Refined semi-analytical design sensitivities

Boer, H. de; Keulen, Fred van

doi:10.1016/s0020-7683(99)00322-4

Cited by 45 publications

(27 citation statements)

References 24 publications

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“…This model represents the most general and complete case that can be considered with the modeling approach presented in this research, and therefore serves as a representative problem. The configuration considered is the deterministic optimal design, and sensitivities computed using global finite difference (GFD), direct semi-analytical (SA) and direct refined semi-analytical (RSA, Van Keulen, 2000b, Van Keulen andDe Boer, 1998b)) methods are compared. In the mechanical finite difference case, the perturbed analysis is started from the final nominal configuration, which raises the efficiency of this method significantly.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In many cases of computational response analysis, gradient information can often be obtained at a fraction of the computing time as compared to the analysis itself (De Boer and Van Keulen, 2000a, Van Keulen and De Boer, 1998a. This sensitivity information can be used in addition to the function values to construct Gradient Enhanced Response Surfaces (GERS) Vervenne, 2004, Vervenne and.…”

Section: Anti-optimizationmentioning

confidence: 99%

“…This problem is attributed to increased errors in the finite difference components used for the pseudo-load calculation. Various remedies have been suggested, including the use of higher order finite difference formulae, an "exact" formulation (Olhoff et al, 1993) and the so-called "refined" semi-analytical formulation, which is based on exact differentiation of the rigid body modes of elements Van Keulen, 2000b, Van Keulen andDe Boer, 1998b). Element rigid body modes are displacement fields that do not generate internal forces, i.e.…”

Section: Discrete Approaches: Semi-analytical Design Sensitivitiesmentioning

confidence: 99%

See 2 more Smart Citations

Design Optimization of Shape Memory Alloy Structures

Langelaar¹

2004

10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Anti-optimizationmentioning

confidence: 99%

Section: Discrete Approaches: Semi-analytical Design Sensitivitiesmentioning

confidence: 99%

See 1 more Smart Citation

Design Optimization of Shape Memory Alloy Structures

Langelaar¹

2004

10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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“…In the case of a linear analysis, r e k can be formulated as a function of the nodal co-ordinates x only, see Reference [12]. However, for geometrically non-linear analyses r e k also depends on the nodal displacements [15]. As this paper will focus on linear analyses, only the dependence on the nodal co-ordinates is relevant here.…”

Section: Consistency Conditions For a Single Finite Elementmentioning

confidence: 99%

“…This is easily veriÿed using the fact that F e r e k =0. For more details about this decomposition, the reader is referred to Reference [15].…”

Section: Consistency Conditions For a Single Finite Elementmentioning

confidence: 99%

Refined second order semi‐analytical design sensitivities

Boer

Keulen

Vervenne

2002

Numerical Meth Engineering

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SUMMARYAccurate and e cient calculation of second order design sensitivities in a ÿnite element context is often di cult. The semi-analytical (SA) method is e cient and easy to implement but has accuracy problems even for ÿrst order shape design sensitivities. To overcome accuracy problems a reÿned semianalytical (RSA) method has been developed for ÿrst order sensitivities. The present paper investigates the application of the RSA method to second order design sensitivities. It is found that second order RSA sensitivities are signiÿcantly more accurate than their SA counterparts.

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Improvement of semi‐analytical design sensitivities of non‐linear structures using equilibrium relations

Parente

Vaz

2001

Numerical Meth Engineering

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SUMMARYThe accuracy problem of the semi-analytical method for shape design sensitivity analysis has been reported for linear and non-linear structures. The source of error is the numerical di erentiation of the element internal force vector, which is inherent to the semi-analytical approach. Such errors occur for structures whose displacement ÿeld is characterized by large rigid body rotations of individual elements. This paper presents a method for the improvement of semi-analytical sensitivities. The method is based on the element free body equilibrium conditions, and on the exact di erentiation of the rigid body modes. The method is e cient, simple to code, and can be applied to linear and non-linear structures. The numerical examples show that this approach eliminates the abnormal errors that occur in the conventional semi-analytical method.

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Refined semi-analytical design sensitivities

Cited by 45 publications

References 24 publications

Design Optimization of Shape Memory Alloy Structures

Design Optimization of Shape Memory Alloy Structures

Refined second order semi‐analytical design sensitivities

Improvement of semi‐analytical design sensitivities of non‐linear structures using equilibrium relations

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