CN112883619B - Topological optimization method and system for mortise-tenon interlocking connection multi-component structure - Google Patents
Topological optimization method and system for mortise-tenon interlocking connection multi-component structure Download PDFInfo
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Abstract
The invention provides a topological optimization method and a topological optimization system for a mortise-tenon interlocking connection multi-component structure, wherein the method comprises the following steps: acquiring a three-dimensional solid model and material mechanics parameters of a first assembly structure and/or a second assembly structure under a preset working condition; carrying out disassembly and segmentation on the three-dimensional solid model by interlocking mortise and tenon structures at the interface to obtain a disassembly model; carrying out topology optimization on the disassembled model based on the solid isotropic material punishment model to obtain an optimized first assembly structure and/or second assembly structure; judging whether the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property test or not; carrying out actual processing inspection on the optimized first component structure and/or the optimized second component structure; and determining the optimized first component structure and/or the optimized second component structure as a target structure. The invention can convert an entity model into a hollow model through topology optimization and computational analysis, thereby realizing the engineering requirements of light weight, high efficiency and energy conservation.
Description
Technical Field
The invention relates to the field of structural topology optimization, in particular to a method and a system for topological optimization of a multi-component structure in mortise and tenon interlocking connection.
Background
In many practical engineering problems today, it is difficult to avoid some bearing members with large volume and containing many sub-members, and welding and riveting are the most widely used means for connecting the sub-members: welding, also known as fusion welding, is a manufacturing process and technique for joining metals or other thermoplastic materials, such as plastics, in a heated, high temperature or high pressure manner; riveting, that is, rivet connection, is a mechanical vocabulary, and is a method for connecting a plurality of parts by upsetting a rivet rod in a rivet hole of the part and forming a rivet head by using axial force. However, although the welding method is convenient and has good sealing performance, the welding method is easy to generate large stress concentration in some working conditions, has large welding residual prestress and deformation, also has the defects of generating welding defects, having uneven joint performance, being easy to break and the like, and can cause engineering accidents seriously; the application range of riveting is relatively small, large-section matched connection is difficult to complete, and the cost and the technical requirements are friendly. In addition, some large-scale engineering structures have the problem of being too heavy, so that energy waste and material redundancy during work are caused, and light-weight design considering connection of the engineering structures is urgently needed.
Disclosure of Invention
The embodiment of the invention provides a topological optimization method for a mortise-tenon interlocking connected multi-component structure, which can reduce the weight of a model according to a preset requirement based on the structural design of topological optimization after the model is designed through interfaces similar to mortise-tenon connection, and can maintain the strength requirement and the function requirement of a component under the original working condition without being influenced. An entity model can be converted into a hollow model through topological optimization and computational analysis, so that the engineering requirements of light weight, high efficiency and energy conservation are met.
In a first aspect, an embodiment of the present invention provides a topology optimization method for a mortise-tenon interlocking connected multi-component structure, where the mortise-tenon interlocking connected multi-component structure includes a first component structure and a second component structure, and the first component structure and the second component structure are connected by mortise-tenon interlocking, and the method includes the following steps:
acquiring a three-dimensional solid model and material mechanics parameters of the first assembly structure and/or the second assembly structure under a preset working condition;
performing disassembly and segmentation of all mortise and tenon structure interlocking at the interface of the three-dimensional solid model based on a computer graphics algorithm to obtain a disassembly model;
carrying out topology optimization on the disassembled model based on a solid isotropic material punishment model to obtain an optimized first assembly structure and/or second assembly structure;
performing working condition simulation on the optimized first assembly structure and/or the optimized second assembly structure according to the preset working condition to judge whether the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property test or not;
if the optimized mortise and tenon structure passes the preset mechanical property inspection, carrying out actual processing inspection on the optimized first component structure and/or the optimized second component structure;
and if the optimized first assembly structure and/or the optimized second assembly structure pass the actual processing inspection, determining the optimized first assembly structure and/or the optimized second assembly structure as a target structure.
Optionally, the computer graphics algorithm-based method for performing disassembly and segmentation of the three-dimensional solid model by interlocking all mortise and tenon structures at the interface to obtain a disassembled model includes:
selecting a cutting point of the three-dimensional solid model;
carrying out plane cutting at any angle on the three-dimensional solid model according to the cutting point to obtain a cutting block corresponding to the first component structure and/or the second component structure;
and carrying out mortise and tenon connection on the cutting block to obtain the disassembly model.
Optionally, the step of performing topology optimization on the disassembled model based on the solid isotropic material penalty model to obtain an optimized first component structure and/or a second component structure includes:
based on a solid isotropic material punishment model, establishing a discretization optimization model by taking a disassembled model part subjected to finite element force analysis as a design domain, wherein the discretization optimization model takes the minimum flexibility or the maximum rigidity as an optimization target and takes a volume factor as a constraint condition, and the disassembled model part is a model part for keeping mortise and tenon connection undamaged;
and carrying out iterative solution on the discretization optimization model to obtain an optimized first component structure and/or component second structure, wherein the optimized first component structure and/or component second structure comprises an optimized material distribution mode.
Optionally, the step of performing iterative solution on the discretized optimization model to obtain an optimized first component structure and/or an optimized second component structure includes:
carrying out iterative solution on the discretization optimization model to obtain an optimized material distribution mode;
and carrying out post-processing on the optimized material distribution mode through a sensitivity and density filter and a projection method to obtain an optimized mortise and tenon structure.
Optionally, the step of performing working condition simulation on the optimized first component structure and/or second component structure according to the preset working condition to determine whether the optimized first component structure and/or second component structure passes a preset mechanical property test includes:
establishing a computer simulation working condition according to the preset working condition;
and checking whether the optimized first component structure and/or the optimized second component structure meet the preset mechanical property check under the computer simulation working condition through finite element analysis.
