar to the invention, analysis of the behavior of a structure when a predetermined amount of load is input to a plurality of locations of the structure and the structure is displaced by a predetermined amount is easily and accurately performed even in a proof stress reduction region. be able to.

  As described above, according to the present invention, the structure model representing the structure to be analyzed and the loading points provided at a plurality of locations of the structure model between different loading points and the dummy nodes for displacement input are used. Analysis when a predetermined amount of displacement is applied to a dummy node after setting an initial value of spring rigidity for each spring element for an analysis target model including a group of spring elements each composed of a plurality of spring elements. Calculate the stress and displacement of each part of the target model, calculate the magnitude of the load input to each loading point of the structure model via each spring element, and calculate the load input to each loading point. When the deviation between the size ratio and the specified ratio exceeds the allowable value, the spring stiffness set for the spring elements other than the specific spring element is corrected so that they match, and each part of the model to be analyzed is corrected. Calculate stress and displacement The calculation of the magnitude of the load input to each loading point of the structure model is performed until the deviation between the ratio of the load magnitude input to each loading point and the predetermined ratio is within the allowable value. Since it is repeated, analysis of the behavior of the structure when a certain amount of load is input to a plurality of locations of the structure and the structure is displaced by a predetermined amount can be easily and accurately performed even in the proof stress reduction region. It has the excellent effect of being able to.

  Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings.

[First Embodiment]
Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 shows a computer 10 to which the present invention can be applied. The computer 10 includes a CPU 10A, a memory 10B composed of ROM, RAM, etc., and a non-volatile storage unit 10C composed of HDD (Hard Disk Drive), flash memory, etc., and a display 12, keyboard 14, Each mouse 16 is connected.

  A behavior analysis program for performing behavior analysis processing to be described later is installed in the storage unit 10C of the computer 10. This behavior analysis program corresponds to the static analysis program according to claims 10 and 11. The computer 10 corresponds to the computer according to any one of claims 9 to 11, and functions as a static analysis device according to the invention according to claim 1 or the like when the CPU 10A executes the behavior analysis program. . The storage unit 10C also stores displacement history data. The displacement history data is configured such that a plurality of displacement data representing the magnitude of displacement given to the dummy nodes of the analysis target model in a behavior analysis process described later are arranged in time series in the order of input to the dummy nodes. In this embodiment, a building is applied as a structure to be analyzed. In order to analyze the behavior of the building during an earthquake, the displacement history data is set so as to simulate the earthquake motion that the building receives during an earthquake. (An example is shown in FIG. 11). The displacement history data corresponds to the inventions described in claims 7 and 8.

  The computer 10 is preferably a personal computer (PC), but is not limited to this. For example, a workstation or a general-purpose large computer may be used.

  Next, as an operation of the first embodiment, behavior analysis processing realized by the CPU 10A executing a behavior analysis program will be described with reference to FIG. The behavior analysis process is a process to which the static analysis method according to the present invention is applied. First, in step 30, the attribute information of the building as the structure to be analyzed (for example, the mass and floor height of each floor, the object of modeling) A structure model that models the structure (building) is generated on the basis of information indicating the arrangement and material of members such as columns, beams, and walls. The building attribute information may be stored in the storage unit 10C in advance, or may be obtained by displaying a message or the like for requesting input from the operator on the display 12 and allowing the operator to input via the keyboard 14 or the like. It may be. Thereby, as shown in FIG. 3 as an example, a structure model including a plurality of nodes is generated. FIG. 3 shows, as an example, a simplified structure model that models a four-story building.

  In step 32, one dummy node for displacement input is set at a position separated from the structure model generated in step 30. In the next step 34, a plurality of loading points to which a load is input at the time of the earthquake are extracted from the respective nodes constituting the structure model, and between the extracted loading points and the dummy nodes set in step 32. Each of the loading springs is arranged to add a loading spring group composed of a plurality of loading springs to the structure model. As shown in FIG. 3, each loading spring is arranged between each loading point and the dummy node so that the direction of the spring reaction force coincides with the input direction of the load to the loading point. The The loading spring corresponds to the spring element according to the present invention (specifically, the spring element according to claim 2), the loading spring group corresponds to the spring element group according to the present invention, and a structure in which the loading spring group is added. The whole body model corresponds to the analysis target model according to the present invention.

