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Nonlinear structural design sensitivity analysis for path dependent problems. I: General theory. (English) Zbl 0724.73158
Summary: Two procedures (direct differentiation and adjoint structure) for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper. Continuum formulation is used and both geometric and material nonlinearities are included in the derivations. Incremental nonlinear analysis based on the total Lagrangian concept is adopted. The reference volume concept is used to unify the shape and nonshape design problems. To show the generality of the theory, the derived expressions are reduced to some special cases that have been treated previously in the literature. In Part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory. The theory has also been discretized elsewhere using finite element approximations for implementation into structural analysis programs. These developments offer a firm foundation for design optimization of complex structural systems.

MSC:
74P99Optimization in solid mechanics
74H45Vibrations (dynamical problems in solid mechanics)
74S05Finite element methods in solid mechanics