CN110069843B - ANSYS-based structural topology optimization design method considering traveling wave effect - Google Patents
ANSYS-based structural topology optimization design method considering traveling wave effect Download PDFInfo
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Abstract
The invention provides a traveling wave effect-based structural topology optimization design method based on ANSYS, and relates to the technical field of structural topology optimization under random excitation. The invention comprises the following steps: step 1: obtaining a space earthquake motion time-course curve of the uneven uniform field considering the traveling wave effect, and converting the space earthquake motion time-course curve into a random excitation acceleration value; step 2: establishing a finite element structure model; inputting an excitation acceleration on the model to obtain a rod piece internal force and a rod piece stress; and 3, step 3: establishing a topology optimization model: optimizing the finite element structure model by taking the stress of the rod member in accordance with the allowable stress of the rod member as a constraint condition; and 4, step 4: repeating the step 2 to the step 3, traversing the data in the sectional area set to obtain a new rod piece sectional area set; and 5: carrying out time course analysis on the data obtained in the step 4, and repeating the step 3 to the step 4 until the sectional area of the rod piece meets the traveling wave effect and the total structural mass reaches the minimum; the method can save steel and protect the structure from damage.
Description
Technical Field
The invention relates to the technical field of structural topology optimization under random excitation, in particular to an ANSYS-based structural topology optimization design method considering a traveling wave effect.
Background
The earthquake is a sudden natural disaster with great destructiveness, when the earthquake occurs, the ground motion process is complex, the waves generated by the earthquake are influenced by the mechanism of the earthquake source and the geological conditions of the foundation and are transmitted to the surface of the bottom layer, and each mass point on the ground is subjected to different vibration conditions, or because a certain distance exists between the mass points on the ground and the earthquake source, the time for generating the earthquake waves has a certain difference and different reaction results are obtained. The variability of the complex seismic motion is mainly reflected in the variation of time and space, including traveling wave effect, local field effect, partial coherence effect and the like, and the traveling wave effect is most remarkable. In building earthquake resistance design specifications (GB 50011-2010), it is also stated that special research should be done on the traveling wave effect when a multi-point input computational analysis is to be performed on a span-degree spatial structure beyond a certain range. At present, a plurality of scholars deeply explore the traveling wave effect, prove that the traveling wave effect has great influence on the internal force, the displacement and the like of the structure along with the increase of the apparent wave speed, and propose to consider the traveling wave effect, but do not specifically propose effective measures for resisting or reducing the traveling wave effect. According to the traditional thinking, only the problem that the internal force redistribution is caused by the fact that the cross section area of the rod piece which is greatly influenced by the traveling wave effect is increased is considered, so that the utilization efficiency of the rod piece is low and the like, therefore, the traveling wave effect is considered in the structural design, and a series of measures which are economical and effectively solve the adverse effect caused by the traveling wave effect are provided, so that the problem which needs to be solved urgently is solved.
Disclosure of Invention
The invention aims to solve the technical problem of the prior art and provides a structural topology optimization design method considering the travelling wave effect based on ANSYS, wherein a time-course analysis method is adopted to convert an artificially generated seismic wave time-course curve into force excitation to be applied to a structure, and according to a full stress criterion, when the stress of each rod piece of the structure reaches the full stress under the travelling wave effect, the structure has the lightest weight, and the purposes of saving steel and protecting the structure from being damaged are achieved.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the invention provides a traveling wave effect-based structural topology optimization design method based on ANSYS, which comprises the following steps of:
step 1: according to the earthquake proofing standard and the earthquake proofing category, the earthquake proofing intensity and the site condition of the local building, a triangular series method is utilized, a coherent function and an envelope function factor are added to artificially synthesize a spatial earthquake motion time-course curve of the uneven uniform site considering the traveling wave effect, and the spatial earthquake motion time-course curve is converted into a random excitation acceleration value with the traveling wave effect.