Optionally, the step of establishing a discretization optimization model by using the disassembled model part subjected to finite element force analysis as a design domain based on the penalty model of the solid isotropic material and the initial values of the internal stress and the strain data of the disassembled model includes:
assigning a Boolean value ρ per voxel in the design domaineWhere ρ ise∈{0,1}；
From the set of surrounding voxels of the voxel e and the Boolean values ρ of the surrounding voxelsiObtaining a Boolean value of voxel e
And material distribution
And constructing a discretization optimization model by taking the static elasticity equation Ku-f under the action of the external force vector f as a constraint condition and taking the minimum flexibility or the maximum rigidity as an optimization target.
Optionally, the method further includes:
and determining a surrounding voxel set of the voxel e according to the center of mass of each voxel and a preset influence radius.
Optionally, the step of performing post-processing on the optimized material distribution mode through a sensitivity and density filter and a projection method to obtain an optimized first component structure and/or second component structure specifically includes:
constructing a sensitivity and density filter according to a preset constraint radius and a weighting factor;
filtering the optimized material distribution mode through the sensitivity and density filter to obtain a filtering result;
and carrying out binarization projection on the filtering result to obtain a projection model, and determining the optimized first component structure and/or second component structure according to the projection model.
Optionally, the step of performing actual processing inspection on the optimized first component structure and/or second component structure includes:
3D printing is carried out on the optimized first assembly structure and/or the optimized second assembly structure, and a 3D printing model is obtained;
and carrying out actual processing inspection on the 3D printing model to obtain a test result of the 3D printing model as a test result of the optimized first component structure and/or second component structure.
In a second aspect, an embodiment of the present invention further provides a system for optimizing a mortise and tenon structure, where the multi-component structure in mortise and tenon interlocking connection includes a first component structure and a second component structure, and the first component structure and the second component structure are in mortise and tenon interlocking connection, and the system includes:
the acquisition module is used for acquiring a three-dimensional solid model and material mechanics parameters of the first assembly structure and/or the second assembly structure under a preset working condition;
the segmentation module is used for carrying out disassembly and segmentation on the three-dimensional solid model by adopting mortise and tenon structure interlocking at the interface based on a computer graphics algorithm to obtain a disassembly model;
the optimization module is used for carrying out topology optimization on the disassembled model based on the solid isotropic material punishment model so as to obtain the optimized first assembly structure and/or second assembly structure;
the simulation test module is used for carrying out working condition simulation on the optimized first assembly structure and/or the optimized second assembly structure according to the preset working condition so as to judge whether the optimized first assembly structure and/or the optimized second assembly structure passes the preset mechanical property test or not;
the actual processing inspection module is used for performing actual processing inspection on the optimized first assembly structure and/or the optimized second assembly structure if the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property inspection;
a determining module, configured to determine that the optimized first component structure and/or the optimized second component structure is a target structure if the optimized first component structure and/or the optimized second component structure passes the actual machining inspection.
In the embodiment of the invention, a three-dimensional solid model and material mechanics parameters of the first assembly structure and/or the second assembly structure under a preset working condition are obtained; performing disassembly and segmentation of all mortise and tenon structure interlocking at the interface of the three-dimensional solid model based on a computer graphics algorithm to obtain a disassembly model; carrying out topology optimization on the disassembled model based on a solid isotropic material punishment model to obtain an optimized first assembly structure and/or second assembly structure; performing working condition simulation on the optimized first assembly structure and/or the optimized second assembly structure according to the preset working condition to judge whether the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property test or not; if the optimized mortise and tenon structure passes the preset mechanical property inspection, carrying out actual processing inspection on the optimized first component structure and/or the optimized second component structure; and if the optimized first assembly structure and/or the optimized second assembly structure pass the actual processing inspection, determining the optimized first assembly structure and/or the optimized second assembly structure as a target structure. After the interface design of the multi-component structure of the model through similar mortise and tenon interlocking connection is carried out, the model is lightened according to the preset requirement based on the structural design of topological optimization, and the strength requirement and the functional requirement of the component are not influenced under the original working condition. An entity model can be converted into a hollow model through topological optimization and computational analysis, so that the engineering requirements of light weight, high efficiency and energy conservation are met.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a topology optimization method for a mortise-tenon interlocking connection multi-component structure according to an embodiment of the present invention;
fig. 1a is a schematic view of a mortise and tenon interlocking connection multi-component structure provided in an embodiment of the present invention;
FIG. 1b is a schematic diagram of a cutting unit provided in an embodiment of the present invention;
FIG. 2 is a flowchart of a topology optimization method for a first component structure and/or a second component structure according to an embodiment of the present invention;
FIG. 2a is a schematic diagram of an elastic modulus and a penalty factor according to an embodiment of the present invention;
FIG. 2b is a schematic diagram of a checkerboard phenomenon provided by an embodiment of the present invention;
FIG. 2c is a comparison diagram illustrating a post-projection processing of a result of topology optimization according to an embodiment of the present invention;
FIG. 2d is a schematic diagram of a design domain of a mortise and tenon interlocking connection multi-component structure provided in an embodiment of the present invention;
fig. 2e is a schematic diagram of a multi-component structural design domain of another mortise and tenon interlocking connection provided by the embodiment of the invention;
FIG. 3a is a schematic diagram of a multi-component structure of mortise and tenon interlocking connection after topological optimization;
FIG. 3b is an assembly schematic diagram of a multi-component structure of square cross-section mortise and tenon interlocking connection after topological optimization;
FIG. 3c is a schematic diagram of another mortise and tenon interlocking connection multi-component structure after topological optimization;
FIG. 3d is an assembly schematic diagram of a multi-component structure of 7-shaped section mortise and tenon interlocking connection after topological optimization.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a topological optimization method of a multi-component structure in mortise-tenon interlocking connection, which can replace the traditional welding and riveting mode by mortise-tenon splicing of multiple components of a product, so that the interfaces are mutually embedded by materials same as the components. The model work piece is through the mortise and tenon structural design of interface, and each part can directly the concatenation shaping, at this point, compares in the comparatively loaded down with trivial details welding of processing and riveting, has reduced time and economic cost greatly. Adopt mortise and tenon complex mode at the kneck, compare in the riveting, the leakproofness is better, has solved the interface inefficiency moreover, connects the problem of heaviness. By topology optimization, the distribution of a given amount of material is optimized under a given external load (preset operating conditions), forming a porous structure. Compared with a solid model, the method has the advantages that the material consumption is reduced, the material resource is saved, the weight of the workpiece is greatly reduced, and the lightweight design is of great significance in the fields of transportation, aerospace and the like which need large engineering structures. The method has the advantages that the universality is high, entities with various shapes under different working conditions can be used as research objects, the optimization design can be carried out according to different weight reduction requirements, constraint conditions and the like, the results can be relatively accurately detected through finite element simulation, the effect experiment is carried out by applying the 3D printing technology, and the detection cost is greatly reduced.