In the next step 36, an initial value Kinit of the spring stiffness set for each loading spring is determined. The initial value Kinit of the spring stiffness is a value sufficiently larger than the stiffness of the entire structure model, for example, a value that is sufficiently stiffer than the stiffness of the entire structure model (preferably 10 ⁴ of the stiffness of the entire structure model). Double the value) can be set. The initial value Kinit of the spring stiffness described above is a value suitable for the master spring selected in the next step 38, but in the behavior analysis processing according to the present embodiment, the springs of other loading springs (slave springs) Since the stiffness is appropriately corrected, the initial value Kinit of the spring stiffness determined in step 36 may be used in common for the master spring and the slave spring. The initial value of the spring stiffness for the slave spring and the initial value of the spring stiffness for the master spring may be determined separately. Step 36 corresponds to setting means according to the present invention (more specifically, setting means according to claim 3).

  In the next step 38, the loading point to be subjected to displacement control (the loading point whose displacement is to be accurately controlled according to the above-described displacement history data during the behavior analysis process) is selected from the plurality of loading points of the structure model. The loading spring connected to the loading point of the displacement control object selected by the operator is selected as the master spring among the plurality of loading springs of the loading spring group, and the selected loading spring is the master spring. And information indicating that the remaining loading spring is a slave spring is stored in the memory 10B or the like. The master spring corresponds to the specific spring element according to the present invention. In step 40, referring to the attribute information of the building modeled as a structure model, the load input to each floor of the building when the building is subjected to earthquake motion based on the mass and floor height of each floor. The ratio is calculated, and the calculated load ratio is determined as the ratio of the load input to each loading point of the structure model via each loading spring.

  By the above-described processing, for example, for the structure model shown in FIG. 3, four nodes (nodes A to D) of the structure model are extracted as loading points, and between these nodes and the dummy nodes. Each of the loading springs is arranged, and a loading spring group including a total of four loading springs is added to the structure model. When the loading point subject to displacement control is the node A, the loading spring connected to the node A is the master spring m, and the other loading springs are the slave springs s1, s2, and s3. Then, the ratio of loads (for example, “1: αs1: αs2: αs3” shown in FIG. 3) input to the individual loading points of the structure model via these loading springs is determined.

  In step 42, 1 is substituted into the variable n, and in the next step 44, the displacement amount given to the dummy node of the analysis target model in the nth analysis (static analysis) from the displacement history data stored in the storage unit 10C. Is extracted. In step 46, the initial value Kinit of the spring stiffness determined in the previous step 36 is set as the spring stiffness of each loading spring of the model to be analyzed. In the next step 48 and subsequent steps, static analysis is performed to search for a balance point of the analysis target model when the displacement amount represented by the displacement data extracted in step 44 is given to the dummy node.

  In other words, members to be modeled such as building columns, beams, walls, etc. are made of various materials (for example, steel, wood, RC, etc.), but depending on the materials, these members may be force and displacement (or stress and strain). ) Is not a proportional relationship. For this reason, in the structure model that models the building, each member constituting the building to be modeled is a linear element in which the relationship between force and displacement (or stress and strain) is proportional, or force and displacement ( Alternatively, the relationship between stress and strain) is modeled as a nonlinear element that does not have a proportional relationship. In step 48, a certain value is assumed as the stiffness of each nonlinear element included in the structure model, and extracted in step 44. The stress and displacement at each location of the model to be analyzed when the displacement amount represented by the displacement data is given to the dummy node are calculated. In addition, by giving a displacement to the dummy node, a load is input to each loading point of the structural body model via each loading spring. At this time, at least the master spring among the individual loading springs has a spring rigidity that is sufficiently larger than the rigidity of the entire structure model. Therefore, the displacement of the structure model to which the master spring is connected. A displacement having a magnitude approximately equal to the displacement given to the dummy node is given to the loading point to be controlled. In step 48, the stress and displacement of each part of the model to be analyzed in the state where the load and displacement are applied to the structure model (for example, the state shown in FIG. 6B) are calculated.

