First and Second Order Design Sensitivity at a Bifurcation Point

Mróz, Z.; Piekarski, J.

doi:10.1007/978-94-011-0453-1_10

Advances in Structural Optimization

1995

DOI: 10.1007/978-94-011-0453-1_10

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First and Second Order Design Sensitivity at a Bifurcation Point

Z. Mróz

J. Piekarski

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Cited by 3 publications

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Sensitivity computation and shape optimization for a non-linear arch model with limit-points instabilities

Aubert¹,

Rousselet

1998

Int. J. Numer. Meth. Engng.

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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. ? 1998 John Wiley & Sons, Ltd.

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Sensitivity computation and shape optimization for a non-linear arch model with limit-points instabilities

Aubert¹,

Rousselet

1998

Int. J. Numer. Meth. Engng.

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Second-order shape sensitivity analysis for nonlinear problems

Taroco

Buscaglia

Feljóo

1998

Structural Optimization

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First-and second-order shape sensitivity analyses in a fully nonlinear framework are presented in this paper. Using the fixed domain technique and the adjoint approach, integral expressions over the domain are obtained. The Guillaume-Masmoudi lemma allows these expressions to be rewritten as integrals over the domain boundary. The formalism is then applied to the steady creep of a bar in torsion, as an example of power-law nonlinearities that occur not only in creep problems but also in viscoplastic fluid flow. Finally, a problem with known analytical solution is presented in order to show the equivalence between exact differentiation and the shape sensitivity approach.

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Design sensitivity of post-buckling states including material constraints

Godoy¹,

Taroco²

2000

Computer Methods in Applied Mechanics and Engineering

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First and Second Order Design Sensitivity at a Bifurcation Point

Cited by 3 publications

References 1 publication

Sensitivity computation and shape optimization for a non-linear arch model with limit-points instabilities

Sensitivity computation and shape optimization for a non-linear arch model with limit-points instabilities

Second-order shape sensitivity analysis for nonlinear problems

Design sensitivity of post-buckling states including material constraints

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