It should be noted that the mortise and tenon structure is a structure form commonly used in the ancient wooden building in china, the structure is exquisite, the fastening effect is stable, the connection form allows deformation in a certain range, the protruding part in the component is called as a tenon, and the recessed part is called as a mortise.
In an embodiment of the present invention, the multi-component structure in mortise and tenon interlocking connection includes a first component structure and a second component structure, and the first component structure and the second component structure are in mortise and tenon interlocking connection. Of course, the first assembly structure may be a mortise, and the second assembly structure may be a tenon. The number of the first component structures may be one or more, and the number of the second component structures may be one or more.
Referring to fig. 1, fig. 1 is a flowchart of a topology optimization method for a mortise and tenon interlocking connection multi-component structure according to an embodiment of the present invention, as shown in fig. 1, including the following steps:
101. and acquiring a three-dimensional solid model and material mechanics parameters of the first assembly structure and/or the second assembly structure under a preset working condition.
In the embodiment of the present invention, the preset working condition may be understood as a given external load, and the engineering structures required to be used in different fields are different, and the corresponding working conditions are also different. The embodiment of the invention can preset corresponding working condition according to engineering structures in different fields.
The mortise and tenon interlocking connection multi-component structure can also be called a mortise and tenon structure, the mortise and tenon structure comprises a protruding part and a recessed part, and the mortise and tenon structure is specifically shown in figure 1 a.
The material mechanical parameters are generated by the material and the structure thereof, and further, the material mechanical parameters can include known or obtainable mechanical parameters such as young's modulus, poisson's ratio, density and the like. Further, the material mechanical parameters of the three-dimensional solid model are known or obtainable. The three-dimensional solid model may also be referred to as a three-dimensional solid member.
The three-dimensional solid model of the first component structure and/or the second component structure may be a single three-dimensional solid model of the first component structure, a single three-dimensional solid model of the second component structure, or a three-dimensional solid model of a combination of the first component structure and the second component structure. Therefore, the topology optimization in the embodiment of the invention can optimize only the first component structure in the multi-component structures in mortise and tenon interlocking connection, can optimize only the second component structure in the multi-component structures in mortise and tenon interlocking connection, and can optimize both the first component structure and the second component structure in the multi-component structures in mortise and tenon interlocking connection. The first assembly structure and the second assembly structure are connected in a mortise-tenon interlocking manner. The first assembly structure and the second assembly structure can also be called as a first mortise and tenon connecting structural member and a second mortise and tenon connecting structural member.
Optionally, the stress analysis of a three-dimensional solid model under corresponding working conditions can be performed; establishing an analyzable model as a three-dimensional solid model through computer aided design; obtaining an initial value of internal force data of the three-dimensional solid model under the condition through finite element analysis according to the material mechanics parameters of the three-dimensional solid model; the internal force data may be internal stress. The Finite Element Analysis (FEA) can be used to simulate real physical systems (structure geometry and load conditions) by using mathematical approximation. Simple and interactive elements, namely unit cells, can be used to approximate a real physical system of infinite unknowns with a finite number of unknowns. Finite element analysis is solved by replacing a complex problem with a simpler one. It considers the solution domain as consisting of many small interconnected subdomains called finite elements, assuming a suitable (simpler) approximate solution for each unit cell, and then deducing the overall satisfaction conditions (e.g., structural equilibrium conditions) for solving this domain to arrive at a solution to the problem.
Specifically, a multi-physical-field simulation software can be utilized to input material mechanical property parameters and external force parameters, finite element analysis simulation calculation is carried out on the three-dimensional solid model, and initial data values such as internal stress and strain of the three-dimensional solid model are obtained before mortise and tenon structure interlocking and topology optimization technology is not adopted; the initial values of the internal stress, strain energy and other data of the three-dimensional solid model before the mortise and tenon structure interlocking and topological optimization technology can be used for comparing with the internal stress, strain and other data of the three-dimensional solid model after the mortise and tenon structure interlocking and topological optimization technology. The mortise and tenon interlocking means that the first assembly structure and the second assembly structure are connected in a mortise and tenon interlocking manner.
102. And (3) carrying out disassembly and segmentation of the three-dimensional solid model by interlocking all mortise and tenon structures at the interface based on a computer graphics algorithm to obtain a disassembly model.
In an embodiment of the present invention, the three-dimensional solid model is obtained by performing a structural design according to interface features of the first component structure and/or the second component structure. The computer graphics algorithm means that the three-dimensional entity model is imaged through the algorithm, so that the computer can perform related calculation on the three-dimensional entity model.