Step 2: establishing a finite element structure model by using finite element analysis software; setting a member sectional area set according to the earthquake-resistant standard requirement and the actual engineering requirement
Wherein i represents the number of the rod member, and an arbitrary sectional area A is selected for the rod member i Applying static load to the finite element structure model, carrying out static analysis, and judging the rationality of the finite element structure model; if the stress is not reasonable, searching unreasonable reasons and re-establishing a finite element structure model, if the stress is reasonable, calling the finite element model, reading in the random excitation acceleration with the traveling wave effect generated in the step 1 in ANSYS, and performing seismic response analysis on the finite element structure model by using a time course analysis method in consideration of the traveling wave effect to obtain the rod internal force and the rod stress sigma i 。
And step 3: establishing a topological optimization model, taking the sectional area of the rod piece as a design variable, and calculating the minimum total mass minW of the structural rod piece according to the mass density rho of the material and the length l of the rod piece, wherein the formula of the minimum total mass minW is as follows:
the rod member stress obtained by considering the traveling wave effect is consistent withThe allowable stress of the rod piece is taken as a constraint condition to carry out optimization design on the finite element structure model; the method comprises the following specific steps: extracting stress value sigma of rod piece by time course analysis method in step 2 by using ANSYS post-processing program i Will obtain the stress value sigma of the rod i Comparing the allowable stress value sigma' of the rod piece to obtain a ratio
If the ratio is greater or less>
In the range from 0.8 to 0.9, the lever area is not changed, if the ratio->
Out of this range, the ratio is->
Multiplied by the initial setting of the bar, cross-section area A i Obtaining a new rod section area A', and utilizing an EMODIF command in finite element software to change the rod section area from A i Change to in cross-sectional area A i Is larger than A' and adjacent to A in the collection of the cross-sectional areas of the rod pieces m 。
Step 4, repeating the steps 2 to 3, traversing all data in the rod section area set to obtain a new traversed rod section area set
And 5: for a obtained in step 4 m Analyzing the time course to obtain new rod internal force and rod stress; repeating the step 3 and the step 4 until the sectional area of the structural rod piece meets the traveling wave effect and the total structural mass reaches the minimum; the rod piece with the minimum total structural mass is the optimization result considering the traveling wave effect.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: according to the ANSYS-based structural topology optimization design method considering the traveling wave effect, the structural sectional area optimization result can be obtained after 20 times of iterative cycles, the effect caused by the traveling wave effect is considered, measures for reducing the effect caused by the traveling wave effect in a mode of changing the sectional area of a rod piece are provided, and the total mass of the obtained structure is the minimum under the condition of meeting the structural stress. The method adopts a time-course analysis method to convert an artificially generated earthquake wave time-course curve into force excitation to be applied to a structure, and according to a full stress criterion, when the stress of each rod piece of the structure reaches the full stress under the travelling wave effect, the structure has the lightest mass, saves steel materials after reaching the full stress, and can protect the structure from being damaged under the action of earthquake response, particularly the travelling wave effect; the structural optimization is considered, the sectional area of the rod piece seriously affected by the traveling wave effect is increased, the traveling wave effect is effectively avoided, and the traveling wave effect is considered in the specification.
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Fig. 1 is a flowchart of a method provided in an embodiment of the present invention.
Detailed Description
The following detailed description of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The method of this example is as follows.
The invention provides a structural topology optimization design method considering traveling wave effect based on ANSYS, as shown in FIG. 1, comprising the following steps:
step 1: according to the earthquake proofing standard and the earthquake proofing category, the earthquake proofing intensity and the site condition of the local building, a triangular series method is utilized, a coherent function and an envelope function factor are added to artificially synthesize a spatial earthquake motion time-course curve of the uneven uniform site considering the traveling wave effect, and the spatial earthquake motion time-course curve is converted into a random excitation acceleration value with the traveling wave effect.
Specifically, the method for generating the spatial seismic motion time-course curve is as follows, and the acceleration power spectral density function matrix S (v ω) for the earthquake at each point on the ground is expressed as follows:
in the formula, S vv (omega) and S vj (omega) is a self-power spectrum density function and a cross-power spectrum density function respectively, wherein v belongs to n, and j belongs to n; performing Cholesky decomposition on the S (v omega) to obtain a triangular complex matrix L (v omega) and a Hermite matrix L H (v ω) product:
S(vω)＝L(vω)L H (vω)
a stationary spatial seismic time interval u in the time domain range at the nth point is generated K (t) is represented by the following formula:
where h =1,2, …, n, ω is the circular frequency, t is the time, ω is l ＝l△ω，△ω＝ω N N,. DELTA.omega. Is the angular frequency,. Omega l Expressed as the l-th discrete frequency, ω N Represents the upper cut-off frequency;
is a random phase angle uniformly distributed in [0,2 pi ], h and l represent the seismic oscillation point number in different directions of the card, A γ (ω l ) And theta γ (ω l ) The amplitude and phase angle of the time course curve can be expressed by the following formula:
wherein L is γ And L γ A value obtained by performing Cholesky decomposition for S (v ω);
step 2: establishing a finite element structure model by using finite element analysis software; setting a member sectional area set according to the earthquake-resistant standard requirement and the actual engineering requirement
Wherein i represents the number of the rod member, and an arbitrary sectional area A is selected for the rod member i Applying static load to the finite element structure model, carrying out static analysis, and judging the rationality of the finite element structure model; if the acceleration is not reasonable, inputting the random excitation acceleration with the traveling wave effect generated in the step 1 on the finite element structure model, and performing seismic response analysis on the finite element structure model by using a time course analysis method in consideration of the traveling wave effect to obtain the rod internal force and the rod stress sigma i ；
