A topological optimization method for the mobile base structure of a rigid frame structure considering the selection of beam section type and placement angle

Abstract

The present invention belongs to the technical field of rigid frame structure layout, and specifically relates to a method for topological optimization of a mobile base structure of a rigid frame structure considering the selection of beam section type and placement angle, including a method for forming a rigid frame layout after the rigid frame structure optimization of movable nodes and the design variable update; the rigid frame structure optimization of the movable nodes is used for optimization iteration of the frame structure layout by calculating the sensitivity of the objective function to the node position design variable; the rigid frame structure optimization of the movable node adopts the node position of the frame structure, the cross-sectional area of ​​the beam unit, the placement angle of the main direction of the beam, and the cross-sectional type of the beam as the optimized design variables, and the main direction of the beam itself will change with the node position. The present invention can calculate the sensitivity of the objective function to each design variable and use the moving asymptote optimization algorithm for iteration, and finally find the optimal layout of the frame structure and allow beams of multiple cross-sectional types to exist simultaneously in the layout design.

Description

Technical Field

[0001] The invention belongs to the technical field of rigid frame structure layout, and in particular relates to a topological optimization method for a mobile base structure of a rigid frame structure taking into account beam section type selection and placement angles. Background Art

[0002] Frame structures are commonly found in the design of load-bearing structures for mesh roofs of large venues and tower or mast-type buildings. Compared with continuous solid structures, the materials of frame structures are more sparsely distributed in space, which also enables frame structures to meet the structural design requirements of large loads and large spans at low cost and low deadweight. Therefore, how to optimize the layout of discrete frame structures such as large trusses and rigid frames is also a problem that structural design engineers are widely concerned about.

[0003] Topology optimization can solve large-scale layout optimization problems of discrete structures such as trusses and rigid frames, as well as seek the optimal material distribution of continuum structures. Since this method can effectively control manufacturing costs and improve structural performance, it is widely used in various industrial fields. Research on the optimization design of frame structures based on topology optimization methods can be divided into two categories: optimization methods based on continuum and optimization methods based on discrete structures.

[0004] Continuum topology optimization methods such as the moving deformable component method or the level set method can map the beam geometry model described by explicit parameters to the background grid, so as to consider the geometric characteristics of the beam component within the framework of continuum structure design. The continuum structure topology optimization method uses solid units for finite element calculation, so it has high simulation accuracy, but this also makes the characteristic description of the beam model complicated. A beam with an irregular cross-section in a bar system often requires hundreds or even thousands of solid units to be described more accurately. At the same time, considering the sparse distribution of materials in discrete truss / rigid frame structures in three-dimensional space, the amount of calculation caused by using solid models to describe medium and large-scale frame structures and optimize them will be unbearable.

[0005] Different from the continuum structure optimization method using solid elements, the discrete structure optimization method using bar elements or beam elements achieves a very simple frame layout description, finite element calculation and topology optimization of large-scale bar structures at the expense of model geometric details. The base structure method is a numerical method for discrete structure topology optimization based on bar / beam elements. This method limits the bar layout to dense connections of a finite number of nodes, and selects the optimal connection relationship and material distribution scheme from them, thus avoiding the problem of unclear optimal configuration caused by too many bars in analytical methods and early numerical methods. The optimal configuration of the traditional base structure method can only be obtained by connecting fixed nodes. The fixed node feature greatly limits the design space of the optimization work. Although the discrete structure topology optimization method based on movable nodes has been proposed and applied in two-dimensional and three-dimensional problems, it does not consider the design problem of rigid frame structures with irregular beam sections and the influence of different section types on the optimal design of rigid frame structures. The rigid frame structure layout optimization method using only circular or circular beam sections obviously cannot meet the engineering design needs of more irregular beam section types such as L-shaped beams or I-beams. Summary of the invention

[0006] The purpose of the present invention is to provide a topological optimization method for a mobile base structure of a rigid frame structure taking into account the selection of beam section types and the placement angles. The method can calculate the sensitivity of the objective function to each design variable and iterate using a moving asymptote optimization algorithm to ultimately find the optimal layout of the frame structure and allow beams of various section types to coexist in the layout design.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A topological optimization method for a mobile base structure of a rigid frame structure considering the selection of beam section types and placement of rotation angles, including a method for optimizing the rigid frame structure of movable nodes and forming a rigid frame layout after updating design variables;

