Combined numerical and graphical grid and matrix cross-section analysis method for use in structural simulation calculations

Abstract

Disclosed is a combined numerical and graphical grid and matrix cross-section analysis method for use in structural simulation calculations. The method comprises the following steps: decomposing and discretizing an analyzed component object, and on the basis of grid locations occupied by units after decomposition and discretization, determining a cross-sectional shape and locations of the units; using a mathematical tool capable of performing a matrix operation, using a grid to express a cross-section, determining coordinates by means of a cross-section grid, and using a matrix sequence to represent a cross section of the entire component; implementing matricization of component information by means of combined graphical and numerical value assignment simulation of all cross sections. The present invention uses a spatial grid to simulate a cross section of a component, and by means of establishing discrete grid units, using combined numerical and graphical means, using a matrix positioning method for grid coordinates, and using a multi-dimensional digital matrix to record data, it is possible to establish a unified structural component input and analysis module, which can implement simulation of a structural system in the most intuitive and concise way, and provide considerably effective analysis result display.

Description

A numerical-geometric combined grid matrix section analysis method for structural simulation calculation TECHNICAL FIELD

[0001] The present application belongs to the field of computer-aided engineering and finite element analysis, and particularly relates to a numerical-geometric combined grid matrix section analysis method for structural simulation calculation. BACKGROUND

[0002] The structural analysis by the finite element method is to discretize the structure into a multi-degree-of-freedom system with a finite number of nodes as generalized coordinate points, and currently a fiber model or a multi-spring model is generally used to simulate the structural beams, columns and shear walls, and the optimal solution is sought between the reasonable simplification degree and the necessary calculation accuracy by gradually refining the spring element number. By selecting the degrees of freedom of the nodes, the element stiffness matrix, mass matrix, damping matrix and node force matrix are established, and then the motion equation of the entire system is established and the known boundary conditions and initial conditions are processed, and then the dynamic characteristics and structural responses under complex multi-working conditions are solved.

[0003] However, the implementation of structural finite element calculation by using a program language is a complex process, involving multiple steps such as geometric modeling, meshing, material property definition, boundary condition and load application, stiffness matrix assembly, equation solving and result post-processing. The development setting and calculation simulation of the complex program of the currently developed large-scale structural finite element software are basically a black box for the majority of structural engineers, and are shrouded in mystery. The program writers have little understanding of the principles and technical details of structural mechanics, and rarely understand the origin and development of the calculation. Structural engineers have little knowledge of the simulation of structural calculation software and consider it obscure and difficult to understand. For civil engineering, the inability to precisely simulate materials and numerous simplifying assumptions makes the structural analysis accuracy rough and cannot be further investigated.

[0004] Numerical matrices play a key role in almost all fields of modern science and engineering, and the stiffness, mass and external force are stored and measured by numerical matrices for structural analysis, which has the advantages of strong mathematical expression ability and calculation efficiency. However, the limitation of this method is that a large amount of data needs to be preprocessed, and if the real existence of the component cannot be reasonably simulated and simplified, the entire calculation simulation will become infeasible due to the complexity of processing a large amount of data. It is a challenge to completely map the complex structure of the real world into a mathematical model, which requires interdisciplinary knowledge integration. SUMMARY

[0005] The present application aims to use a multi-dimensional matrix to represent the section and material information of the component by using a numerical-geometric combined method, and then form the stiffness matrix of the component and structure, so as to realize the rapid calculation and simulation of the structure, use the numerical-geometric combined grid matrix section diagram method, and propose a matrix simulation analysis method to provide an analysis method for the digital simulation of objective matter.

[0006] The technical scheme adopted by the present application to solve its technical problems is:

[0007] A numerical and geometrical combined grid matrix section analysis method for structural simulation calculation, comprising the following steps:

[0008] Discretizing the input member, determining the section shape and the location of each unit according to the grid position occupied by each unit after discretization;

[0009] Using a mathematical tool capable of matrix operation, representing the section by a grid, determining the coordinates of the section grid, and representing the entire member section by a matrix array;

[0010] Realizing the matrix of the member information through the numerical and geometrical combined assignment simulation of all sections;

[0011] Using the matrix member to participate in the corresponding structural simulation analysis.

[0012] Preferably, for each unit grid after discretization, each grid has a corresponding grid number position (x, y) in the local coordinates, and according to the grid precision a*a, the unit coordinates of the grid a*(x-1)+a / 2, a*(y-1)+a / 2] are obtained.

