Simultaneous topology and shape optimization of pressure loaded structures

It is common practice in engineering design to carry out lightweight structural optimization under pressure load. As the loaded boundary is designable, existing topology optimization techniques related to fixed loads are unable to deal with this kind of problem. In this article, CAD parametric splines or B-splines are used directly to represent the pressure loaded surface. A simultaneous topology and shape optimization method is proposed to ensure that the structure achieves lightweight, functionality and smoothness of the boundary shape needed in practice. Likewise, background grid and density point techniques are developed to favor the definition of topology pseudo density variables when the mesh updating is made along with the boundary variation of the structure. This makes it possible to ensure an automatic transfer of material density results from one mesh to another after each iteration. Meanwhile, shape sensitivity analysis is made available using the mesh morphing scheme. Four numerical examples are presented to demonstrate the validity of the proposed method. The design solution of an aero-engine support highlights the importance of the method in aeronautical applications.