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Sensitivity computation and shape optimization for a nonlinear arch model with limit-points instabilities. (English) Zbl 0927.74054

The paper deals with optimal design of beams and arches with geometric nonlinearities. The proposed optimization method is based on a sensitivity gradient which is computed by means of an adjoint state equation. To increase the rate of convergence near critical points, the authors use second derivatives of critical load with respect to state and shape variables. The derivatives are calculated by means of software packages for analytical differentiation. Numerical solutions of linear and nonlinear examples are compared with analytical solutions. The proposed method is proved to be efficient, and it remains stable at the turning point. In most cases, sufficiently good approximations are obtained in the second iteration.

MSC:

74P10 Optimization of other properties in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65K10 Numerical optimization and variational techniques
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