[0013] Preferably, the matrix array representing the entire member section comprises the following steps:

[0014] Defining a two-dimensional matrix according to the size of the section and the number of unit grids, and assigning a value of 0 to obtain a two-dimensional zero matrix;

[0015] Inputting the grid number of the member section, i.e. the row and column number of the matrix, and defining three-dimensional arrays YZ(:,:1) and XY(:,:2) to record the position of each grid in the local coordinate system; in the concrete grid unit, the input value of the occupied grid is 1, the input value of the overlapping place of the steel grid and the concrete grid unit is 2, and the value of the remaining matrix elements is 0; the matrix records the information of each grid unit of the entire section, and each element of the matrix is a numerical integral point;

[0016] According to the type and size of the member, the complete coverage grid size is selected, represented by a two-dimensional matrix, and then assigned one by one to represent the division of each unit of the section.

[0017] Preferably, for various cross-section forms, various material columns, beams and wall structures, the initial value of the member is considered by considering different shear deformations and stiffness values, the stiffness and cross-section mechanical characteristics of the grid element are obtained in turn by matrix operation assignment, the stiffness matrix of the element is further condensed and integrated, the element stiffness matrix, mass matrix, damping matrix and node force matrix are established, the stiffness matrix and mass matrix of the whole structure system are formed, and then the motion equation of the whole system is established, finally, the dynamic characteristics and structural response of the system are solved by processing the known boundary conditions and initial conditions, and the structural dynamic analysis is realized.

[0018] Preferably, the simulated structural members and related structural analysis are displayed and simulated by matrix value pseudo-color display and contour map.

[0019] Preferably, in the post-processing of structural calculation, the stress-strain values of the cross-section of the member are stored by multi-dimensional matrix, and the cross-section stress or strain nephogram is directly formed by matrix slicing.

[0020] Preferably, for the strain analysis of each section of the cross-section of the structural member under bidirectional seismic action, the displacement response real value of each node is stored at each time step, the displacement of the two nodes of each member unit is obtained through the conversion of the degree of freedom, and the stress-strain values of each section of the cross-section of the member are calculated by using the network matrix combining numerical and geometric shapes.

[0021] Preferably, for the nonlinear analysis of the simulated structure, the material failure condition and degradation performance of each cross-section unit in the structural analysis are determined by assigning the material hysteresis curve and performance and stress-strain values.

[0022] Compared with the prior art, the present application has the following beneficial effects:

[0023] The present application uses the grid matrix cross-section diagram combining numerical and geometric shapes, simulates the member matrix, provides a new way for realizing the integration of figures and numbers, and is a method of abstracting objects or systems in the real world into mathematical matrices for calculation and analysis.

[0024] The method is intuitive and effective, the numerical and geometric matrix is directly derived from the shape of the object and the material assignment, with the development of calculation technology and computing power, efficient algorithms and powerful computing capacity, the method can be used not only in various mechanical action scenes such as structural mechanics and fluid mechanics, but also can be used to simulate everything connected, and provides a new intuitive and effective method for matrix simulation of the Internet of Things. BRIEF DESCRIPTION OF DRAWINGS

[0025] In order to make the purpose, technical scheme and advantages of the present disclosure clearer, the technical scheme of the present disclosure is further described in detail below in combination with specific embodiments and with reference to the following drawings.

[0026] Fig. 1 is a three-dimensional schematic diagram of an embodiment of an L-shaped member;

[0027] Fig. 2 is a three-dimensional schematic diagram of an embodiment of a ten-shaped member;

[0028] Fig. 3 is a spatial discrete unit structure diagram of an embodiment of an L-shaped member;

[0029] Fig. 4 is a spatial discrete unit structure diagram of an embodiment of a ten-shaped member;

[0030] Fig. 5 is a planar schematic diagram of a cross section of an embodiment of an L-shaped member;

[0031] Fig. 6 is a planar schematic diagram of a cross section of an embodiment of a ten-shaped member;

[0032] Fig. 7 is a spatial matrix schematic diagram of an embodiment of a ten-shaped column;

[0033] Fig. 8 is a spatial cross section schematic diagram of an embodiment of a ten-shaped column;

[0034] Fig. 9 is a cross section stress schematic diagram of an embodiment of an L-shaped column;

[0035] Fig. 10 is a cross section strain schematic diagram of an embodiment of a ten-shaped column.