In the embodiment of the present invention, the three-dimensional solid model may be divided, the three-dimensional solid model is subdivided into smaller unit bodies, for example, the three-dimensional solid model is equivalent to a plurality of unit bodies of squares with the same size, and each unit body is cut. The segmented three-dimensional solid model can be disassembled into a plurality of unit bodies. The cut structure is equivalent to a puzzle block in an abstract linkage puzzle, the puzzle blocks are mutually linked to form an entity model, and the combination breakdown is prevented through a mortise and tenon connecting structure. Through a specific assembling or disassembling sequence, any three-dimensional solid model can be segmented, disassembled and assembled.
Further, a cutting point of the three-dimensional solid model can be selected; carrying out plane cutting of any angle on the three-dimensional entity model according to the cutting point to obtain a cutting block corresponding to mortise and tenon structure interlocking; and carrying out mortise and tenon connection on the cutting block to obtain a disassembled model.
Specifically, referring to fig. 1b, the algorithm for cutting the three-dimensional solid model based on the computer graphics algorithm may be implemented by configuring a visualization tool function library (VTK)17-91 on a Windows-based platform, and the three-dimensional solid model used for cutting at any angle may also be reconstructed by using two methods, namely volume rendering and surface rendering, in the VTK function library. The cutting at any angle is to find a point in the three-dimensional solid model, the normal vector of the cutting surface is given, the cutting surface can be correspondingly obtained, and the work is finished by two functions of SetOrigin (x, y, z) and SetNormal (i, j, k) in a program. SetOrigin (x, y, z) defines (x, y, z) as a point in three-dimensional space and also a point on the cutting plane, and then the normal vector (i, j, h) of the cutting plane is given by SetNormal (i, j, h) to obtain the corresponding cutting plane.
After the three-dimensional solid model is cut, the cut plane can be added to the reconstructed model map by using a function AddClippingPlane (), and the code is as follows: volumeMapper- > adddlipingplane (plane); the plane is the corresponding cut surface. This allows the information in the plane to be seen and a cut to be made.
103. And carrying out topology optimization on the disassembled model based on the solid isotropic material punishment model to obtain the optimized first component structure and/or the optimized second component structure.
In the embodiment of the invention, the Solid isotropic material punishment model (SIMP: Solid isotropic material with Penalification) is a density-stiffness interpolation model, the Solid isotropic material punishment model assumes that the material density is constant in a unit and takes the constant as a design variable, the material characteristics are simulated by an exponential function of the unit body density, the calculation can be simple and convenient, and the calculation efficiency is improved.
In the optimization process, the distribution of a given amount of material can be optimized at a given external load, such that the first component structure and/or the component second structure form a porous structure. I.e., a portion of the unit cell is considered redundant, and this portion of the unit cell is removed to form a porous structure, thereby reducing the use of material and the weight of the first assembly structure and/or the second assembly structure.
Optionally, the topological optimization of the multi-component structure in mortise and tenon interlocking connection may be understood as topological optimization of the first component structure and/or the second component structure, that is, the first component structure may be subjected to topological optimization alone, the second component structure may be subjected to topological optimization alone, or a combination of the first component structure and the second component structure may be subjected to topological optimization, specifically referring to fig. 2, where fig. 2 is a flowchart of a topological optimization method for the first component structure and/or the second component structure provided in an embodiment of the present invention, and as shown in fig. 2, the method includes the following steps:
201. based on a solid isotropic material penalty model, a discretization optimization model is established by taking a disassembled model part which is subjected to finite element force analysis as a design domain.
In the embodiment of the invention, the discretized optimization model takes the minimum flexibility or the maximum rigidity as an optimization target and the volume factor as a constraint condition, and the disassembled model part is a model part which keeps mortise and tenon connection from being damaged.
Optionally, the disassembled model may be placed in a steady-state static physical field for finite element analysis, and initial values of data such as internal stress, strain energy, and the like of the disassembled model after segmentation are obtained.
Further, the minimum compliance corresponds to the maximum stiffness, and therefore, only one of the minimum compliance or the maximum stiffness is required as an optimization target.
Optionally, in the embodiment of the present invention, a design domain of the disassembly model may be optimized by using a variable density topology optimization, where the design domain may be a cross-sectional area of mortise and tenon interlocking, as shown in fig. 2d and fig. 2 e. Specifically, topology optimization essentially represents design variables as numerical values between 0 and 1, and solves the optimal distribution of materials under the constraints of objective functions, volumes and the like. Topology optimization is typically performed by solving for the volume constraint G0A and a material distribution x for minimizing the objective function c under other constraintsi(i ═ 1.. m). The variable (x) of the distribution density ρ is 0 or 1, and since many design variables exist during topology analysis, if planning is performed according to discrete design variables, combinatorial explosion occurs, and thus optimization calculation cannot be performed. To address this problem, embodiments of the present invention change discrete {0,1} variables to continuous (0,1) variables by relaxation.
Further, in the embodiment of the present invention, from the discrete optimization model to the continuum optimization model, the value of the design variable (x) representing the relative density variable may be changed from {0,1} to [0,1], so that an intermediate density unit is introduced and converted into a continuous optimization problem. However, since the intermediate density unit is difficult to realize and manufacture in reality, it is necessary to limit the intermediate density unit to avoid the excessive generation amount of the intermediate density unit and reduce the generation amount of the intermediate density unit as much as possible.
Further, a Boolean value ρ may be assigned to each voxel in the design domaineWhere ρ iseE {0,1 }; from the set of surrounding voxels of voxel e and the boolean value ρ of the surrounding voxelsiObtaining a Boolean value of voxel e
And material distribution
And constructing a discretization optimization model by taking the static elasticity equation Ku-f under the action of the external force vector f as a constraint condition and taking the minimum flexibility or the maximum rigidity as an optimization target. And, a set of surrounding voxels of the voxel e may be determined according to the respective voxel centroid and a preset influence radius.