[0009] The optimization of the rigid frame structure of the movable nodes is used for optimization iteration of the frame structure layout by calculating the sensitivity of the objective function to the node position design variables;

[0010] The optimization of the rigid frame structure of the movable node adopts the node position of the frame structure, the cross-sectional area of ​​the beam unit, the main direction placement angle of the beam, and the cross-sectional type of the beam as the optimization design variables, and the main direction of the beam itself will change with the node position;

[0011] In the above mentioned rigid frame structure optimization system, the total number of movable nodes is M, the number of beam sections that can be designed is N, then x= Design variables for node coordinates; is the cross-sectional area design variable of the beam, where a i >0,i=1,2,…,N; is the design variable of the beam’s main direction rotation angle, where -π / 2<θ j <π / 2,j=1,2,…,N; is the design variable of the beam section type weight, where 0<ω k <1,k=1,2,…,N;

[0012] Use an artificial mixed interpolation assumption for the multi-section type design of beams:

[0013]

[0014] in, is the stiffness tensor of the beam element, a e is the cross-sectional area of ​​unit e, and is the stiffness tensor corresponding to the two cross-section types Contribution to the element stiffness tensor;

[0015] The design variables of this optimization problem are The optimization formula for minimizing the compliance problem is:

[0016]

[0017] Among them, F, U, K represent the node load vector, node displacement vector and global stiffness matrix of the frame structure respectively, V is the sum of the beam volumes in the frame layout, Denotes the Dirichlet frontier Γ U The displacement boundary conditions on is the design space of the design variable γ.

[0018] The total compliance of the beam volume of the rigid frame structure is:

[0019]

[0020]

[0021] Among them, u e is the displacement vector of the unit, x e is the coordinate vector of the nodes at both ends of the element, L e is the length of the beam unit, and the strain energy C of the unit in formula (4) e It can be expressed as:

[0022]

[0023] in, Represents the element stiffness matrix after global coordinate transformation, which is related to the node coordinates x at both ends of the element. e , beam unit cross-sectional area a e 、Beam main direction rotation angle θe And the proportion of cross-section types ω e Related;

[0024] For a rigid frame structure with M nodes and N beam elements, each node has multiple coordinate values, and each beam element has a cross-sectional area variable, a main direction rotation variable, and a cross-sectional type ratio variable. The main direction of the beam cannot be rotated in two dimensions, and the number of design variables is 2M+2N; in three-dimensional problems, the number of design variables becomes 3M+3N.

[0025] The method for forming the rigid frame layout after the design variables are updated adopts the following contents:

[0026] Beam element pointing vector From the left and right nodes P 1 With P 2 Determine that the other two of the three principal directions of the beam element and It cannot be determined by the positions of the nodes at both ends, and the two main directions in the perpendicular direction are obtained by rotating the corresponding main directions of the initial design;

[0027] Given a beam element P in the initial layout design 1 P 2 , and the beam element P after the node on one side is moved 1 P′ 2 , the position change of the beam element is regarded as a vector rotation around the axis n by an angle θ, and the rotation method is applied to dir y and dir z Get the two main directions dir′ generated after the node position moves y and dir′ z .

[0028] The method for forming the rigid frame layout after the design variables are updated is completed by the following steps:

[0029] S1: node position change;

[0030] S2: the main direction changes with the node position;

[0031] S3: main direction angle application;

[0032] Among them, the node from Move to P 3 The process changes the pointing vector dir of the node connecting the beam element x And the length L e , arrive The change in position is regarded as a rotation operation, and the rotation method is obtained by the Rodriguez rotation formula;

[0033] set up Then the vector rotation is written as:

[0034] v′=Rv (6)

[0035]

[0036] Among them, the rotation angle β of the vector v to v′ and the unit axis n are:

[0037]

[0038]

[0039] The vector cross product is replaced by a matrix multiplication:

[0040]

[0041] The change in the position of the beam causes the dir x 、dir y 、dir z The update rules for the three main directions are as follows:

[0042]

[0043] Among them, dir′ x is the unit vector of v′ after the node position is updated, and dir′ y and dir′ z Then through the initial main direction dir y and dir z Multiply it by the same rotation matrix R on the left to get .