[0036] Fig. 11 is a flow chart of a cross section analysis method of a numerical shape combined grid matrix used for structural simulation calculation of an embodiment. DETAILED DESCRIPTION

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0038] The present application simulates and stores member shape cross section, material performance and spatial position information through multi-dimensional matrix, and realizes relevant structural mechanics calculation through matrix calculation, thereby providing a theory and a specific method for digital measurement of everything. It involves using mathematical matrix as a tool to simulate object surface and internal material information, and uses matrix operation to analyze the interaction between the member and the surrounding system, and further simulates the interaction between the object and various information and phenomena in the real world.

[0039] As shown in FIG. 11, the numerical and geometrical combined grid matrix section analysis method for structural simulation calculation of the present embodiment comprises the following steps: decomposing and discretizing the input member, determining the section shape and the location of each unit according to the grid position occupied by each unit after discretization; using a mathematical tool capable of matrix operation to represent the section with a grid, and using the grid coordinates to represent the entire member section with a matrix array; realizing the matrix of the member information through the numerical and geometrical combined assignment simulation of all sections; and using the matrix member to participate in the corresponding structural simulation analysis.

[0040] As shown in FIGS. 1 and 2, when the L-shaped and ten-shaped members are analyzed as reinforced concrete column members, their spatial forms and sections can be first discretized into steel bar units and concrete units, as shown in FIGS. 3 and 4. On this basis, the grid is used for division, and the numerical matrix is further used for representation. Other rectangular, circular and various types of section members can be realized through similar simplification, and the steps are as follows:

[0041] Step one, in common calculation or programming tools such as Python, Matlab and Maple, the codes of the grid occupied by each unit after discretization of the input member are input to determine the section shape and the location of each unit:

[0042] First, the position code (x, y) of each grid in the local coordinates is recorded, and the unit coordinates of the grid are obtained according to the grid accuracy a*a, that is, a*(x-1)+a / 2, a*(y-1)+a / 2].

[0043] In the present embodiment, the grid accuracy is 100mmX100mm, and the unit coordinates of the grid are [100*(x-1)+50, 100*(y-1)+50].

[0044] When the grid accuracy is 50mmX50mm, the unit coordinates of the grid are [50*(x-1)+25, 50*(y-1)+25], and the center positions of each unit of the section can be marked with the corresponding grid coordinate code.

[0045] As shown in FIG. 5, the grid coordinates of the middle unit of the L-shaped column are (2, 6), and the local coordinates are (150, 550); as shown in FIG. 6, the grid coordinates of the middle unit of the cross-shaped column are (10, 10), and the local coordinates are (475, 475).

[0046] Step two, using a mathematical tool capable of matrix operation (such as Python, Matlab and Maple), the spatial grid is used to represent the section, and the grid is used to represent the section.

[0047] By the cross-section grid coordinate (a virtual grid covering the component cross-section and the calculation accuracy), the whole component cross-section is represented by a matrix series. In this embodiment, a two-dimensional matrix K (16, 16) (the number of rows and columns of the matrix is 16) is defined and assigned as 0, and then a 16x16 two-dimensional matrix is obtained. Then the grid occupied by the cross-shaped component cross-section, i.e. the row and column numbers of the matrix, is inputted. Then a three-dimensional array YZ ( :, : 1), XY ( :, : 2) is defined to record the position of each grid in the local coordinate system. The grid occupied by the concrete spring element is inputted as 1, the grid overlapped by the steel spring and the concrete spring element is inputted as 2, and the rest of the matrix elements are 0. The matrix records the information of each spring element of the whole cross-section, as shown in the numerical matrix of Fig. 5. Each element of the matrix is a numerical integration point.

[0048] Further according to the type and size of the component, the complete grid size is selected, represented by a two-dimensional matrix, and then assigned one by one to represent the division of each element of the cross-section.

[0049] Taking a T-shaped column as an example, the limb thickness is 200 mm, the limb height to thickness ratio is 3, and a 12*12 grid is used. Through the conversion and transposition of the matrix, the change of the cross-section can be realized, such as cross-section rotation. The change of the matrix row and column can be realized by simple and basic matrix operation. K represents the orientation, k = 1, 2, …, respectively representing the rotation of k*90 degrees counterclockwise on the basis of the original position, and the matrix schematic T-shaped cross-section is shown in Table 1 and Table 2.

