Shape design sensitivity analysis of eigenvalues using “exact” numerical differentiation of finite element matrices

Lund, Erik; Olhoff, Niels

doi:10.1007/bf01742934

Cited by 28 publications

(3 citation statements)

References 11 publications

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“…In Figure 10 the in uence of these separate parts on the accuracy is given. Firstly, only the e ect of the ÿrst improvement, as given by (12), is studied. Secondly, the e ect of both improvements, given by (15), is given.…”

Section: Pure Bending Of Cylindrical Panelmentioning

confidence: 99%

Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions

Keulen

Boer

1998

Int. J. Numer. Meth. Engng.

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In the recent past inaccuracy problems have been reported that arise when computing shape design sensitivities by the semi-analytical method. Since both the analytical and the global ÿnite-di erence method do not show these severe inaccuracies, it has been concluded that these errors are due to the numerical di erentiation of the ÿnite-element sti ness matrices, which is inherent in the semi-analytical method. Moreover, it has also been observed that these inaccuracies become especially dominant when relatively large rigid body motions can be identiÿed for individual elements. So far, improvements to the semi-analytical method are focusing on the numerical di erentiation of the ÿnite-element sti ness matrices. It is shown in the present paper that the contribution to the design sensitivities corresponding to the rigid body motions can be evaluated by exact di erentiation of the rigid body modes. This approach requires only minor programming e ort and the additional computing time is very small. As shown by numerical examples, the proposed method eliminates the problem of abnormal errors occurring in the semi-analytical method. ? 1998 John Wiley & Sons, Ltd.

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Section: Pure Bending Of Cylindrical Panelmentioning

confidence: 99%

Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions

Keulen

Boer

1998

Int. J. Numer. Meth. Engng.

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“…where k and m are element matrices and ne is the number of finite elements. A general computer program has been developed to evaluate the sensitivities with both sizing and shape design variables[12] employing an analytical approach[23].…”

Section: Gradient Calculationmentioning

confidence: 99%

Optimum design of plate structures with frequency constraints

Salajegheh

1997

Engineering Computations

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Achieves efficient structural optimization of plate structures while the design constraints are multiple frequency constraints. Reduces the computational cost of optimization by approximating the frequencies using the Rayleigh quotient. Uses an optimality criteria method to solve each of the approximate problems. The creation of a high quality approximation is the key to the efficiency of the method. Also, with the great number of design variables, the optimality criteria methods are robust approaches. Thus the combination of approximation concepts and optimality criteria methods forms the basis of an efficient tool for optimum design of plate structures with frequency constraints. Presents examples and compares the results with previous work.

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“…Within semi‐analytical sensitivity analysis, finite differentiation is applied to finite element matrices and causes errors in some cases. But this drawback seems to be a matter of the past as different methods were developed to eliminate the mentioned errors, see for more details.…”

Section: Introductionmentioning

confidence: 99%

Variational sensitivity analysis of a nonlinear solid shell element

Gerzen

Barthold

Klinkel

et al. 2013

Numerical Meth Engineering

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SUMMARY The paper is concerned with variational sensitivity analysis of a nonlinear solid shell element, which is based on the Hu–Washizu variational principle. The sensitivity information is derived on the continuous level and discretized to yield the analytical expressions on the computational level. Especially, the pseudo load matrix and the sensitivity matrix, which dominate design sensitivity analysis of shape optimization problems, are derived. Because of the mixed formulation, condensation of the pseudo load matrix on the element level is performed to compute the sensitivity matrix. An illustrative example from the field of geometry‐based shape optimization demonstrates the possible application of the presented formulation. Copyright © 2013 John Wiley & Sons, Ltd.

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Shape design sensitivity analysis of eigenvalues using “exact” numerical differentiation of finite element matrices

Cited by 28 publications

References 11 publications

Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions

Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions

Optimum design of plate structures with frequency constraints

Variational sensitivity analysis of a nonlinear solid shell element

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