Design sensitivity analysis and optimization of nonlinear structures with hyperelastic materials

A unified methodology is developed for design sensitivity analysis (DSA) and optimization of nonlinear structures with hyperelastic (or incompressible) materials. The continuum DSA method for structural responses with respect to shape and material properties is discussed. Both geometric and material nonlinearities are treated.; The nonlinear analysis method of hyperelastic material employed for DSA is based on a mixed variational principle. Both hydrostatic pressure and displacement are considered as independent variables in this principle. Effects of large displacements, large strains, and material nonlinearities are included in analysis, using appropriate kinematics and constitutive relations.; The material property and shape design sensitivity using both direct differentiation and adjoint variable methods are discussed. For DSA, the incremental forms of nonlinear equilibrium equation and its linearization are used to obtain the first variations of energy form and load linear form. The total and updated Lagrangian formulations are used for material property DSA, and the total Lagrangian formulation is used for shape DSA. 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. Several types of structural performance measures such as displacement, stress, deformation gradient, and hydrostatic pressure are considered. The feasibility and accuracy of the proposed DSA method are demonstrated through numerical examples using the finite element analysis code ABAQUS.; Mathematical models for shape design optimization of structures with incompressible material are defined. A computational algorithm used for design optimization is discussed. Both hydrostatic pressure and structural stiffness are considered as constraints in the optimization problem. The shape design optimization is carried out by integrating the shape design parameterization, design velocity computation, structural analysis, and optimization methods. Examples such as an engine mount and a bushing are presented to demonstrate the feasibility of the proposed optimization method for the designing of structures with incompressible materials.