[0050] Table 1 T-shaped matrix plane schematic

[0051] Table 2 T-shaped matrix plane schematic rotated 90 degrees clockwise

[0052] Step three, the matrix of the component information is realized by simulating the combination of the graph number of all cross-sections and the assignment. For columns, beams and wall structures of various cross-section forms and various materials, the same method can be used. Only the grid and the consideration of different shear deformation and stiffness values need to be modified to obtain the initial stiffness of each structural component. Each grid represents different materials, such as the grid element representing concrete, whose elastic modulus and shear modulus adopt the value of concrete material. The axial stiffness and shear stiffness of the concrete grid element are considered, and the steel element only considers the axial stiffness, which are superimposed to form a sub-pole element. The area of each concrete element is divided according to the cross-section division described above, and the required degree of accuracy is determined, and the areas are equal. The steel simulation element is divided according to the wall reinforcement, and each element is located at the center of the grid it simulates.

[0053] Through the operation of the matrix in step two, the stiffness and cross-section mechanical characteristics of the grid unit can be obtained in sequence, the stiffness matrix of the integrated component is further condensed and integrated, the dynamic characteristics and structural response of the system are solved, and the structural dynamic analysis is realized.

[0054] For example, the parameters of the material (steel, concrete or steel) are defined first (such as elastic modulus, strength, etc.). Then, according to the cross-section of the grid division, the cross-sectional area, moment of inertia, centroid position, and related cross-sectional characteristics and mass characteristics are calculated. Among them, k um , k vm , k wm are the axial stiffness and shear stiffness along the y and z directions of the mth grid unit, respectively:

[0055] where A m , n are the equivalent area of the mth grid unit and the total number of grid units, respectively; the element stiffness matrix, mass matrix, damping matrix and node force matrix are established, and the stiffness matrix and mass matrix of the entire structure system are formed, and then the motion equation of the entire system is established. Finally, the boundary conditions are introduced into the integrated stiffness matrix, and appropriate modifications are made to eliminate the singularity of the structural stiffness matrix. When the node displacement x j =a is given, the jth equation is modified as follows: the diagonal element K jj is multiplied by a large number μ (μ can be of the order of 1010), and P j is replaced by μK jj a. After this treatment, x j =a always exists in the equation solving process. This method is suitable for any given displacement (zero or non-zero value) and does not change the order of the equation and the displacement of the node.

[0056] The grid matrix cross-section method is used to simulate the structural member and perform the related structural analysis. The obtained data are all numerical multidimensional matrices. The matrix slicing, pseudo-color map and contour map are used to fill the color of the matrix numerical value display. The information of each cross-section and the analysis response value of each grid element can be directly understood. The matrix numerical visualization of the structural member and the stress analysis is realized (Fig. 7, Fig. 8). For example, in the post-processing of structural calculation, the stress-strain values of the cross-section of the member are stored in the multidimensional matrix. The matrix numerical pseudo-color map is used for display. The cross-section stress or strain nephogram can be directly formed by matrix slicing (Fig. 9, Fig. 10). In this way, the data results can be simply and directly displayed. The stress condition of each cross-section simulation can be understood. For example, the strain analysis of each element of the cross-section of the structural member under the action of bidirectional earthquake can be performed. The displacement response real value of each node at each time step can be stored. The displacement of the two end nodes of each member element is obtained through the degree of freedom conversion. The stress-strain values of each section of each cross-section of the member can be calculated by using the network matrix of the combination of numbers and shapes.

[0057] By using the space grid simulation member cross-section, the discrete grid elements are established, the combination of numbers and shapes is used, the matrix positioning method of grid coordinates is used, the grid data are recorded by using the multidimensional digital matrix, the unified structural member input and analysis module can be established. The structural system can be simulated in the most intuitive and simplest way. The effective analysis result display can be provided. The material hysteresis curve, the performance and the stress-strain value are given a proper assignment range. The material failure condition and the degradation performance of each cross-section element in the structural analysis are determined. The structural nonlinear analysis can be simulated. For example, when the stress / strain of the matrix numerical element of the simulated steel bar in the matrix is greater than the set limit stress / strain value, the matrix array element of the element is degraded to zero element or maximum value when the new stiffness matrix is re-condensed. The element participates in the solution of the structural equation again.

[0058] Because the finite element calculation is essentially matrix calculation, all the structures are stored and represented by multidimensional matrix arrays. The material member itself is also represented by a numerical matrix by using the grid matrix cross-section method. The numerical value of the obtained matrix is directly related to the cross-section. The stress-strain value of the cross-section becomes the element value of the matrix representing the cross-section. The matrix data visualization can be directly realized by using matplotlib, seaborn and other libraries in Python. MATLAB also has rich plotting functions and tools. The matrix visualization is very convenient.

[0059] The application can be applied to the following fields:

[0060] Entity structure data: the shape and properties of various things are abstracted into numerical matrices, and organized according to the rows and columns of the matrix, each row and column representing a specific attribute or characteristic of an entity unit. Virtual reality is simulated.

