Stress-related Topology Optimization Of Shell Structures Under Explicit Topology Optimization Framework

Topology optimization is a method to obtain the optimal material distribution under certain constraints,which can be applied to practical projects in various fields.The stress-related topology optimization problem is a hot topic that researchers have paid close attention to in recent years.Compared to the optimization considering the global structural performances,the problem has three challenges:stress singularity phenomenon,computational cost of local stress constraints,the accuracy of stress calculation.There have been amount of works proposed to overcome the challenges.But most of the work is based on implicit optimization framework with lots of design variables,unclear structural boundaries and the isolation from CAD/CAE system.On the other hand,shell structure was considered by few researchers in the study of stress-related topology optimization as one of the common structural forms in modern industry.It is mainly because the structural response is very sensitive to the geometry of the shell midplane,so that the accuracy of the model description is the key to solving the problem.But the implicit optimization framework and traditional FEM cannot guarantee the accuracy.In this paper,a new topology optimization explicit framework is proposed for the above problems,which is composed of isogeometric analysis and moving morphable void method.As a novel analysis method,isogeometric analysis let the basis function of the description model be the physics interpolation function.Not only can the analysis model be consistent with the geometric model of shell structures,but also can guarantee the accuracy of high-order physical field on a low-scale grid.The moving morphable void method breaks the limitation of the conventional topology optimization method.It uses the parameters describing the void as the design variables,and uses the movement,deformation,and fusion of the voids to describe the topology to achieve the explicit optimization results.The explicit framework formed by the combination of the two methods can not only ensure the high-precision performance of the entire problem at low calculation costs,but also directly link with the engineering CAD/CAE software,which is a significant for actual engineering.The stress-related topology optimization of the shell structure is completed based on the proposed explicit framework and Reissner-Mindlin shell theory,The surface trimming technology will be introduced in the isogeometric analysis to enhance the accuracy of stress response,the regularization optimization formulation will be introduced so that it will not get singular solutions,and the global stress description function based on the stress gradient will be employed,which replaces multiple local stress constraints and reduces the amount of calculation.