Sensitivity computation and shape optimization for a non-linear arch model with limit-points instabilities
✍ Scribed by P. Aubert; B. Rousselet
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 282 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0029-5981
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✦ Synopsis
A shape optimization method for geometrically non-linear structural mechanics based on a sensitivity gradient is proposed. This gradient is computed by means of an adjoint state equation and the structure is analysed with a total Lagrangian formulation. This classical method is well understood for regular cases, but standard equations 1 have to be modiÿed for limit points and simple bifurcation points. These modiÿcations introduce numerical problems which occur at limit points. 2 Numerical systems are very sti and the quadratic convergence of Newton-Raphson algorithm vanishes, then higher-order derivatives have to be computed with respect to state variables. 3 A geometrically non-linear curved arch is implemented with a ÿnite element method via a formal calculus approach. Thickness and=or shape for di erentiable costs under linear and non-linear constraints are optimized. Numerical results are given for linear and non-linear examples and are compared with analytic solutions.