  In step 50, the residual force of the structure model is calculated based on the calculation result of step 48. This residual force is the difference between the external force and the internal force, and corresponds to the calculation error in step 48 (the error of the stiffness of the nonlinear element assumed in step 48 with respect to the actual stiffness). For this reason, in step 52, it is determined whether or not the residual calculated in step 50 is less than a preset allowable value. If the determination in step 52 is negative, the process proceeds to step 54, where the stiffness of each nonlinear element included in the structure model is corrected according to the residual force calculated in step 50, and then the process proceeds to step 48. Return. Thus, steps 48 to 54 are repeated until the determination in step 52 is affirmed, and the rigidity of each nonlinear element is adjusted so that the residual force is less than the allowable value. Steps 48 to 54 correspond to the first calculation means according to the present invention (more specifically, the first calculation means according to claim 4).

  Regarding the correction (adjustment) of the stiffness of the nonlinear element in the above-described step 48 to step 54, as shown in FIG. 4A, there is a displacement (or strain) from the known stiffness (stiffness at point A) of the nonlinear element. The case where the unknown stiffness (stiffness at the point B) is obtained as an example will be further described as an example. First, in step 48 described above, as shown in FIG. 4 (B), the tangent of the nonlinear curve at the point A It is assumed that there is a solution on the rigidity, and the calculation is performed assuming that the solution (the rigidity at the point B1) is the rigidity of the nonlinear element. Next, in step 50 described above, an error (residual force) is calculated, and this residual force is defined as the assumed nonlinear element stiffness (stiffness at point B1) as shown in FIG. This corresponds to a deviation from the determined nonlinear curve. Subsequently, when the residual force is determined to be greater than or equal to the allowable value in the above-described step 52, in the above-described step 54, as shown in FIG. It is corrected to a solution (stiffness at point B2) close to the rigidity at point B). By repeating the above processing until the residual force becomes less than the allowable value (until the determination in step 52 is affirmed), rigidity at point B is obtained as shown in FIG. By setting the stiffness of the element, the residual force becomes less than the allowable value.

  If the determination in step 52 is affirmed, the process proceeds to step 56, and the structure is passed through each loading spring based on the stress and displacement at each location of the analysis target model finally obtained by the calculation in step 48. The load (stress generated in each loading spring) input to each loading point of the model is calculated, and the deviation (residual) of the calculated load ratio with respect to the load ratio determined in the previous step 40 is calculated. . This step 56 corresponds to the second calculation means according to the present invention.

  In the next step 58, it is determined whether or not the load ratio residual calculated in step 56 is less than a preset allowable value. If the determination is negative, the process proceeds to step 60 so that the load ratio input to each loading point of the structure model via each loading spring matches the load ratio determined in the previous step 40. The spring rigidity of each slave spring in the loading spring group is corrected.

  Specifically, for example, when the displacement amount of the master spring m calculated from the calculation result of step 48 is “δm” shown in FIG. 5A, the spring stiffness Km of the master spring m is fixed (= initial value). Kinit), the stress P generated in the master spring m (the load Fm input to the loading point via the master spring m) is obtained by the product (Km · δm) of the spring stiffness Km and the displacement amount δm. On the other hand, in the load ratio determined in step 40, when the load input to the loading point via the slave spring s1 is αs1 times the load input to the loading point via the master spring m, the slave spring s1 Since the load input to the loading point via “αs1 · Fm” needs to be divided by the displacement δs1 of the slave spring s1 calculated from the calculation result of step 48, the slave A new spring stiffness Ks1 ′ of the slave spring s1 is calculated and set to make the load αs1 times the load input via the master spring m via the spring s1. By performing the above processing for each individual slave spring, the spring stiffness of each slave spring is adjusted so that the load ratio input via the individual loading spring matches the load ratio determined in the previous step 40. Can be corrected.