[0044] After the main direction of the beam element follows the node change, an artificial rotation angle θ of the main direction of the beam is introduced. The rotation is expressed as v′ or As the axis, it rotates clockwise or counterclockwise in a specified direction in a plane perpendicular to the axis v'. The rotation rules are as follows:

[0045] [dir" y dir″ z ]=[dir′ y dir′ z ]R e (θ e )

[0046]

[0047] Among them, the beam section type only affects the moment of inertia or bending / torsion performance of the beam unit in each direction, and does not affect the placement position and rotation angle of the beam unit.

[0048] The method for optimizing the frame structure of movable nodes and forming the frame layout after the design variables are updated is based on the differences in the model update mode and sensitivity calculation caused by the increase of design variables, and at the same time introduces a strategy for merging overlapping nodes to optimize the process.

[0049] The technical effects achieved by the present invention are:

[0050] A topological optimization method for a mobile base structure of a rigid frame structure considering the selection of beam section types and placement corners of the present invention realizes the optimization of the rigid frame structure considering irregular cross-section beams under the premise of using movable nodes. The existing related research on the optimization of rigid frame structures based on movable nodes is often based on circular cross-section beams, and therefore cannot realize the placement corner design of irregular cross-section beams. The beam section types considered by this method include not only circular or circular ring cross-section beams, but also irregular cross-section beams commonly used in engineering, such as L-shaped cross-section beams and I-beams, which greatly expands the design space of rigid frame structure optimization problems.

[0051] Compared with the method of simulating irregular cross-section beams using a continuum topology optimization method, the present invention's method for topology optimization of a mobile base structure of a rigid frame structure that takes into account the selection of beam section types and the placement of corners more flexibly considers the differences in component performance caused by different cross-sectional characteristics, and realizes the topology optimization of medium and large-scale rigid frame structures that is difficult to achieve with solid grid analysis.

[0052] The optimal rigid frame configuration obtained by the topological optimization method of the mobile base structure of the rigid frame structure considering the selection of beam section types and the placement of the rotation angle of the present invention has two or more beam components of different section types, so that the performance of different types of beam sections in terms of bending or torsion can be better utilized. Compared with the traditional method, the optimal configuration calculated by the method considering the section selection will have better objective function values ​​and mechanical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a schematic diagram of the main direction of the beam unit of an embodiment of the present invention;

[0054] Figure 2 is a schematic diagram of the variation of the main direction of the beam unit with the position of the node according to an embodiment of the present invention;

[0055] Figure 3 is a schematic diagram of beam position change caused by node movement in an embodiment of the present invention;

[0056] Figure 4 is a schematic diagram of the change of the main direction of the beam caused by the movement of the node in an embodiment of the present invention;

[0057] Figure 5 Schematic diagram of the rotation angle of the main direction of the beam unit artificially applied in an embodiment of the present invention;

[0058] Figure 6is an optimization flow chart of an embodiment of the present invention;

[0059] Figure 7 It is a plan view diagram of the main focus of the initial design of the embodiment of the present invention;

[0060] Figure 8 It is a schematic diagram of the initial configuration "unit cell" design of an embodiment of the present invention;

[0061] Fig. 9 is a schematic diagram of a cantilever beam calculation example of an embodiment of the present invention;

[0062] Fig.10 is a schematic diagram of an initial design of a cantilever beam optimization example according to an embodiment of the present invention;

[0063] Fig.11 1 is a schematic diagram comparing optimization results corresponding to three types of design spaces in a cantilever beam calculation example of an embodiment of the present invention;

[0064] Fig.12 It is an iterative history statistical diagram of the objective function and the constraint function of the embodiment of the present invention;

[0065] Fig.13 is a schematic diagram of a calculation example of a torsion beam according to an embodiment of the present invention;

[0066] Fig.14 1 is a schematic diagram comparing optimization results corresponding to three design space types in a torsion beam calculation example of an embodiment of the present invention;

[0067] Fig.15 Schematic diagram of the initial design of a twisted sphere calculation example according to an embodiment of the present invention;

[0068] Fig.16 It is a schematic diagram of truss analysis of a torsion ball calculation example according to an embodiment of the present invention. DETAILED DESCRIPTION

[0069] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0070] Embodiment 1:

[0071] like Figure 1-Figure 14 As shown, a topological optimization method for a mobile base structure of a rigid frame structure considering the selection of beam section types and the placement of rotation angles, including a method for optimizing the rigid frame structure of movable nodes and forming a rigid frame layout after updating design variables;

[0072] The optimization of the rigid frame structure with movable nodes is used for the optimization iteration of the frame structure layout by calculating the sensitivity of the objective function to the node position design variables; stiffness is the most basic performance indicator of the frame load-bearing structure, and the adjoint method can be used to solve the sensitivity of the objective function to the design variables of maximizing the overall stiffness and minimizing the flexibility. At the same time, the weight of the structure can be regarded as a constraint of the optimization problem.

