An integrated approach to structural shape optimization

An integrated approach to structural shape optimization is discussed. The proposed approach couples the finite element method and the optimization process together by implementing design sensitivity analysis. The design sensitivities are obtained by directly differentiating finite element equations. The design element concept is employed to represent the geometry of a structure and an isoparametric mapping technique is used to automatically generate and regenerate the finite element mesh. Move limits, constraint equations, and B-spline functions are introduced to obtain a realistic optimum shape that meets the manufacturing requirements. The search for the final shape of a structure is performed by a linear programming technique based on the sensitivity information. The approach is implemented by a FORTRAN program. Several examples are provided to demonstrate the capabilities of this approach.