Study On Multi-scale Topology Optimization Of Composite Materials Considering Stress Constraints

Structural topology optimization technology has become increasingly important in the initial conceptual design phase of engineering applications.At present,the most mature application direction of topological optimization technology is to solve the problem of the softness minimization of volume constraints,although some scholars also study the design of lightweight topology optimization of stress constraints,but due to the complexity of the problem itself,there is still a lot of room for study on the related problems of stress constraints.Unlike the traditional design method with stiffness as the optimization target,the introduction of stress constraint makes it difficult for the model to have strange phenomena,local stress characteristics and highly nonlinearity.Based on the variable density method and the widening Lagrange equation,a topological optimization method of local stress constraints is proposed by polygon mesh modeling and multi-resolution matching techniques.The algorithm is extended to multi-scale optimization,and after combining flexible pretreatment methods such as polygon mesh generator,the stress constraint problem of multi-scale parallel topology optimization is compared and verified,and the applicability of multi-scale aspects is obtained.In this paper,both the traditional rod beam model and some complex configurations are used for study verification,so the stress constraint topology optimization of two-dimensional statics is analyzed in a comprehensive way.In order to solve the problem of global constraint limitation and design cost,an optimization algorithm that combines polygon mesh and multi-resolution matching method modeling,and solves the local stress constraint lightweight problem by augmenting lagrange equation,uses the polynomial disappearance constraint to combine the local stress constraint with the volume fraction to establish a static variational equilibrium equation.Starting from the continuous problem,analyzing the variational problem of stress constraints,the application of the material and volume double interpolation function strives to reduce the influence of the target and constraint interference.A P-norm global stress constraint scheme based on lagrangian multiplier method is introduced as a comparison term,the adjunct method is used to analyze and derive the sensitivity of the two constraint schemes,and finally through several representative examples,the local stress constraint based on the augmented Lagrange equation is verified,although it is not as simple to calculate as the P norm of cluster constraint,but it has advantages over the number of iterations and the target effect,because the local stress constraint takes each stress evaluation point into account the equation of state.Therefore,the resulting optimization results are more reliableIn order to satisfy the optimal performance of the macroscopic structure of the stress constraint model,the finite element mesh division of different irregular design domains is completed in the pre-processing combination with the polygon mesh generator,the regularized cloth based on the projection threshold function is then obtained,the basis is provided for microresearch,the reliability of multi-scale parallel optimization of the grid generator is tested,and the macro-efficiency evaluation of the microstructure of different design structures is carried out.Several studies are designed for the softness of volume constraints to minimize multi-scale parallel topology optimization,microstructures are designed using non-homogeneous hollow structures,and finally the structural stress levels in the case of non-stress constraint multiscale are compared with simulation software.In order to obtain the multi-scale parallel topology optimization design with stress constraints,the augmented Lagrange method is introduced into the multi-scale parallel topology optimization method,which is used to design macro and micro structures under stress constraints.A larger number of elements is introduced,layered local stress constraints are used to deal with a large number of stress constraints,and the adjoint method is also introduced for microscopic sensitivity analysis.This paper analyzes the macro and micro topology and stress distribution under the action of concentrated load and homogeneous load,and discusses the influence of microstructures of different initial volume fractions on the optimization of overall stress constraints.Finally,it is concluded that the augmented Lagrangian stress constraint scheme is suitable for macroscopic and microscopic multi-scale stress constraint topology optimization problems.