Recent Advances in Design Sensitivity Analysis and Its Use in Structural Design Process

This paper presents a summary of recently developed unified method of continum design sensitivity analysis of linear and nonlinear structural systems. Sizing design variables, such as thickness and cross sectional areas, and shape design variables, such as length and geometric shape, of structural components of built-up structures are considered. For design sensitivity analysis of nonlinear structures, both geometric and material nonlinearities are considered using the total and updated Lagrangian formulations. For sizing design variables, a distributed parameter structural design sensitivity analysis approach that retains the continum elasticity formulation throughout the derivation of design sensitivity analysis results is used. For shape design variables, the material derivative concept of continuum mechanics is used to relate variations in structural shape to measures of structural performance. Both domain and boundary methods of shape design sensitivity analysis are developed to incorporate with the finite element and boundary element methods for numerical computation, respectively. Adjoint variable and direct differentiation methods are used to derive expressions for design sensitivity in terms of sizing and shape design variations in the continuous setting which can be evaluated numerically using analysis results of finite element or boundary element analysis codes. A numerical method is developed to carry out design sensitivity calculations outside established finite element analysis codes, using postprocessing data only. It is proposed in this paper to use the design sensitivity information in four step structural design process to put the control of design process in the hands of the designer rather than computer.