| In this dissertation, design sensitivity analysis for structural systems with nonlinear response subjected to quasistatic loading is developed. Both geometric and response history dependent material nonlinearities are considered. The total Lagrangian procedure for nonlinear analysis is adopted. To include the effect of large displacement, a rate constitutive equation is employed. This rate constitutive equation includes several different yield conditions and hardening rules used in practice. A general functional unifying the cost and constraint functions is used.;Two approaches for sensitivity analysis, i.e., the direct differentiation (DDA) and the adjoint structure (ASA), are developed. Following the Euler-Lagrange Kinematic Description a fixed reference configuration is defined and used for conventional and shape design problems. The difficulties associated with nonlinear sensitivity analysis and relative advantages and disadvantages of the two approaches are discussed. Based on this research a hybrid approach combining the advantages of DDA and ASA is proposed. The general sensitivity formula is reduced to several simpler cases and is verified with formulas in literatures. Also, analytical examples are given to illustrate the procedures of DDA and ASA, and to identify the history dependent parameters for design sensitivity analysis.;It is shown that design sensitivity analysis for problems involving response history dependent material nonlinearity is history dependent; i.e., the sensitivity at current state depends on the sensitivity at the previous states. So, the procedures for design sensitivity analysis for response history dependent problems are different from those that do not depend on response history. Tangent stiffness matrices at intermediate loading steps are required for design sensitivity analysis. Consequently, this requirement makes it quite difficult to incorporate design sensitivity analysis into existing finite element codes.;The general sensitivity formula developed based on the continuum approach is also discretized using the finite element method. This is compared with the sensitivity formula derived by using the finite element model all the way. Numerical examples for truss and beam structures are given to verify the general formula. Numerical experience with the solution procedures is described and conclusions that can be useful for future research are drawn from this study. |
