Effective Integration of Sensitivity Analysis and Minimization Procedures with Application to Shape Optimization of Three-dimensional Hyperelasticity

1. Abstract The effective application of shape optimization procedures based on the FEM to engineering problems requires a fully integration of concepts and sofwate modules for geometric modelling, finite element analysis, sensitivity analysis, minimization procedures, mesh generation, updating and distortion control. In this sense, the central concept for the connection and communication among all the modules is the velocity fields presented in the expressions of shape sensitivity analysis of the performance functionals. The sensitivity expressions do not manipulate directly the shape design variables but just their respective velocity fields. Therefore, the sensitivity expressions impose theoretical requirements to the velocity field format. The geometric description must provide a general and reusable rule for the determination of the velocity fields. The mesh boundary must always coincide with the geometric boundary along the optimization steps. This work presents an effective integration of the previous concepts. A 3D linear hyperelastic shape optimization problem will be considered to illustrate the features of the algorithms presented.