Accuracy of semi-analytic sensitivity analysis

Cheng, Gengdong; Gu, Yingsong; Zhou, Yunyi

doi:10.1016/0168-874x(89)90039-5

Cited by 55 publications

(17 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The similar arguments were also made by Cheng and Liu [4] and by Yang and Botkin [5]. To solve this problem, Cheng proposed an alternative forward/backward difference scheme [6] and Olhoff et al, proposed a scheme that employs the mean value of forward and backward difference to compute the derivatives of the stiffness matrix [7]. To improve the disadvantage of alternative method, Olhoff et al, proposed so-called 'exact' method which compensate for errors produced by the finite difference method considering correction factor [8].…”

Section: Introductionmentioning

confidence: 57%

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

Section: Introductionmentioning

confidence: 57%

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

show abstract

“…This implies that the associated error factors will be different from each other and that the first parenthesis on the right-hand side of (41) Since, e.g. beam, plate and shell elements possess different types of nodal degrees of freedom and first-order difference schemes are normally used for the numerical differentiation of the stiffness components, it is not surprising that the type of discretization error connected with semi-analytical sensitivity analysis studied in this paper, has indeed manifested itself in practical computations (Haftka and Adelman 1989;Barthelemy and Haftka 1988;Cheng et al 1989).…”

Section: (40) Implies That the N-dependence Of The Error Of The Senmentioning

confidence: 95%

“…1989;Cheng et al 1989) which the method of semi-analytical sensitivity analysis may exhibit when applied in shape optimization of fnite element discretized structures modelled by beam, plate, shell and IIermite elements, manifests itself in a rapidly increasing error of the sensitivity with refinement of the finite element mesh. A similar type of inaccuracy is not found if alternative methods of sensitivity analysis, such as the analytical method and the overall finite difference technique, are employed.…”

Section: Introductionmentioning

confidence: 99%

“…

Abstract The semi-analytical method of sensitivity analysis (Zienldewicz and Campbell 1973; Esping 1983;Cheng and Liu 1987) of finite element discretized structures is attractive due to the balance between computational cost and ease of implementation (Cheng and Liu 1987;Haftka and Adelman 1989), but unfortunately the method may exhibit serious inaccuracies when applied in shape optimization of structures modelled by beam, plate, shell and IIermite elements (Cheng and Liu 1987; Haftka and Arielman 1989;Barthelemy and Haftka 1988;Choi and Twu 1991, Pedersen et al 1989;Cheng et al 1989).In the present paper, we perform an exact analysis of the error of sensitivity for a simple model problem which has earlier been considered by , Haftka (1988), Pedersen et al (1989). The analysis gives a deep insight into the nature of the general inaccuracy problem and enables us to devise methods by which the severe error of the sensitivity can be substantially reduced or removed for the model problem.

…”

mentioning

confidence: 98%

See 1 more Smart Citation

Study of inaccuracy in semi-analytical sensitivity analysis — a model problem

Olhoff

Rasmussen

1991

Structural Optimization

View full text Add to dashboard Cite

The semi-analytical method of sensitivity analysis (Zienldewicz and Campbell 1973; Esping 1983;Cheng and Liu 1987) of finite element discretized structures is attractive due to the balance between computational cost and ease of implementation (Cheng and Liu 1987;Haftka and Adelman 1989), but unfortunately the method may exhibit serious inaccuracies when applied in shape optimization of structures modelled by beam, plate, shell and IIermite elements (Cheng and Liu 1987; Haftka and Arielman 1989;Barthelemy and Haftka 1988;Choi and Twu 1991, Pedersen et al. 1989;Cheng et al. 1989).In the present paper, we perform an exact analysis of the error of sensitivity for a simple model problem which has earlier been considered by , Haftka (1988), Pedersen et al. (1989). The analysis gives a deep insight into the nature of the general inaccuracy problem and enables us to devise methods by which the severe error of the sensitivity can be substantially reduced or removed for the model problem. The results of the paper are illustrated via an example.A method of error elimination for an extended class of semianalytical analysis problems is developed and presented in a companion paper (Olhotf and Rasmussen 1991).

show abstract

“…Di erent techniques have been used to tackle the accuracy problem. Popular techniques are the higher order or alternative ÿnite di erence schemes, for example References [6][7][8]. The method presented in Reference [9] is based on the 'natural approach' and consistency conditions for rigid body modes (RBM).…”

Section: Introductionmentioning

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

Accuracy of semi-analytic sensitivity analysis

Cited by 55 publications

References 2 publications

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

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

Study of inaccuracy in semi-analytical sensitivity analysis — a model problem

Refined second order semi‐analytical design sensitivities

Contact Info

Product

Resources

About