Nonlinear Dynamic Topology Optimization Using Moving Morphable Components Approach

For the nonlinear dynamic topology optimization problems such as crash optimization,if the traditional gradient based optimization algorithm is used,the dynamic equations need to be solved in each optimization iteration to evaluate the objective function and constraints,which is extremely resourced-consuming.The traditional structural optimization is usually carried out under the static linear condition,so the optimization results may not satisfy the performance requirements of the structure in the nonlinear dynamic condition,so this method is not suitable in the actual engineering.At present,for this kind of nonlinear dynamic topology optimization problems,the optimization results usually have no clear geometric boundary.In response to the above-mentioned problems,a method combining the equivalent static load method and the moving morphable components approach is proposed.In this paper,by combining the moving morphable components approach with the equivalent static load method,the nonlinear dynamic topology optimization can obtain clear geometric boundary,which facilitates the interaction with the computer-aided design system.To solve the problems of mesh distortion that may appear in the nonlinear dynamic analysis during each iteration,this paper uses the transformation variable to filter the topology optimization results of the last iteration,and gives some suggestions on the numerical selection of the transformation variable.To reduce the calculation time of this optimized system,the equivalent static load method based on critical time points is adopted in this paper.In the optimization process,the equivalent static load method is decoupled from the moving morphable components approach.Through the progress of optimization,the linear static system is continuously approaching the nonlinear dynamic system until the convergence condition is satisfied.Because the hollow thin-walled beam structure has a higher stiffness-to-mass ratio,it is widely used in engineering.In this paper,the boolean operation between the moving morphable components is used to realize the hollow structure,and the specific implementation process is given.In addition,to meet the manufacturing constraints,a penalty function including angle control and distance control between threedimensional cuboid components is designed,and the sensitivity of the penalty function to design variables is derived.The effectiveness of the component control method and the hollow moving morphable components approach is verified by numerical examples.In this paper,the objective function of the numerical examples is defined as the minimum compliance,and the constraint is defined as the volume fraction.Based on the equivalent static load method,the moving morphable components approach is compared with the solid isotropic material penalty method.The results show that the optimized result is reasonable and the shape is better.