Specifically, in the embodiment of the present invention, the penalty model for the solid isotropic material may be represented by the following formula:
Ei＝f(xi)E0
f(xi)＝xi p
wherein E isiDenotes the modulus of elasticity, E, of the unit i0Modulus of elasticity, x, representing a unit material density of 1iFor the cell relative density, P is a penalty function. The variation of the elastic modulus with the penalty factor p is shown in FIG. 2 a.
In embodiments of the present invention, for a discretized design domain Ω of a given design shape, each unit cell, also referred to as a volume element (i.e., voxel) e, has a Boolean value ρeE {0,1} is assigned to represent a solid voxel (ρ)e1), or one empty voxel (p)e0). Thus, a binary system can be usedThe field p represents the distribution of material in the design domain omega.
In the embodiment of the present invention, the definition of
To quantify the distribution of (local) material in the neighboring voxels e. In particular, the percentage of solid voxels in all voxels Ne within a defined area is measured, namely:
ne is the set of all surrounding voxels whose centroid is closer than the given radius of influence Re to the centroid of voxel e, i.e.:
Ne＝{i||xi-xe||≤Re}
wherein xiAnd xeIs the voxel's centroid. In the embodiment of the present invention, the position and the length are measured in units of voxels. Local volume fraction ρe＝0.0(ρe1.0) means that all defined voxels are empty (solid), values between 0.0 and 1.0 indicating the presence of both empty and real voxels.
Thus, the discretized optimization model can establish:
s.t.Ku＝f
in the above discretized optimization model, the objective is to minimize compliance, as measured by strain energy c, u is the displacement vector, and K is the stiffness matrix. And obtaining a displacement vector u by solving a static elastic equation under the action of the external force vector f. While limiting the design variables to take discrete values of 0 (empty) or 1 (real).
202. And carrying out iterative solution on the discretization optimization model to obtain the optimized first component structure and/or second component structure.
In an embodiment of the present invention, the optimized first module structure and/or the optimized second module structure include an optimized material distribution mode. Specifically, the material distribution mode of the optimized first assembly structure may be, the material distribution mode of the optimized second assembly structure may be, or the material distribution mode of the combination of the optimized first assembly structure and the optimized second assembly structure may be.
Furthermore, iterative solution can be carried out on the discretization optimization model to obtain an optimized material distribution mode; the optimized material distribution is post-processed by a sensitivity and density filter and a projection method to obtain an optimized first component structure and/or second component structure.
Further, the established discretization optimization model can be subjected to iterative solution through an MMA numerical solution algorithm so as to solve and design an optimal material distribution mode; MMA is a continuous convex approximation inner point method constructed based on target and constraint gradient information, and an optimal material distribution mode can be calculated more accurately and conveniently.
Further, a sensitivity and density filter can be constructed according to a preset constraint radius and a weighting factor; filtering the optimized material distribution mode through the sensitivity and density filter to obtain a filtering result; and performing binarization projection on the filtering result to obtain a projection model, and determining the optimized first component structure and/or second component structure according to the projection model.
In the embodiment of the present invention, the first component structure and/or the second component structure after topology optimization may have unstable values, which include gray level cells, checkerboards, local extrema and grid dependencies, and the occurrence of these conditions may affect the optimality and manufacturability of the structure, where the checkerboards are shown in fig. 2b, the gray level cells are excessive cells, as shown in fig. 2c, and in fig. 2c, the results of the filtered projection are sequentially the results of the unfiltered projection from left to right, and the results of the filtered projection are performed. As can be seen from fig. 2c, the result of the filtered projection is clearer, and therefore, the optimized first component structure and/or second component structure needs to be post-processed.
Optionally, the sensitivity and density filter may also be referred to as a filter, and the sensitivity and density filter calculates a weighted average of neighboring voxels, and the expression is as follows:
in the formula, MeA set of voxels, which are neighboring voxels e, defined as:
Me＝{i|||xi-xe||≤re}
rethe filter radius, which is different from the constraint radius in the local material, is weighted by a factor omegai,eDepending on the distance between the pixels, the following equation is used:
after filtering through the sensitivity and density filter, a filtering result is obtained, gray transition materials (i.e. gray scale units) may be formed between solid and pore areas in the filtering result, and in order to obtain an optimized structure with clear boundary definition, the embodiment of the invention projects the filtered density to 0 or 1 (empty or real) space through a relaxed Heaviside function. In particular, the projection phi～The purpose of p is to ensure a 0 or 1 solution (i.e. no gray value, a binary scheme with only 0 or 1). The intermediate value between 0.0 and 1.0 is set 1/2 to divide into a discrete 0 or 1 value. Again, this equation is not trivial and for numerical optimization, ρ is determinedeIs a scalar threshold function and approximates the invariability byThe micro equation:
through the processing of the logarithm solution, an optimization result with good manufacturability is obtained and is shown in the right graph of fig. 2c, and a model file of a mortise and tenon structure can be derived.
104. And performing working condition simulation on the optimized first assembly structure and/or the optimized second assembly structure according to preset working condition conditions to judge whether the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property test.
In the embodiment of the present invention, while performing topology optimization calculation in step 103, calculation data of the optimized first assembly structure and/or second assembly structure under a preset working condition is obtained, where the calculation data includes data of internal stress, strain energy, displacement, and the like, so as to check whether the optimized first assembly structure and/or second assembly structure meets the strength requirement, that is, detect whether the optimized first assembly structure and/or second assembly structure passes a preset mechanical property test.
The indexes to be tested can be indexes including maximum stress and total strain energy or other indexes capable of representing structural strength, and the maximum stress sigma is adopted in the embodiment of the inventionmaxAnd total strain energy Ws, which can be specifically represented by the following formula:
σmax≤[σ]
Ws≤[Ws]
wherein [ σ ] and [ Ws ] are respectively a preset maximum stress index and a preset total strain energy index.