  If the process of step 60 is performed, it will return to step 48 and will repeat step 48-step 60 until determination of step 58 is affirmed. Steps 56 to 60 correspond to the control means according to the present invention.

  Thereby, in the above-mentioned step 48 to step 54, the state after the load input to the loading point via the individual slave springs is changed with the correction of the spring stiffness of the slave springs in step 60 (for example, FIG. The calculation of the stress and displacement of each part of the model to be analyzed in the state shown in (C)) while correcting (adjusting) the stiffness of the nonlinear element so that the residual force of the structure model is less than the allowable value After the repetition, in step 56 described above, the load input to the loading point via each loading spring is calculated to calculate a load ratio deviation (residual), and the load ratio residual is an allowable value. If it is above (when determination of step 58 is denied), the process which corrects the spring rigidity of a slave spring in the above-mentioned step 60 is repeated. During this time, the structure model transitions from the initial state shown in FIG. 6A to, for example, the state shown in FIG. 6B and the state shown in FIG. When the load at the ratio determined in step 40 is input to the loading point via the loading spring group, the loading point of the displacement control target of the structure model is displaced by the displacement amount represented by the displacement data extracted in step 44. It will converge to a state corresponding to the balance point of the structure model.

  If the determination in step 58 is affirmed, the process proceeds to step 62, where the displacement data extracted in step 44 is the analysis result (stress and displacement at each location of the analysis target model finally obtained by the calculation in step 48). It is stored in the memory 10B or the storage unit 10C in association with the displacement amount to be expressed. In the next step 64, it is determined whether or not the analysis process is completed by determining whether or not all the displacement data is extracted from the displacement history data. If the determination is negative, the process proceeds to step 66, the value of the variable n is incremented by 1, and the process returns to step 44. Therefore, by repeating Step 44 to Step 66 until the determination of Step 64 is affirmed, the analysis target model when the displacement of the displacement amount represented by the individual displacement data constituting the displacement history data is given to the structure model. The behavior (stress and displacement at each location) is calculated and analyzed in order. If the determination in step 64 is affirmed, the process proceeds to step 68, where the analysis result stored in the memory 10B or the storage unit 10C is output on the display 12 or the like, and the behavior analysis process is terminated. As a result, it is possible to grasp the behavior when the building as the analysis target structure is subjected to the earthquake motion represented by the displacement history data.

  As described above, the behavior analysis processing according to the first embodiment is a method of searching for a balance point by determining the amount of displacement given to the loading point of the displacement control target via the master spring, and is similar to the displacement control method. In addition, it is possible to calculate and analyze the behavior when the structure model is in the proof stress reduction region, and depending on the value of the control parameter as in the arc length method, the path (path along which the relationship between load and displacement) is reversed. It can also be prevented that the solution cannot be obtained by following the direction. In addition, the amount of displacement applied to the loading point is determined only for the loading point subject to displacement control, and the ratio of the load input via the loading spring is determined for the other loading points. Since the calculation is repeated so that the load ratio input to each loading point matches the determined load ratio, it is not necessary to determine the displacement amount for all loading points, and the structure model under the multi-point loading condition The behavior can be easily calculated and analyzed. Furthermore, by making the spring stiffness of the master spring sufficiently larger than the stiffness of the entire structure model, the amount of displacement applied to the loading point of the displacement control object via the master spring is approximately matched to the amount of displacement of the dummy node. In addition, the displacement amount of the loading point to be subjected to displacement control of the structure model can be accurately changed according to the repeated loading condition represented by the displacement history data, and high-precision calculation / analysis can be performed.

[Second Embodiment]
Next, a second embodiment of the present invention will be described. Since the second embodiment has the same configuration as that of the first embodiment, the same reference numerals are given to the respective parts, description of the configuration is omitted, and the operation of the second embodiment will be described below.

