The lightweight topology optimization of plate/shell structures with different mechanical performance constraints

The plate/shell structures are popular among in engineering because they show great potential in lightweight design under pressure loads. This paper develops a lightweight topology optimization method of plate/shell structures considering different mechanical performances based on independent, continuous and mapping (ICM) method. A mathematical formulation is established to describe the plate/shell topology optimization problem with minimum volume or mass as objective, the critical buckling load and nodal displacement as constraints. The finite element model is employed to subdivide the design domain and the existing state of each element is described as a topology design variable. In addition, linear buckling and static analyses are used to get the critical buckling load and nodal displacement of plate/shell structures and relevant information of elements and nodes used in the process of topology optimization. The filter functions are introduced to recognize element properties and map the 0-1 integer programming model into a formulation with continuous variables. Sensitivity analysis and Taylor expansion are applied to achieve a standard quadratic programming model. Finally, numerical examples are provided to test the effectiveness and feasibility of the theory above, and discuss the influence of constraints on optimal structures. This study can provide a theoretical basis for the lightweight topology optimization of plate/shell structures.