Design sensitivity analysis and shape optimization of structural components with hyperelastic material (Q1577240)

The paper deals with design sensitivity analysis of strtictural components made of hyperelastic materials. A mixed variational principle and the total Lagrangian formulation are used for nonlinear analysis. Effects of large displacements, large strains, and material nonlinearities are included in the analysis, using appropriate kinematics and constitutive relations. The authors perform material and shape design sensivity analysis using both the direct differentiation method and the adjoint variable method. In shape design sensitivity analysis, the material derivative concept is used to compute effects of 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, nonlinear analysis, and an optimization procedure. Examples, such as engine mount and bushing, demonstrate the feasibility of the proposed method for designing structural components of hyperelastic materials.