  In the loading spring group described in the first embodiment, the individual loading springs are respectively connected to the same (single) dummy nodes, and the side of the individual loading springs connected to the dummy nodes. The position of the end (the position along the input direction of the load to the loading point) is the same. For this reason, in step 38 of the behavior analysis process (FIG. 2) described in the first embodiment, the loading point of the displacement control target selected by the operator has a displacement amount corresponding to the load input to each loading point. When it is not the maximum loading point, as shown in FIG. 9 (A) as an example, a loading spring connected to the loading point showing a displacement larger than the loading point of the displacement control target (FIG. 9 (A)). In this example, the sign of the stress generated in the slave springs s1, s2 is different from the sign of the stress generated in the other loading springs including the master spring (one spring element is tension and the other spring element is compression). ), There is a risk that a correct solution cannot be obtained.

  The second embodiment solves the above-described problem, and with reference to FIG. 7, the behavior analysis processing (FIG. 2) described in the first embodiment is the same as the behavior analysis processing according to the second embodiment. Only the different parts will be described.

In the behavior analysis processing according to the second embodiment, after generating a structure model obtained by modeling the structure (building) to be analyzed in step 30, in a next step 33, the position is separated from the structure model. Set the same number of dummy nodes for displacement input as the loading points of the structure model.
Then, in the next step 34, as shown in FIG. 8 as an example, by placing the loading springs between different loading points and different dummy nodes, a loading spring group comprising a plurality of loading springs. Is added to the structure model. In the second embodiment, as shown in FIG. 8, each loading spring has a spring reaction force between the individual loading points and the individual dummy nodes. Arranged to match the input direction. The loading spring corresponds to the spring element according to the present invention (specifically, the spring element according to claims 2 and 5), and the loading spring group corresponds to the spring element group according to the present invention, and the loading spring group is added. The entire structure model corresponds to the analysis target model according to the present invention (more specifically, the analysis target model according to claim 5).

  Further, in the behavior analysis processing according to the second embodiment, after determining the ratio of the load to be input to each loading point via each loading spring in Step 40, the connection to the master spring is performed in the next Step 41. Ratio of displacement given to the dummy nodes (dummy nodes s1, s2, s3 in FIG. 8) to the displacement given to the dummy nodes (dummy node m in FIG. 8) to the displacements given to the dummy nodes (βs1 shown in FIG. 8) , βs2, βs3). The displacement ratio is input to each loading point of the structure model via each loading spring in a state where the initial value Kinit is set as the spring stiffness for each loading spring. It is sufficient that the direction of the load (the sign of the stress generated in each loading spring) is the same (corresponding to the invention of claim 6), and it is fixedly determined so as to satisfy this condition in various cases. It may be an extremely large value (for example, a value of “100” or more). Further, the ratio of the displacement amount applied to each dummy node connected to each slave spring may be the same (βs1 = βs2 = βs3) or different (βs1 ≠ βs2 ≠ βs3).

  Further, in the behavior analysis processing according to the second embodiment, after the displacement data is extracted from the displacement history data in step 44, in the next step 45, the displacement amount represented by the displacement data extracted in step 44 is set to the previous step 41. By multiplying the ratio determined in step 1, the amount of displacement given to each dummy node connected to each slave spring is calculated. In step 48, the displacement amount represented by the displacement data extracted in step 44 is given to the dummy node connected to the master spring, and the displacement amount calculated in step 45 is applied to each dummy node connected to each slave spring. The stress and displacement at each location of the model to be analyzed when given are calculated.

  As a result, in step 48, as shown in FIG. 9B as an example, each dummy node connected to each slave spring is displaced larger than the dummy node connected to the master spring (FIG. 9B In the example of), the behavior of the model to be analyzed (stress and displacement at each location) under the condition of 3 times the displacement) is calculated and analyzed, and the loading point of the displacement control target has the maximum displacement. Even if it is not a loading point, it is possible to align the sign of the stress generated in each loading spring (the direction of the load input to each loading point of the structure model via each loading spring). It is possible to prevent inconveniences such as failure to obtain a correct solution.

