Design sensitivity analysis and shape optimization of structural components with hyperelastic material

Abstract

A continuum-based design sensitivity analysis (DSA) method is developed for structural components with hyperelastic (incompressible) material. A mixed variational principle (MVP) and the total Lagrangian formulation are used for nonlinear analysis. Effects of large displacements, large strains, and material nonlinearities are included in the analysis model, using appropriate kinematics and constitutive relations. The material property and shape DSA using both the direct differentiation method (DDM) and the adjoint variable method (AVM) are discussed. For shape DSA, the material derivative concept is used to compute effects of the shape variation. The boundary displacement and isoparametric mapping methods are employed to compute the design velocity field. Both hydrostatic pressure and structural stiffness are considered as constraints for design optimization, which is carried out by integrating shape design parameterization, design velocity computation, DSA, nonlinear analysis, and the optimization method. Examples such as, an engine mount and a bushing demonstrate the feasibility of the proposed optimization method for designing structural components using hyperelastic material.