In a possible embodiment, the calculated data of the first component structure and/or the second component structure obtained and optimized under the preset working condition may be compared with the initial values of the internal stress, the strain and the like of the three-dimensional solid model before the mortise and tenon structure interlocking and topology optimization technology is not adopted, or the calculated data of the first component structure and/or the second component structure obtained and optimized under the preset working condition may be compared with the initial values of the internal stress, the strain energy and the like of the disassembled model after the separation. In this way, the variation of the data of internal stress, strain energy and the like of the first component structure and/or the second component structure at each stage can be obtained.
105. And if the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property test, carrying out actual processing test on the optimized first assembly structure and/or the optimized second assembly structure.
In the embodiment of the invention, the optimized first component structure and/or second component structure can be subjected to 3D printing to obtain a 3D printing model; and carrying out actual measurement inspection on the 3D printing model to obtain an actual measurement result of the 3D printing model as a test result of the optimized first component structure and/or second component structure.
Furthermore, the three-dimensional entity model of the optimized first assembly structure and/or the optimized second assembly structure can be exported to be a printable file, and the size of the three-dimensional entity model and external force parameters under the preset working condition are scaled in a certain proportion, so that entity test and inspection are performed. In this way, the reliability of the optimized first and/or second component structure can be detected to the greatest extent.
Specifically, a refined grid can be used to ensure model accuracy, and model reconstruction is performed on each block of the first component structure and/or the second component structure obtained through calculation optimization to form a printable file; the sizes of the first assembly structure and/or the second assembly structure are properly scaled according to a proportion, and certain interference is set so as to ensure the splicing stability of printed finished products and print and form the printed finished products; and connecting the interfaces of each printed model, splicing and molding, and applying the scaled actual load corresponding to the working condition to perform an experiment after self-locking is stable.
106. And if the optimized first assembly structure and/or the optimized second assembly structure pass the actual processing inspection, determining the optimized first assembly structure and/or the optimized second assembly structure as the target structure.
In the embodiment of the invention, a three-dimensional solid model and material mechanics parameters of the first assembly structure and/or the second assembly structure under a preset working condition are obtained; performing disassembly and segmentation of all mortise and tenon structure interlocking at the interface of the three-dimensional solid model based on a computer graphics algorithm to obtain a disassembly model; carrying out topology optimization on the disassembled model based on a solid isotropic material punishment model to obtain an optimized first assembly structure and/or second assembly structure; performing working condition simulation on the optimized first assembly structure and/or the optimized second assembly structure according to the preset working condition to judge whether the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property test or not; if the optimized mortise and tenon structure passes the preset mechanical property inspection, carrying out actual processing inspection on the optimized first component structure and/or the optimized second component structure; and if the optimized first assembly structure and/or the optimized second assembly structure pass the actual processing inspection, determining the optimized first assembly structure and/or the optimized second assembly structure as a target structure. After the interface design of the multi-component structure of the model through similar mortise and tenon interlocking connection is carried out, the model is lightened according to the preset requirement based on the structural design of topological optimization, and the strength requirement and the functional requirement of the component are not influenced under the original working condition. An entity model can be converted into a hollow model through topological optimization and computational analysis, so that the engineering requirements of light weight, high efficiency and energy conservation are met.
In the embodiment of the present invention, the mortise and tenon interlocking connection may have two types of multi-component structural forms, one of the two types of multi-component structural forms is a first component structure and a second component structure, a mortise and tenon interlocking connection surface of the first component structure and the second component structure is an upper plane and a lower plane, the first component structure and the second component structure are connected in a mortise and tenon interlocking manner and then combined into a square cross section, and a specific working condition is P ═ 200KPa, as shown in fig. 3a, fig. 3a is a schematic diagram of a multi-component structure in a mortise and tenon interlocking connection after topology optimization. As shown in fig. 3b, fig. 3b is an assembly schematic diagram of a multi-component structure after topological optimization of a square-section mortise-tenon interlocking connection, in fig. 3b, a first component structure after topological optimization can be connected with a second component structure without topological optimization in a mortise-tenon interlocking manner to form a multi-component structure of a first mortise-tenon interlocking connection, a second component structure after topological optimization can be connected with the first component structure without topological optimization in a mortise-tenon interlocking manner to form a multi-component structure of a first mortise-tenon interlocking connection, and a first component structure after topological optimization can be connected with the second component structure without topological optimization in a mortise-tenon interlocking manner to form a multi-component structure of a third mortise-tenon interlocking connection.
The other type is that the mortise and tenon interlocking connection surface of the first assembly structure and the second assembly structure is an upper inclined surface and a lower inclined surface, the first assembly structure and the second assembly structure are combined into a 7-shaped section after mortise and tenon interlocking connection, the specific working condition is P (100 KPa), and as shown in fig. 3c, fig. 3c is a multi-assembly structure of the mortise and tenon interlocking connection and a schematic diagram of the multi-assembly structure after topology optimization. As shown in fig. 3d, fig. 3d is an assembly schematic diagram of a multi-component structure after topological optimization of a mortise and tenon interlocking connection with a 7-shaped cross section, in fig. 3d, a first component structure after topological optimization can be in mortise and tenon interlocking connection with a second component structure without topological optimization to form a multi-component structure of a first mortise and tenon interlocking connection, a second component structure after topological optimization can be in mortise and tenon interlocking connection with a first component structure without topological optimization to form a multi-component structure of a first mortise and tenon interlocking connection, and a first component structure after topological optimization can be in mortise and tenon interlocking connection with a second component structure after topological optimization to form a multi-component structure of a third mortise and tenon interlocking connection.
As can be seen from fig. 3a to 3d, after the topology optimization, a porous mortise and tenon connection structural member can be obtained, and the strength is less affected while the weight of the first assembly structure and/or the second assembly structure is reduced.