[0073] The optimization of the rigid frame structure with movable nodes uses the node position of the frame structure, the cross-sectional area of ​​the beam unit, the main direction placement angle of the beam, and the cross-sectional type of the beam as the optimization design variables. The main direction of the beam itself will change with the node position; therefore, the design variable of the main direction rotation of the beam should be applied to each beam component after the node coordinates are updated, resulting in a change in the main direction of the beam.

[0074] In the frame structure optimization system, the total number of movable nodes is M, and the number of beam sections that can be designed is N. Design variables for node coordinates; is the cross-sectional area design variable of the beam, where a i >0,θ=1,2,…,N; is the design variable of the beam’s main direction rotation angle, where -π / 2<θ j <π / 2,j=1,2,…,N; is the design variable of the beam section type weight, where 0<ω k <1,k=1,2,…,N;

[0075] Use an artificial mixed interpolation assumption for the multi-section type design of beams:

[0076]

[0077] in, is the stiffness tensor of the beam element, a e is the cross-sectional area of ​​unit e, and is the stiffness tensor corresponding to the two cross-section types Contribution to the element stiffness tensor;

[0078] The design variables of this optimization problem are The optimization formula for minimizing the compliance problem is:

[0079]

[0080] Among them, F, U, K represent the node load vector, node displacement vector and global stiffness matrix of the frame structure respectively, V is the sum of the beam volumes in the frame layout, Denotes the Dirichlet frontier Γ U The displacement boundary conditions on is the design space of the design variable γ.

[0081] The total compliance of the beam volume of the rigid frame structure is:

[0082]

[0083]

[0084] Among them, u e is the displacement vector of the unit, x e is the coordinate vector of the nodes at both ends of the element, L e is the length of the beam unit, and the strain energy C of the unit in formula (4) e It can be expressed as:

[0085]

[0086] in, Represents the element stiffness matrix after global coordinate transformation, which is related to the node coordinates x at both ends of the element. e , beam unit cross-sectional area a e 、Beam main direction rotation angle θ e And the proportion of cross-section types ω e Related;

[0087] For a rigid frame structure with M nodes and N beam elements, each node has multiple coordinate values, and each beam element has a cross-sectional area variable, a main direction rotation variable, and a cross-sectional type ratio variable. The main direction of the beam cannot be rotated in two dimensions, and the number of design variables is 2M+2N; in three-dimensional problems, the number of design variables becomes 3M+3N.

[0088] The method for forming the rigid frame layout after the design variables are updated adopts the following contents:

[0089] like Figure 1 As shown, the beam element points to the vector From the left and right nodes P 1 With P 2 Determine that the other two of the three principal directions of the beam element and It cannot be determined by the positions of the nodes at both ends, and the two main directions in the perpendicular direction are obtained by rotating the corresponding main directions of the initial design;

[0090] like Figure 2 As shown, given a beam element P in the initial layout design 1 P 2 , and the beam element P after the node on one side is moved 1 P′ 2, the position change of the beam element is regarded as a vector rotation around the axis n by an angle θ, and the rotation method is applied to dir y and dir z Get the two main directions dir′ generated after the node position moves y and dir′ z .

[0091] like Figure 3 As shown, the method for forming the rigid frame layout after the design variables are updated is completed by the following steps:

[0092] S1: node position change;

[0093] S2: the main direction changes with the node position;

[0094] S3: main direction angle application;

[0095] Among them, the node from Move to P 3 The process changes the pointing vector dir of the node connecting the beam element x And the length L e , arrive The change in position is regarded as a rotation operation, and the rotation method is obtained by the Rodriguez rotation formula;

[0096] set up Then the vector rotation is written as:

[0097]

[0098] Among them, the rotation angle β of the vector v to v′ and the unit axis n are:

[0099]

[0100] like Figure 4 As shown, the vector cross product is replaced by a matrix multiplication:

[0101]

[0102] like Figure 5 As shown, the change in the position of the beam causes dir x 、dir y 、dir z The update rules for the three main directions are as follows:

[0103]

[0104] Among them, dir′ x is the unit vector of v′ after the node position is updated, and dir′ y and dir′z Then through the initial main direction dir y and dir z Multiply it by the same rotation matrix R on the left to get .