  The displacement applied to each dummy node connected to the slave spring is a convenience for inputting the load to the loading point connected to the slave spring. While the displacement given to the loading point changes in accordance with the spring stiffness of the slave spring, as described in the first embodiment, the spring stiffness of the slave spring depends on the magnitude of the load input to each loading point. Since the ratio is adjusted so as to match the ratio determined in step 40, even if each dummy node connected to each slave spring is given a larger displacement than the dummy node connected to the master spring, the analysis is adversely affected. Will not affect.

  In the above description, the mode of calculating and analyzing the behavior when the building as the structure to be analyzed is subjected to the earthquake motion represented by the displacement history data has been described. However, the present invention is not limited to this. Any structure as a structure to be analyzed can be applied to calculation / analysis of behavior in which seismic motion or any other external force is input.

  In the above description, the behavior analysis program corresponding to the static analysis program according to the present invention is stored (installed) in the storage unit 10C of the computer 10 in advance. However, the static analysis program according to the present invention is It is also possible to provide the information recorded in a recording medium such as a CD-ROM or a DVD-ROM.

It is a block diagram which shows schematic structure of the computer which concerns on this embodiment. It is a flowchart which shows the content of the behavior analysis process which concerns on 1st Embodiment. It is a conceptual diagram which shows an example of the analysis object model in 1st Embodiment. It is explanatory drawing for demonstrating the process which calculates the rigidity of the nonlinear element of a structure model among behavioral analysis processes. It is a diagram for demonstrating correction of the spring rigidity of a slave spring. It is a conceptual diagram which shows an example of the change of the displacement (and stress) of a structure model accompanying the repetition calculation in a behavior analysis process. It is a flowchart which shows the content of the behavior analysis process which concerns on 2nd Embodiment. It is a conceptual diagram which shows an example of the analysis object model in 2nd Embodiment. It is explanatory drawing for demonstrating the effect | action of 2nd Embodiment. (A), (B) is a conceptual diagram for demonstrating the analysis in multipoint loading, (C) is a diagram which shows an example of the relationship between a displacement and a load. It is a diagram which shows an example of repeated loading conditions.

Explanation of symbols

10 Computer 10B Memory 10C Storage 12 Display 14 Keyboard

Claims (11)

