Topological optimization method based on meshfree RKPM (reproducing kernel particle method) for thermal structure of anisotropic material

Abstract

The invention discloses a topological optimization method based on a meshfree RKPM (reproducing kernel particle method) for a thermal structure of an anisotropic material. The method comprises a step of establishing a meshfree RKPM thermal stiffness matrix of the structure of the anisotropic material with a transformation matrix method, and the step comprises the following sub-steps: (1) solving dynamic influence domain radius of each calculation point according to coordinate information of input nodes and Gaussian points; (2) solving relative density of each RKPM node according to an RAMP (rational approximation of material properties) material interpolation model; (3) searching Gaussian points in a design domain, and establishing thermal conductivity tensor of each node according to the thermal conductivity of the anisotropic material, an orthotropic factor and a material direction angle; (4) taking a dot product of a thermal conductivity coefficient matrix and a geometric matrix of each node as an RKPM thermal stiffness matrix of the node; (5) forming the integral RKPM thermal stiffness matrix in the design domain. According to the method, topological optimization of the thermal structure of the anisotropic material is performed on the basis of the meshfree RKPM, the transformation matrix method and the RAMP material interpolation model, and the numerical stability is high.

Description

technical field [0001] The invention belongs to the field of optimization design in computer-aided engineering, and in particular relates to a topology optimization method for anisotropic material thermal structure based on a meshless reproducing kernel particle method (Reproducing Kernel Particle Method, RKPM). Background technique [0002] Composite materials are a kind of mixture, which can be mainly divided into two categories: structural composite materials and functional composite materials, such as fiber-reinforced composite materials and functionally graded materials. Compared with traditional materials, composite materials have many advantages such as good heat resistance, light weight, high specific strength, high specific modulus, good fatigue resistance and vibration isolation performance, and have advantages that traditional single materials cannot match. However, a remarkable feature of composite materials is anisotropy, which has different force and thermal pr...

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Problems solved by technology

In order to solve the problems such as the numerical instabilities generated when the thermal structure design of anisotropic materials is carried out only relying on thermal experience or using the finite element method, the present invention proposes a method based on the meshless reconstruction nuclear particle method (meshless RKPM) )’s anisotropic material thermal structure topology optimization design method, which introduces a hypothetical material with a variable relative density between 0 and 1 according to the Rational Approximation of Material Properties (RAMP) model and selects the design domain The relative density of the discrete nodes of the meshless RKPM is used as the design variable to construct the relative density field, and the minimum heat dissipation weakness is used as the objective function of the thermal topology optimization, and the total volume of the structure is used as the constraint condition to establish an anisotropic material thermal structure topology optimization The meshless RKPM mathematical model of the problem, and write the algorithm program to find the optimal thermal topology for different anisotropic materials

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