[0105] After the main direction of the beam element follows the node change, an artificial rotation angle θ of the main direction of the beam is introduced. The rotation is expressed as v′ or As the axis, it rotates clockwise or counterclockwise in a specified direction in a plane perpendicular to the axis v'. The rotation rules are as follows:

[0106] [dir" y dir″ z ]=[dir′ y dir′ z ]R e (θ e )

[0107]

[0108] Among them, the beam section type only affects the moment of inertia or bending / torsion performance of the beam unit in each direction, and does not affect the placement position and rotation angle of the beam unit.

[0109] like Figure 6 As shown, the method of optimizing the frame structure of movable nodes and forming the frame layout after the design variables are updated is different through the model updating method and sensitivity calculation caused by the increase of design variables. At the same time, the strategy of merging overlapping nodes is introduced to optimize the process.

[0110] Embodiment 2:

[0111] Numerical example:

[0112] First, the initial configuration of the optimization problem is introduced, including the arrangement of beam elements in the structural unit cell and the initial main direction setting. Then, a three-dimensional cantilever beam example and a three-dimensional torsion beam example are shown respectively. By controlling the design space of the cantilever beam example, the problem is degenerated into a two-dimensional case, and the influence of the node movement range on the final configuration is shown. By controlling the boundary of the node movement in the three-dimensional torsion beam example, the optimal configuration of the torsion beam in the two design spaces of slender cube space and spherical space is obtained.

[0113] Different types of beam elements have different bending stiffness, which will also affect the final calculated rigid frame configuration. If the dimensionless method is used for finite element calculation and structural design, the section inertia moment will be impossible to select. Therefore, a set of more common steel material design parameters is selected, the elastic modulus is E = 210GPa, and the Poisson's ratio is 0.3. The initial width of the rectangular section is set to 1mm, and the initial radius of the circular section is This ensures that the initial areas of the two cross sections are equal. In order to achieve topological changes in the structural layout, it is considered that beam elements with cross-sectional areas less than 0.001 times the initial area can be eliminated in the final design. The moving asymptote (MMA) method is used to update the design variables, and the iteration is terminated when the relative change of the objective function value in the last 5 steps is less than 0.0004.

[0114] Embodiment 3:

[0115] Cantilever beam example:

[0116] like Figure 7-Figure 12 As shown in Figure 1, the initial design configuration of the rigid frame structure is first introduced, as Figure 7 As shown in the figure, considering the need to retain three coordinate planes and sufficiently complex structural connection relationships in planes with an angle of 45° with these planes, a "unit cell" consisting of 44 beam units is used to stack the initial design. The overall structure is a cubic frame structure consisting of 12 beam units, and the outer surface is an oblique orthogonal structure consisting of 6 groups of 4 beam units each. A separate node is set in the center of the "unit cell" and 8 beam units are used to connect all the endpoints of the cube. It should be noted that the "unit cell" mentioned above is not a strict concept of a unit cell, because the overall layout is not a curved "unit cell" densely stacked, and the "unit cell" in this article only selects the local structure of the initial design for illustration.

[0117] In the cantilever beam example, the method will be demonstrated to solve the three-dimensional frame layout optimization design problem and its degradation to a two-dimensional problem in an appropriate design space. Fig. 9 As shown, the optimization is performed 2, 4, and 2 times in the x, y, and z directions respectively. Figure 8 As shown, the initial design configuration of the unit cell stack.

[0118] Given 3 design spaces:

[0119] The first type is that the movable space of each node is a spherical domain with a diameter equal to the side length of the cube unit cell, and the upper limit of the cross-sectional area of ​​the beam unit is set to 16 times the initial design. The setting of the upper limit of the cross-sectional area will not allow the material to be densely distributed in a small range, so that the final configuration will be relatively evenly distributed in the three-dimensional design space;

[0120] The second type is that the movable space of the node is the same as the previous one, but the cross-sectional area restriction of the beam element is cancelled. Since the load acts on a single node and in a single direction, the optimization problem in this case will degenerate into two dimensions, and the material of the final configuration is distributed in the plane where the load is located;

[0121] In the third case, the movable space of the node is expanded to the entire three-dimensional design domain, and the material in the final configuration is also distributed in the two-dimensional plane, but there are some differences between this configuration and the second case. In the optimization method based on beam elements, the material is distributed on a line segment with no width, so ideally the material can be infinitely stacked in a narrow space, and there is no need to consider the impact of the maximum material filling limit on the performance of the rigid frame structure.

