J121041 薄板中のスリットやリブの最適位置問題の解法([J121-04]解析・設計の高度化・最適化(4))

Abstract

Slits are often used for unstiffening or functionalizing thin plate structures. In contrast, ribs are used for stiffening them. This paper describes an optimization method for designing the shape and position of slits or ribs on a thin plate structure. The slit and rib are assumed to be movable in the tangential directions to the plate surface. As an application of this solution, the compliance minimization problem subject to a slit or rib length constraint is formulated as a distributed-parameter shape optimization problem, and the shape gradient function is derived using the material derivative method. The optimal shape and position is determined by the H1 gradient method for shell. The re-meshing is introduced to maintain the mesh regularity. Design examples show that the optimal shape and position of slits or ribs are obtained by this approach while maintaining the mesh regularity.