Improved Optimization Criterion Algorithm For Structural Topology Optimization Under Inertial Load

In structural optimization design,we always hope to distribute materials in the most reasonable places and increase the utilization rate of materials.Structural topology optimization provides a scientific exploration method,which can be solved in a given design domain through the load and boundary conditions of the structure.The best distribution of materials.Since structural topology optimization was proposed,the research scope has ranged from static loads to thermal loads,inertial loads,dynamic loads,etc.,from single material solution to multi-material,micro-materials,etc.At the same time,various methods of structural topology optimization have been continuously proposed.Inertial loads mainly include self-weight and centrifugal force.The influence of inertial loads is very important in structural optimization.However,the research on the topology optimization of structures under inertial loads started late and there are few discussions.Therefore,there are still many problems in the topology optimization of structures under inertial loads.The main difficulties are the uncertainty of the unit sensitivity value,the failure of volume constraints and the "attachment" phenomenon of low-density units.At the same time,it is found that traditional gray-scale suppression methods will lead to the optimization ability of the algorithm when suppressing the gray-scale of structural topology results under inertial load.The problem of descent.Aiming at the above difficulties,this paper proposes an improved optimization criterion method based on the optimization criterion method.The improved algorithm greatly improves the stability,accuracy and efficiency of the structural topology optimization solution under inertial loads.The specific research content of this paper is as follows:(1)Introduce the theoretical basis of continuum topology optimization,establish a mathematical model of variable density topology optimization,and discuss the two commonly used material interpolation models SIMP and RAMP models in variable density topology optimization,and discuss the effects of the two on the element stiffness and structural flexibility in the optimization.The mathematical model of topology optimization is established separately.(2)Use optimization criterion method to solve the established mathematical model,and obtain the iterative formulas of different interpolation models under static load and inertial load.Refer to the guide weight method to change the Lagrangian multiplier solution method,and propose dynamic volume constraints,dynamic grayscale suppression and load sensitivity correction methods to solve the difficulties of structural topology optimization under inertial loads one by one,and obtain improved optimization suitable for inertial load topology optimization Principles of law.(3)The improved optimization criterion method is used to solve the structural topology optimization under the action of inertial load,and the improved optimization criterion method of the optimization criterion method,the fixed gray scale suppression and the dynamic gray scale suppression is verified through the example analysis and comparison of the optimized optimization criterion method for the dynamic gray scale suppression.The superiority of the method in terms of optimization ability,gray scale suppression,and solution efficiency.(4)Propose a multi-material interpolation model based on the variable density method,establish a multi-material topology optimization mathematical model,and use the improved optimization criterion method to solve the multi-material topology optimization under inertial loads.Numerical examples verify the accuracy of the improved optimization criterion method in solving the topology optimization of multimaterial structures under inertial loads.