It should be noted that the topology optimization method for a multi-component structure by mortise and tenon interlocking connection provided in the embodiment of the present invention may be applied to a system, a computer, a server, and other devices that can optimize a first component structure and/or a second component structure.
Optionally, in the system for optimizing a multi-component structure in mortise and tenon interlocking connection provided in an embodiment of the present invention, the multi-component structure in mortise and tenon interlocking connection includes a first component structure and a second component structure, and the first component structure and the second component structure are connected by mortise and tenon interlocking, and the system includes:
the acquisition module is used for acquiring a three-dimensional solid model and material mechanics parameters of the first assembly structure and/or the second assembly structure under a preset working condition;
the segmentation module is used for carrying out disassembly and segmentation on the three-dimensional solid model by adopting mortise and tenon structure interlocking at the interface based on a computer graphics algorithm to obtain a disassembly model;
the optimization module is used for carrying out topology optimization on the disassembly model based on the solid isotropic material punishment model so as to obtain an optimized first assembly structure and/or second assembly structure;
the simulation test module is used for carrying out working condition simulation on the optimized first assembly structure and/or the optimized second assembly structure according to the preset working condition so as to judge whether the optimized first assembly structure and/or the optimized second assembly structure passes the preset mechanical property test or not;
the machining test inspection module is used for carrying out actual machining inspection on the optimized first assembly structure and/or the optimized second assembly structure if the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property inspection;
and the determining module is used for determining the optimized first assembly structure and/or second assembly structure as a target structure if the optimized first assembly structure and/or second assembly structure passes the actual processing inspection.
Optionally, the segmentation module is further configured to perform the following steps:
selecting a cutting point of the three-dimensional solid model;
carrying out plane cutting of any angle on the three-dimensional entity model according to the cutting point to obtain a cutting block corresponding to the mortise and tenon structure in an interlocking manner;
and carrying out mortise and tenon connection on the cutting block to obtain the disassembly model.
Optionally, the optimization module is further configured to perform the following steps:
based on a solid isotropic material punishment model, establishing a discretization optimization model by taking a disassembled model part subjected to finite element force analysis as a design domain, wherein the discretization optimization model takes the minimum flexibility or the maximum rigidity as an optimization target and takes a volume factor as a constraint condition, and the disassembled model part is a model part for keeping mortise and tenon connection undamaged;
and carrying out iterative solution on the discretization optimization model to obtain an optimized first assembly structure and/or a second assembly structure, wherein the optimized first assembly structure and/or the optimized second assembly structure comprise an optimized material distribution mode.
Optionally, the optimization module is further configured to perform the following steps:
carrying out iterative solution on the discretization optimization model to obtain an optimized material distribution mode;
post-processing the optimized material distribution pattern by a sensitivity and density filter and a projection method to obtain an optimized first component structure and/or second component structure.
Optionally, the simulation test module is further configured to perform the following steps:
establishing a computer simulation working condition according to the preset working condition;
and checking whether the optimized first component structure and/or the optimized second component structure meet the preset mechanical property check under the computer simulation working condition through finite element analysis.
Optionally, the optimization module is further configured to perform the following steps:
assigning a Boolean value ρ per voxel in the design domaineWhere ρ ise∈{0,1}；
From the set of surrounding voxels of the voxel e and the Boolean values ρ of the surrounding voxelsiObtaining a Boolean value of voxel e
And material distribution
And constructing a static elastic equation Ku-f under the action of the external force vector f as a constraint condition by taking the minimum flexibility or the maximum rigidity as an optimization targetAnd building a discretization optimization model.
Optionally, the optimization module is further configured to perform the following steps:
and determining a surrounding voxel set of the voxel e according to the center of mass of each voxel and a preset influence radius.
Optionally, the optimization module is further configured to perform the following steps:
constructing a sensitivity and density filter according to a preset constraint radius and a weighting factor;
filtering the optimized material distribution mode through the sensitivity and density filter to obtain a filtering result;
and carrying out binarization projection on the filtering result to obtain a projection model, and determining the optimized first component structure and/or second component structure according to the projection model.
Optionally, the actual processing inspection module is further configured to perform the following steps:
3D printing is carried out on the optimized first assembly structure and/or the optimized second assembly structure, and a 3D printing model is obtained;
and carrying out actual measurement inspection on the 3D printing model to obtain a test result of the 3D printing model as an experimental result of the optimized first component structure and/or second component structure.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
The above disclosure is only for the purpose of illustrating the preferred embodiments of the present invention, and it is therefore to be understood that the invention is not limited by the scope of the appended claims.
Claims (10)
1. A topological optimization method for a multi-component structure in mortise and tenon interlocking connection is characterized in that the multi-component structure in mortise and tenon interlocking connection comprises a first component structure and a second component structure, and the first component structure and the second component structure are connected in mortise and tenon interlocking manner, and the method comprises the following steps:
acquiring a three-dimensional solid model and material mechanics parameters of the first assembly structure and/or the second assembly structure under a preset working condition;
performing disassembly and segmentation of all mortise and tenon structure interlocking at the interface of the three-dimensional solid model based on a computer graphics algorithm to obtain a disassembly model;
carrying out topology optimization on the disassembled model based on a solid isotropic material punishment model to obtain an optimized first assembly structure and/or second assembly structure;
performing working condition simulation on the optimized first assembly structure and/or the optimized second assembly structure according to the preset working condition to judge whether the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property test or not;
if the optimized mortise and tenon structure passes the preset mechanical property inspection, carrying out actual processing inspection on the optimized first component structure and/or the optimized second component structure;
and if the optimized first assembly structure and/or the optimized second assembly structure pass the actual processing inspection, determining the optimized first assembly structure and/or the optimized second assembly structure as a target structure.