[0122] like Fig.11 and Fig.12 As shown in the figure, no matter how the design space is set, this method can achieve the optimal configuration optimization of the node-connected rigid frame structure and the optimization of the main direction of beam placement. Since there is almost no torque in the cantilever beam example, the section type selection is not involved.

[0123] By controlling the design space, two-dimensional and three-dimensional configurations can be obtained, but in the cantilever beam optimization problem, the two-dimensional configuration is obviously more reasonable and has a lower objective function value. Comparing Type 2 and Type 3, after removing the node movement restriction, the flexibility of the optimal configuration is only reduced by 0.4% compared with the case of applying the node movement restriction. Therefore, the area where the node movement is restricted does not have a significant effect on the flexibility of the optimal configuration.

[0124] In the optimization of three-dimensional continuum, the optimal configuration of the cantilever beam example is often an obvious three-dimensional structure, but the ideal configuration calculated by the discrete structural optimization method based on beam elements is a two-dimensional planar structure. There are two main reasons for this:

[0125] 1. For example, in the continuum structure topology optimization method of the density method, each density unit occupies a part of the design space, so the material cannot be completely stacked on the plane where the load is located, while the discrete structure topology optimization method can;

[0126] 2. The volume fraction in continuum topology optimization is often relatively large, so the structure is clearly distributed in three-dimensional space. The material distribution of the frame structure studied by discrete structure topology optimization is extremely sparse. If the volume fraction in continuum topology optimization is taken as a smaller value, then the material of its optimized configuration will also be approximately distributed on the plane where the load is located, just like the discrete structure optimization structure.

[0127] Embodiment 4:

[0128] Torsion beam example:

[0129] The ability of this method to solve the three-dimensional frame layout optimization design problem will be demonstrated. The load and constraint conditions of the example are as follows Fig.13 As shown, the same initial design configuration as in the cantilever beam example is used;

[0130] Three design spaces are given for the torsion beam problem:

[0131] The first type is that the movable space of each node is a spherical domain with a diameter equal to the side length of the cubic unit cell, which restricts all nodes to be within the cubic space and does not restrict the cross-sectional area of ​​the beam unit;

[0132] The second type, based on the first type, considers two types of beam sections: rectangular section and circular section, and finally obtains a rigid frame structure layout that includes both types of sections, and verifies the superiority of this configuration;

[0133] The third method uses a 4×4×4 initial configuration for optimization based on the first method, and finally obtains a spherical structure that is close to the analytical solution of the truss structure.

[0134] like Fig.14 As shown in the figure, using the optimization results of the second design space, this method realizes the topology optimization task of the rigid frame structure under the torsion beam load and constraint form in three-dimensional space. Type 2 takes into account multiple cross-section types while optimizing the rigid frame structure, and obtains a smaller structural flexibility than type 1. The reason for the small reduction in the objective function value is that most beam elements bear axial forces, so the enhancement of bending or torsional performance brought about by the change of cross-section type does not significantly enhance the structural performance.

[0135] Type 3 uses Figure 15-16 The 4×4×4 initial structure shown in the figure was subjected to torsion sphere design, and a result with a clear topological configuration was obtained. This result is very consistent with the analytical solution of the truss structure design under torsion sphere load and constraint. This feature further illustrates the effectiveness of this method for frame structure optimization.

