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

Aubert, Pierre; Rousselet, Bernard

doi:10.1002/(sici)1097-0207(19980515)42:1<15::aid-nme347>3.0.co;2-n

Cited by 7 publications

(3 citation statements)

References 32 publications

(17 reference statements)

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“…Many optimization problems [4,6,7,15,16,24] are characterized by a non-linear dependence of F with respect to h. Solving such cases requires using a mathematical procedure involving three nested loops. They are schematized in Figure 1, where it becomes apparent that computational demand may be extremely variable not only because of the mathematical form of each problem, but also because of the peculiarities of the algorithm.…”

Section: Coupling the Optimization And Simulation Problemsmentioning

confidence: 99%

Computational techniques for optimization of problems involving non-linear transient simulations

Galarza

Carrera

Medina

1999

Int. J. Numer. Meth. Engng.

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SUMMARYMany optimization problems in engineering require coupling a mathematical programming process to a numerical simulation. When the latter is non-linear, the resulting computer time may become una ordably large because three sequential procedures are nested: the outer loop is associated to the optimization process, the middle one corresponds to the time marching scheme and the innermost loop is required for solving iteratively the non-linear system of equations at each time step. We propose four techniques for reducing CPU time. First, derive the initial values of state variables at each time (innermost loop) from those computed at the previous optimization iteration (outermost loop). Second, select time increment on the basis of those used for the previous optimization iteration. Third, deÿne convergence criteria for the simulation problem on the basis of the optimization process, so that they are only as stringent as really needed. Finally, computations associated to the optimization are shown to be greatly reduced by adopting Newton-Raphson, or a variant, for solving the simulation problem. The e ectiveness of these techniques is illustrated through application to three examples involving automatic calibration of non-linear groundwater ow problems. The total number of iterations is reduced by a factor ranging between 1·7 and 4·6.

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Section: Coupling the Optimization And Simulation Problemsmentioning

confidence: 99%

Computational techniques for optimization of problems involving non-linear transient simulations

Galarza

Carrera

Medina

1999

Int. J. Numer. Meth. Engng.

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“…The significance of locking on shape optimization is discussed by Camprubí et al 4. The shape optimization of shells against buckling is analyzed by Khosravi et al 5 and Aubert and Rousselet 6, and the same problem, taking into account the imperfections of the structure, by Reitinger and Ramm 7.…”

Section: Introductionmentioning

confidence: 99%

“…This method leads to exact derivatives if the adjoint state equation is exactly solved; however, in general, the solution is approximate (being more accurate than the previous alternatives). Such approach is used by Aubert and Rousselet 6. The automatic differentiation (AD) method is an efficient alternative way to perform the sensitivity analysis, being cheaper in terms of computer processing time and exact.…”

Section: Introductionmentioning

confidence: 99%

Shape optimization of shell structures based on NURBS description using automatic differentiation

Espath

Linn

Awruch

2011

Numerical Meth Engineering

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SUMMARYThe consolidation of the link among four fields in computational mathematics and mechanics is the main objective of this work. Surfaces based on NURBS (non-uniform rational B-spline), mathematical optimization, the finite element method (FEM) in structural analysis, and automatic differentiation (AD) are applied in shape optimization of shells. This problem is performed taking into account the fact that material and mechanical characteristics influence both, the structural shape and the thickness variation, in order to obtain the best performance with respect to a specific criterium. Some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation. The shape modification is carried out using an optimization code based on the data obtained by a finite element analysis and gradients evaluation. In this work the optimization procedure is performed using an SQP (Sequential Quadratic Programming) algorithm, where the variables are the control points in homogeneous coordinates, the knot vectors, and the thickness. The functional value is determined by the FEM and gradients are evaluated using AD. Some examples are analyzed and discussed. As a consequence of the shape optimization, shells with high structural performance and aesthetically beautiful shapes can be obtained.

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A boundary-perturbation finite element approach for shape optimization

Givoli

Demchenko

2000

Int. J. Numer. Meth. Engng.

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SUMMARYA numerical method is proposed for the e cient solution of shape optimization problems, which combines the boundary perturbation technique and ÿnite element analysis. The method is computationally e cient in that it requires a number of ÿnite element analyses with a ÿxed geometry, as opposed to standard shape optimization which requires re-analysis with varying geometry. The application of the method to general shape optimization is considered. In addition, a special optimization scheme is devised for a class of problems governed by linear partial di erential equations. The performance of the method is illustrated via an example which involves acoustic wave scattering from an obstacle.

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

Cited by 7 publications

References 32 publications

Computational techniques for optimization of problems involving non-linear transient simulations

Computational techniques for optimization of problems involving non-linear transient simulations

Shape optimization of shell structures based on NURBS description using automatic differentiation

A boundary-perturbation finite element approach for shape optimization

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