2. The topological optimization method for a mortise and tenon interlocking connected multi-component structure according to claim 1, wherein the step of performing disassembly and segmentation on the three-dimensional entity model by mortise and tenon structure interlocking at the interface based on a computer graphics algorithm to obtain a disassembly model comprises the following steps:
selecting a cutting point of the three-dimensional solid model;
carrying out plane cutting at any angle on the three-dimensional solid model according to the cutting point to obtain a cutting block corresponding to the first component structure and/or the second component structure;
and carrying out mortise and tenon connection on the cutting block to obtain the disassembly model.
3. The method for topologically optimizing a mortise and tenon interlocking connected multi-component structure according to claim 2, wherein the step of topologically optimizing the disassembled model based on a solid isotropic material penalty model to obtain an optimized first component structure and/or second component structure comprises:
based on a solid isotropic material punishment model, establishing a discretization optimization model by taking a disassembled model part subjected to finite element force analysis as a design domain, wherein the discretization optimization model takes the minimum flexibility or the maximum rigidity as an optimization target and takes a volume factor as a constraint condition, and the disassembled model part is a model part for keeping mortise and tenon connection undamaged;
and carrying out iterative solution on the discretization optimization model to obtain an optimized first assembly structure and/or a second assembly structure, wherein the optimized first assembly structure and/or the optimized second assembly structure comprise an optimized material distribution mode.
4. The topological optimization method for the mortise and tenon interlocking connected multi-component structure according to claim 3, wherein the step of performing iterative solution on the discretized optimization model to obtain the optimized first component structure and/or the optimized second component structure comprises the following steps:
carrying out iterative solution on the discretization optimization model to obtain an optimized material distribution mode;
post-processing the optimized material distribution pattern by a sensitivity and density filter and a projection method to obtain an optimized first component structure and/or second component structure.
5. The topological optimization method for a mortise and tenon interlocking connected multi-component structure according to claim 4, wherein the step of performing working condition simulation on the optimized first component structure and/or the optimized second component structure according to the preset working condition to judge whether the optimized first component structure and/or the optimized second component structure passes a preset mechanical property test comprises the following steps:
establishing a computer simulation working condition according to the preset working condition;
and checking whether the optimized first component structure and/or the optimized second component structure meet the preset mechanical property check under the computer simulation working condition through finite element analysis.
6. The method for topological optimization of a mortise and tenon interlocking connected multi-component structure according to claim 5, wherein the step of establishing a discretized optimization model for a design domain based on a penalty model of solid isotropic material and initial values of internal stress and strain data of the disassembled model by using the disassembled model part subjected to finite element force analysis comprises:
assigning a Boolean value to each voxel e in the design domain
Wherein, in the step (A),
represents the Boolean value
Taking 0 or 1;
with the Boolean value of any one of said voxels e
And material distribution
And external force vector
Static elastomechanics equation under action
Taking the minimum flexibility or the maximum rigidity as an optimization target as a constraint condition, and constructing and obtaining a discretization optimization model, wherein,
a Boolean value representing any one of said voxels e
Taking the number of 0 or 1 out of the total number,
a Boolean value representing a set of surrounding voxels of any one of the voxels e
Is less than or equal to
K is the stiffness matrix and u is the displacement vector.
7. The method of topological optimization of a multi-component structure of mortise and tenon interlocking connections according to claim 6, further comprising:
and determining a surrounding voxel set of the voxel e according to the center of mass of each voxel and a preset influence radius.
8. The method for topologically optimizing a mortise and tenon interlocking connected multi-component structure according to claim 7, wherein the step of post-processing the optimized material distribution pattern by a sensitivity and density filter and a projection method to obtain an optimized first component structure and/or second component structure specifically comprises:
constructing a sensitivity and density filter according to a preset constraint radius and a weighting factor;
filtering the optimized material distribution mode through the sensitivity and density filter to obtain a filtering result;
and carrying out binarization projection on the filtering result to obtain a projection model, and determining the optimized first component structure and/or second component structure according to the projection model.
9. The method of topological optimization of a mortise and tenon interlocking connected multi-component structure according to claim 8, wherein the step of performing actual machining inspection on the optimized first component structure and/or second component structure comprises:
3D printing is carried out on the optimized first assembly structure and/or the optimized second assembly structure, and a 3D printing model is obtained;
and carrying out actual processing inspection on the 3D printing model to obtain a test result of the 3D printing model as a test result of the optimized first component structure and/or second component structure.
10. The utility model provides a mortise and tenon interlocking connection's multicomponent structure topological optimization system, a serial communication port, mortise and tenon interlocking connection's multicomponent structure includes first component structure and second component structure, first component structure with second component structure passes through mortise and tenon interlocking connection, the system includes:
the acquisition module is used for acquiring a three-dimensional solid model and material mechanics parameters of the first assembly structure and/or the second assembly structure under a preset working condition;
the segmentation module is used for carrying out disassembly and segmentation on the three-dimensional solid model by adopting mortise and tenon structure interlocking at the interface based on a computer graphics algorithm to obtain a disassembly model;
the optimization module is used for carrying out topology optimization on the disassembly model based on the solid isotropic material punishment model so as to obtain an optimized first assembly structure and/or second assembly structure;
the simulation test module is used for carrying out working condition simulation on the optimized first assembly structure and/or the optimized second assembly structure according to the preset working condition so as to judge whether the optimized first assembly structure and/or the optimized second assembly structure passes the preset mechanical property test or not;
the actual processing inspection module is used for performing actual processing inspection on the optimized first assembly structure and/or the optimized second assembly structure if the optimized first assembly structure and/or the optimized second assembly structure pass the preset mechanical property inspection;
a determining module, configured to determine that the optimized first component structure and/or the optimized second component structure is a target structure if the optimized first component structure and/or the optimized second component structure passes the actual machining inspection.
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