[0061] Information multi-dimensional storage and display: the multi-dimensional characteristics of the matrix are used to analyze entities and systems, each dimension representing different levels or different state attributes, and the internal action state of each aspect of the data structure and object can be understood through spatial matrix slicing.

[0062] Analysis result image processing: all the calculation information of the entity component can be converted into a numerical matrix and flexibly converted into a pixel matrix, and the analysis result can be enhanced, recognized and analyzed through matrix operation.

[0063] It is obvious to those skilled in the art that the present application is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be regarded as exemplary and non-limiting, the scope of the present application is defined by the appended claims rather than the above description, and therefore all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present application. Any reference signs in the claims should not be regarded as limiting the claims involved.

Claims

1. A method for section analysis of a number-form combined grid matrix for structural simulation calculation, characterized in that, It comprises the following steps: Decompose and discretize the input member, determine the cross-sectional shape and the location of each unit according to the grid position of each unit after discretization; Use a mathematical tool capable of matrix operation to represent the cross-section with a grid, determine the coordinates of the cross-section grid, and represent the entire member cross-section with a matrix array; Realize matrix of member information through simulation of all cross-sections by combining assignment; Use the matrix member to participate in corresponding structural simulation analysis.

2. A numerical and geometrical combined grid matrix section analysis method for structural simulation calculation according to claim 1, characterized in that, For each unit grid after decomposition and discretization, each grid has a corresponding grid number position (x, y) in the local coordinates, and the unit coordinates of the grid are obtained according to the grid accuracy a*a, that is, a*(x-1)+a / 2, a*(y-1)+a / 2].

3. A numerical and geometrical combined grid matrix section analysis method for structural simulation calculation according to claim 1, characterized in that, The matrix array representing the entire member cross-section comprises the following steps: Define a two-dimensional matrix according to the size of the cross-section and the number of unit grids, and assign it to 0 to obtain a two-dimensional zero matrix; Input the grid number of the cross-section occupied by the matrix, and then define three-dimensional arrays YZ(:,:1) and XY(:,:2) to record the position of each grid in the local coordinate system; the input value of the concrete grid unit is 1, the input value of the steel grid and the concrete grid unit is 2, and the rest of the matrix elements are 0; the matrix records the information of each grid unit of the entire cross-section, and each element of the matrix is a numerical integral point; According to the type and size of the member, select the complete coverage grid size, represent it with a two-dimensional matrix, and then assign it one by one to represent the division of each unit of the cross-section.

4. The method of claim 1, wherein the method is characterized by: For columns, beams and wall structures of various cross-sectional forms and various materials, initialize the member by considering different shear deformations and stiffness values, obtain the stiffness of the grid unit and the mechanical characteristics of the cross-section by matrix operation and assignment operation in turn, further condense and integrate the stiffness matrix of the member, establish the element stiffness matrix, mass matrix, damping matrix and node force matrix, and then form the stiffness matrix and mass matrix of the entire structure system, and further establish the motion equation of the entire system. Finally, by processing the known boundary conditions and initial conditions, the dynamic characteristics and structural response of the system are solved to realize the solution of structural dynamic analysis.

5. A numerical and geometrical combined grid matrix section analysis method for structural simulation calculation according to claim 1, characterized in that, The matrix numerical pseudo-color display simulation of the structural member and the related structural analysis are realized by matrix slicing, pseudo-color map and contour map.

6. A numerical and geometrical combined grid matrix section analysis method for structural simulation calculation according to claim 5, characterized in that, In the post-processing of structural calculation, the stress-strain values of the member cross-section are stored by multi-dimensional matrix, and the matrix numerical pseudo-color map is used for display, and the cross-section stress or strain nephogram is directly formed by matrix slicing.

7. A numerical and geometrical combined grid matrix section analysis method for structural simulation calculation according to claim 5, characterized in that, For strain analysis of each unit of the cross-section of the structural member under bidirectional seismic action, the displacement response real value of each node is stored at each time step, the displacement of the two nodes of each member unit is obtained through degree of freedom conversion, the network matrix of the numerical shape combination is used, and the stress and strain values of each section of the member cross-section are calculated.

8. The method of claim 1, wherein the method is a method of analyzing a cross section of a mesh matrix for structural simulation, characterized by, For simulation of structural nonlinear analysis, the material hysteresis curve and performance and stress-strain values are assigned to determine the material failure condition and degradation performance of each cross-sectional unit in the structural analysis.

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