A physics-based parameterization method for shape optimization

Abstract

A physical approach is presented to provide shape modification of NURBS curve. The movement of the control polygon of NURBS is simulated by a physical frame structure, and the curve deformation is then carried out through changes of the mode coordinates, which are derived from the eigenvectors of the finite element equations of the physical frame system. The shape of the design boundaries is described by a linear combination of the mode shape vectors. Based on the presented design variable representation and p-version finite element analysis, an integrated approach to structural shape optimization is discussed. A method is developed that enables the description of the shape to be adaptively refined during the shape optimization process. Numerical examples are used to demonstrate the applicability of this approach to structural shape optimization.