Concurrent shape and topology optimization involving design-dependent pressure loads using implicit B-spline curves

This work develops a concurrent shape and topology optimization method to solve the design problems of which the pressure loads are applied on designable boundaries. Implicit B-spline curves including open B-spline and closed B-spline are introduced in the form of level-set functions to act as common design primitives for the description of both moving pressure boundary and inner topology boundaries of a structure. Boolean operations are applied to describe mathematically the shape and topology variations. An artificial nondesignable offset domain of small bandwidth is introduced along the moving pressure boundary to ensure reasonably the imposition of pressure loads on solid materials. The pressure loads are numerically discretized onto the control nodes of finite cell method used for structural analysis with fixed mesh. Sensitivities of design-dependent pressure loads with respect to both shape and topology design variables are explicitly derived. Numerical problems are finally solved to illustrate the presented method.