And step 3: establishing a topological optimization model, taking the sectional area of the rod piece as a design variable, and calculating the minimum total mass W of the structural rod piece according to the mass density rho of the material and the length l of the rod piece, wherein the formula of the minimum total mass minW is as follows:
taking the stress of the rod piece obtained by considering the traveling wave effect in accordance with the allowable stress of the rod piece as a constraint condition to carry out optimization design on the finite element structure model; the method comprises the following specific steps: extracting stress value sigma of rod piece by time course analysis method in step 2 by using ANSYS post-processing program i Will obtain the stress value sigma of the rod i Comparing the allowable stress value sigma' of the rod piece to obtain a ratio
If the ratio is greater or less>
In the range from 0.8 to 0.9, the lever area is not changed, if the ratio->
Out of this range, the ratio is->
Multiplied by the initial setting of the bar, cross-section area A i Obtaining a new rod section area A', and utilizing the EMODIF command in the finite element software to change the rod section area from A i Change to in cross-sectional area A i Is larger than A' in the rod member sectional area set and is adjacent to A m . Arranging the sectional areas in the rod piece sectional area set from small to large, and finding out the sectional area which is close to the sectional area A 'and is larger than the sectional area A'; />
Step 4, repeating the step 2 to the step 3, traversing all data in the rod piece sectional area set to obtain a new rod piece sectional area set after traversal
And 5: for a obtained in step 4 m Analyzing the time course to obtain new rod piece internal force and rod piece stress; repeating the step 3 and the step 4 until the sectional area of the structural rod piece meets the traveling wave effect and the total structural mass reaches the minimum; the rod piece with the minimum total structural mass is an optimization result considering the traveling wave effect.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (1)
1. A structural topology optimization design method considering traveling wave effect based on ANSYS is characterized in that: the method comprises the following steps:
step 1: according to the earthquake proofing standard and the earthquake proofing category, the earthquake proofing intensity and the site condition of the local building, a triangular series method is utilized, a coherent function and an envelope function factor are added to artificially synthesize a spatial earthquake motion time-course curve of the uneven uniform site considering the traveling wave effect, and the spatial earthquake motion time-course curve is converted into a random excitation acceleration value with the traveling wave effect;
specifically, a spatial seismic motion time-course curve is generated in the following way, and an acceleration power spectral density function matrix S (v ω) for seismic motion at each point on the ground is expressed as follows:
in the formula, S vv (omega) and S vj (omega) is a self-power spectrum density function and a cross-power spectrum density function respectively, wherein v belongs to n, and j belongs to n; performing Cholesky decomposition on the S (v omega) to obtain a triangular complex matrix L (v omega) and a Hermite matrix L H (v ω) product:
S(vω)＝L(vω)L H (vω)
a stationary spatial seismic time interval u in the time domain range at the nth point is generated K (t) is represented by the following formula:
where h =1,2, …, n, ω is the circular frequency, t is the time, ω is l ＝lΔω，Δω＝ω N N,. DELTA.omega.is the angular frequency,. Omega. l Expressed as the l-th discrete frequency, ω N Represents the upper cut-off frequency;
is a random phase angle uniformly distributed in [0,2 pi ], h and l represent the number of seismic points in different directions of the card, A γ (ω l ) And theta γ (ω l ) The amplitude and phase angle of the time course curve can be expressed by the following formula:
wherein L is γ And L γ A value obtained by performing Cholesky decomposition for S (v ω);
and 2, step: establishing a finite element structure model by using finite element analysis software; setting a member bar section area set according to the seismic standard requirement and the actual engineering requirement
Wherein i represents the number of the rod member, and an arbitrary sectional area A is selected for the rod member i Applying static load to the finite element structure model, carrying out static analysis, and judging the rationality of the finite element structure model; if not, searching unreasonable reasons and rebuilding a finite element structure model, if reasonable, calling the finite element structure model, reading in the random excitation acceleration with the traveling wave effect generated in the step 1 in ANSYS, and performing seismic response analysis on the finite element structure model by using a time course analysis method in consideration of the traveling wave effect to obtain the rod piece internal force and the rod piece stress sigma i ；
And step 3: establishing a topological optimization finite element structure model, taking the sectional area of the rod piece as a design variable, and calculating the minimum total mass W of the structural rod piece according to the mass density rho of the material and the length l of the rod piece, wherein the formula of the minimum total mass minW is as follows:
taking the stress of the rod piece obtained by considering the traveling wave effect in accordance with the allowable stress of the rod piece as a constraint condition to carry out optimization design on the finite element structure model; the method comprises the following specific steps: extracting stress value sigma of rod piece by time course analysis method in step 2 by using ANSYS post-processing program i Will obtain the stress value sigma of the member i Comparing the allowable stress value sigma' of the rod piece to obtain a ratio
If the ratio is greater or less>
In the range from 0.8 to 0.9, the lever area is no longer changed, if the ratio->
Out of this range, the ratio is/are combined>
Multiplied by the initial setting of the bar, cross-section area A i Obtaining a new rod section area A', and utilizing the EMODIF command in the finite element software to change the rod section area from A i Change to in cross-sectional area A i Is larger than A' in the rod member sectional area set and is adjacent to A m ；
Step 4, repeating the steps 2 to 3, traversing all data in the rod section area set to obtain a new traversed rod section area set
And 5: for a obtained in step 4 m Analyzing the time course to obtain new rod piece internal force and rod piece stress; repeating the step 3 and the step 4 until the sectional area of the structural rod piece meets the traveling wave effect and the total structural mass reaches the minimum; the rod piece with the minimum total structural mass is the optimization result considering the traveling wave effect.
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