[0136] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A topological optimization method for a mobile base structure of a rigid frame structure considering the selection of beam section types and the placement of rotation angles, characterized in that: Including the optimization of the frame structure of movable nodes and the formation method of the frame layout after the design variables are updated; The optimization of the rigid frame structure of the movable nodes is used for optimization iteration of the frame structure layout by calculating the sensitivity of the objective function to the node position design variables; The optimization of the rigid frame structure of the movable node adopts the node position of the frame structure, the cross-sectional area of ​​the beam unit, the main direction placement angle of the beam, and the cross-sectional type of the beam as the optimization design variables, and the main direction of the beam itself will change with the node position; In the rigid frame structure optimization system, the total number of movable nodes is , the number of beam sections that can be designed is ,but Design variables for node coordinates; is the design variable of the cross-sectional area of ​​the beam, where ; is the design variable of the beam’s main direction rotation angle, where ; is the design variable for the beam section type weight, where ; Use an artificial mixed interpolation assumption for the multi-section type design of beams: in, is the stiffness tensor of the beam element, Yes Unit The cross-sectional area, and is the stiffness tensor corresponding to the two cross-section types Contribution to the element stiffness tensor; The optimized design variables are , the optimization goal is to minimize the compliance C, and the optimization formula is: in, They represent the node load vector, node displacement vector and global stiffness matrix of the frame structure respectively. is the sum of the beam volumes in the frame layout, In the Dirichlet frontier The displacement boundary conditions on is the design variable design space; The total compliance of the beam volume of the rigid frame structure is: in, is the transpose of the load vector, is the displacement vector of the unit, are the coordinate vectors of the nodes at both ends of the element, is the length of the beam element, and the strain energy of the element in equation (4) is It can be expressed as: in, Represents the element stiffness matrix after global coordinate transformation, which is consistent with the node coordinates at both ends of the element , beam unit cross-sectional area , beam main direction angle And the proportion of cross-section types Related; For the number of nodes The number of beam elements is For a rigid frame structure, each node has multiple coordinate values, and each beam element has a cross-sectional area variable, a main direction angle variable, and a cross-sectional type ratio variable. The main direction of the beam cannot be rotated in two dimensions, and the number of design variables is 2M+2N; in three-dimensional problems, the number of design variables becomes 3M+3N. The method for forming the rigid frame layout after the design variables are updated adopts the following contents: Beam element pointing vector By left and right nodes and Determine that the other two of the three principal directions of the beam element and It cannot be determined by the positions of the nodes at both ends, and the two main directions in the perpendicular direction are obtained by rotating the corresponding main directions of the initial design; Given a beam element in the initial layout design , and the beam element after one side node is moved , the position change of the beam element is regarded as a vector rotating around the axis The angle is The same rotation rules as for beam elements are applied to and Get the two main directions generated after the node position moves and .

2. A method for topological optimization of a mobile base structure of a rigid frame structure considering beam section type selection and placement angle according to claim 1, characterized in that: The method for forming the rigid frame layout after the design variables are updated is completed by the following steps: S1: node position change; S2: the main direction changes with the node position; S3: main direction angle application; Among them, the node from Move to The process changes the pointing vector of the node connecting the beam element and length , The change in position is regarded as a rotation operation, and the rotation method is obtained by the Rodriguez rotation formula; set up , then the vectors can be rotated by the rotation matrix To do the conversion, write: in, Unit axis The direction component of the vector Rotate to Corner With unit axis for: in, Represents the coordinates of the node. The subscript containing initial indicates that the coordinates are the initial position of the node. No subscript indicates that the coordinates are the position after the node is moved. The superscript containing l indicates that the node is the left end node of the beam element. The superscript containing r indicates that the node is the right end node of the beam element.

3. A method for topological optimization of a mobile base structure of a rigid frame structure considering the selection of beam section types and placement angles according to claim 2, characterized in that: The vector cross product is replaced by a matrix multiplication: 。 4. A method for topological optimization of a mobile base structure of a rigid frame structure considering beam section type selection and placement angle according to claim 2, characterized in that: The change in the beam position causes The update rules for the three main directions are as follows: in, After the node position is updated The unit vector of and Then through the initial main direction and Left multiply the same rotation matrix get.

5. A method for topological optimization of a mobile base structure of a rigid frame structure considering the selection of beam section types and placement of rotation angles according to claim 4, characterized in that: After the main direction of the beam element changes with the node, an artificial rotation angle of the main direction of the beam is introduced , the rotation is or The axis is rotated clockwise or counterclockwise in a specified direction perpendicular to the axis. The rotation rules are as follows: Among them, the beam section type only affects the moment of inertia or bending / torsion performance of the beam unit in each direction, and does not affect the placement position and rotation angle of the beam unit.

6. A method for topological optimization of a mobile base structure of a rigid frame structure considering beam section type selection and placement angle according to claim 1, characterized in that: The method for optimizing the frame structure of movable nodes and forming the frame layout after the design variables are updated is based on the differences in the model update mode and sensitivity calculation caused by the increase of design variables, and at the same time introduces a strategy for merging overlapping nodes to optimize the process.

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