A structure model representing a structure to be analyzed, and a plurality of load models arranged between different loading points and displacement input dummy nodes among the loading points provided at a plurality of locations of the structure model. Setting means for setting an initial value of spring stiffness for each spring element of the spring element group for an analysis target model including a spring element group composed of spring elements;
First computing means for computing stress and displacement at each location of the model to be analyzed when a predetermined amount of displacement is applied to the dummy node;
A second calculation for calculating the magnitude of the load input to each loading point of the structural body model via the individual spring elements based on the stress and displacement at each location calculated by the first calculation means. Means,
When the deviation between the ratio of the magnitude of the load input to the individual loading points calculated by the second calculation means and a predetermined ratio is greater than or equal to an allowable value, the individual spring elements are matched to each other. Control means for correcting the spring stiffness set in the spring elements other than the specific spring element, and causing the calculation by the first calculation means and the second calculation means to be performed again,
Including static analysis equipment.   The analysis object model is such that each spring element of the group of spring elements has a spring reaction force direction that coincides with the input direction of the load to the load point described above between the different loading point and the dummy node. The static analysis device according to claim 1, which is disposed in   The specific spring element is a spring element disposed between a specific loading point provided at a location subject to displacement control and the dummy node among a plurality of locations of the structural body model provided with the load point described above, The static analysis apparatus according to claim 1, wherein the setting unit sets a value that is sufficiently stiffer than the rigidity of the entire structure model as an initial value of spring rigidity for the specific spring element.   The first calculation means is configured to set a stress of each portion of the analysis target model when a predetermined amount of displacement is applied to the dummy node in a state where an initial value of rigidity is set to a nonlinear element constituting the analysis target model. After calculating the displacement, the residual force of the structure model is calculated based on the calculated stress and displacement at each location, and if the calculated residual force is greater than or equal to an allowable value, the stiffness set for the nonlinear element 2, and recalculating the stress and displacement at each location of the model to be analyzed when a predetermined amount of displacement is applied to the dummy node until the residual force is less than an allowable value. The static analysis device according to claim 3. In the analysis object model, the same number of dummy nodes as the spring elements are provided, and the individual spring elements of the group of spring elements are respectively disposed between the different loading points and different dummy nodes,
The first calculation means applies a predetermined amount of displacement to a specific dummy node connected to the same specific spring element together with a specific loading point provided at a position to be displaced of the structure model, and the specific dummy node 5. The stress and displacement of each part of the model to be analyzed when a displacement proportional to the predetermined amount and larger than the predetermined amount is applied to a dummy node other than the above is calculated. The static analysis device described.   The ratio between the magnitude of the displacement given to the specific dummy node by the first computing means and the magnitude of the displacement given to the dummy nodes other than the specific dummy node by the first computing means is determined by the setting means by the spring element group. The initial value of the spring stiffness is set for each individual spring element, and is input to each loading point of the structural body model via the individual spring element, which is calculated by the second calculation means. The static analysis apparatus according to claim 5, wherein the directions of loads to be loaded are all set to be the same.   As the magnitude of displacement given to the dummy node, a plurality of values and the order of giving the plurality of values are set in advance, the calculation by the first calculation means and the second calculation means, the processing by the control means, The static analysis device according to claim 1, wherein the static analysis device is repeated while switching the magnitude of the displacement given to the dummy node sequentially in accordance with the plurality of values and the order thereof.   The structure to be analyzed is a building, and a plurality of values representing the magnitude of displacement given to the dummy nodes and the order of giving the plurality of values are set so as to simulate the earthquake motion received by the building. Item 8. The static analysis device according to Item 7. On the computer,
A structure model representing a structure to be analyzed, and a plurality of load models arranged between different loading points and displacement input dummy nodes among the loading points provided at a plurality of locations of the structure model. After setting an initial value of spring stiffness for each spring element of the spring element group for an analysis target model including a spring element group composed of spring elements,
Calculating the stress and displacement of each part of the model to be analyzed when a predetermined amount of displacement is applied to the dummy node;
Based on the calculated stress and displacement at each location, the magnitude of the load input to each loading point of the structure model via the individual spring elements is calculated,
When the deviation between the ratio of the magnitude of the load inputted to the calculated loading point and the predetermined ratio exceeds an allowable value, the specific spring element is selected from the individual spring elements so that they match each other. A process of correcting the spring stiffness set for the other spring elements, calculating the stress and displacement at each location of the model to be analyzed, and calculating the magnitude of the load input to each loading point of the structure model The static analysis method is repeated until the deviation between the ratio of the magnitude of the load inputted to the individual loading points and the predetermined ratio falls within an allowable value. Computer
A structure model representing a structure to be analyzed, and a plurality of load models arranged between different loading points and displacement input dummy nodes among the loading points provided at a plurality of locations of the structure model. Setting means for setting an initial value of spring stiffness for each spring element of the spring element group for an analysis target model including a spring element group of spring elements;
First computing means for computing stress and displacement at each location of the model to be analyzed when a predetermined amount of displacement is applied to the dummy node;
A second calculation for calculating the magnitude of the load input to each loading point of the structural body model via the individual spring elements based on the stress and displacement at each location calculated by the first calculation means. means,
And when the deviation between the ratio of the magnitude of the load inputted to the individual loading points calculated by the second calculating means and a predetermined ratio exceeds an allowable value, the individual values are set so that they match. Static analysis program for correcting a spring stiffness set to a spring element other than a specific spring element among the spring elements and causing the first arithmetic means and the second arithmetic means to perform a calculation again .   A static analysis program for causing a computer to function as the static analysis device according to any one of claims 1 to 8.

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