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

Parente, Evandro; Vaz, Luiz Eloy

doi:10.1002/nme.115

Cited by 22 publications

(15 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This method has been successfully applied in the sensitivity computation of linear structures [36,37], of linearized buckling problems [38], as well as of geometrically non-linear structures [8,9,11], including the sensitivity of limit points. In the present work, this method will be extended in order to deal with non-linear bifurcation points.…”

Section: Reÿned Semi-analytical Methods (Rsam)mentioning

confidence: 99%

“…However, most of them deal only with limit points [5][6][7][8][9][10][11]. There are also works dealing with bifurcation points, but some of them do not speciÿcally address ÿnite element applications [12,13], while others are restricted to the semianalytical approach [2,3].…”

Section: Introductionmentioning

confidence: 99%

“…In order to obtain a computational procedure for the evaluation of the critical load sensitivity of non-linear structures that maintains the positive aspects of the semi-analytical approach, but does not present its accuracy problems, the reÿned semi-analytical approach [8,9,11] will be extended in the present work to deal with non-linear bifurcation loads.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On evaluation of shape sensitivities of non‐linear critical loads

Parente

Vaz

2002

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYThe present paper focuses on the evaluation of the shape sensitivities of the limit and bifurcation loads of geometrically non-linear structures. The analytical approach is applied for isoparametric elements, leading to exact results for a given mesh. Since this approach is di cult to apply to other element types, the semi-analytical method has been widely used for shape sensitivity computation. This method combines ease of implementation with computational e ciency, but presents severe accuracy problems. Thus, a general procedure to improve the semi-analytical sensitivities of the non-linear critical loads is presented. The numerical examples show that this procedure leads to sensitivities with su cient accuracy for shape optimization applications.

show abstract

Section: Reÿned Semi-analytical Methods (Rsam)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On evaluation of shape sensitivities of non‐linear critical loads

Parente

Vaz

2002

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Analogous to ÿrst order sensitivities, the right-hand side of (12) will be referred to as a so-called pseudo-load p p =f ; ij − K ; ij u − K ; j u ; i − K ; i u ; j (13) which is applied to the structure to solve the second order displacement sensitivities. In a SA formulation the pseudo-load vector will be evaluated by using ÿnite di erences.…”

Section: Second-order Design Sensitivitiesmentioning

confidence: 99%

“…The pseudo-load vector p e for second order SA design sensitivities is given by (13). In order to compute the error in the pseudo-load vector, both the analytical solution and the error in each term of the right-hand side of (13) must be computed.…”

Section: Analytical Beam Examplementioning

confidence: 99%

Refined second order semi‐analytical design sensitivities

Boer

Keulen

Vervenne

2002

Numerical Meth Engineering

View full text Add to dashboard Cite

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.

show abstract

A refined semi-analytic design sensitivity based on mode decomposition and Neumann series

Cho

Kim

2004

Int. J. Numer. Meth. Engng

View full text Add to dashboard Cite

SUMMARYAmong various sensitivity evaluation techniques, semi-analytical method (SAM) is quite popular since this method is more advantageous than analytical method (AM) and global finite difference method (GFD). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the pseudo load vector calculated by differentiation using the finite difference scheme. In the present study, an iterative refined semianalytical method (IRSAM) combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives. In eigenvalue problems, the tendency of eigenvalue sensitivity is similar to that of displacement sensitivity in static problems. Eigenvector is decomposed into rigid body mode and pure deformation mode. The present iterative SAM guarantees that the eigenvalue and eigenvector sensitivities converge to the reliable values for the wide range of perturbed size of the design variables. Accuracy and reliability of the shape design sensitivities in static problems and eigenvalue problems by the proposed method are assessed through the various numerical examples.

show abstract

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

Cited by 22 publications

References 14 publications

On evaluation of shape sensitivities of non‐linear critical loads

On evaluation of shape sensitivities of non‐linear critical loads

Refined second order semi‐analytical design sensitivities

A refined semi-analytic design sensitivity based on mode decomposition and Neumann series

Contact Info

Product

Resources

About