Variational method for design sensitivity analysis in nonlinear structural mechanics

Cardoso, J.B.; Arora, Jasbir S.

doi:10.2514/3.9939

Cited by 113 publications

(18 citation statements)

References 22 publications

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“…1986Hou ctal. , 1990Choi and Seong 1986;Haug et al 1986;Haug and Choi, 1986;Belegundu and Rajan 1988;Arora and Cardoso 1989) and the domain parametrization approach (see Arora and Cardoso 1989;Haber 1987;Phelan and Haber 1989;Cardoso and Arora 1988) have been used to derive the shape design sensitivity expressions. The representation of physical phenomena on variable domains and the implicit dependency of all continuum mechanical quantities on the chosen design are carefully considered in these approaches.…”

Section: Introductionmentioning

confidence: 99%

A continuum mechanical-based formulation of the variational sensitivity analysis in structural optimization. Part I: analysis

Barthold

Stein

1996

Structural Optimization

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A variational formulation of shape design sensitivity analysis is outlined, starting from a differential geometry-based representation of continuum mechanics.A rigorous analysis using convected curvilinear coordinates yields a decomposition of all continuum mechanical functions into independent geometry and displacement mappings. Using this representation of geometry and displacements defined on a fixed parameter space, their influence on physical quantities can easily be separated. Consequently, the variations of continuum mechanical quantities with respect to either geometry or displacements can be performed similarly using the well-known linearization techniques in nonlinear mechanics.The proposed methodology for performing variational design sensitivity analysis is formulated for general nonlinear hyperelastic material behavionr using either the Lagrangian or Eulerian description. The differences and similarities of the formulation presented compared with the material derivative approach and the domain parametrization approach are highlighted and discussed.

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Section: Introductionmentioning

confidence: 99%

A continuum mechanical-based formulation of the variational sensitivity analysis in structural optimization. Part I: analysis

Barthold

Stein

1996

Structural Optimization

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“…Since the stiffness and load are functions of design variables, the displacements are implicit functions of these variables (HAUG et al [4]). The objective of the sensitivity analysis is to determine changes in structural response functional with variations of design parameters, i.e.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The first paper on the sensitivity analysis was written by Campbell and Zienkiewicz [2] followed over recent years by an increasing number of paper devoted to this subject. Relatively many papers have been published in the aeronautical periodicals (Haftka and Mróz [3], Aurora and Cardoso [4]). The literature on sensitivity analysis is broad.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis of Cylindrical Shell

Grzywıńskı¹,

Pokorska²

2013

Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series

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The paper deals with some aspects of structural sensitivity analysis in shell structures. The finite element method has been used for modeling of cylindrical structure. The direct differentiation method has been applied in solution of the problem considered. The examples of sensitivity have been presented concerning displacement sensitivity to variations of thickness in cylindrical shell structural element clamped at boundaries under uniformly distributed pressure. The algorithms presented have been prepared and programmed in the POLSAP code system [1].

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“…In their works, the total Lagrangian formulation was used. Arora and Cardoso [2] presented a continuum-shape DSA method for the response functional of non-linear structures. The variational principle and incremental procedure for non-linear analysis are used in their derivation.…”

Section: Introductionmentioning

confidence: 99%

Design sensitivity analysis and optimization of non-linear transient dynamics. Part II?configuration design

Cho

Choi

2000

Int. J. Numer. Meth. Engng.

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SUMMARYFor con"guration design of non-linear dynamic structures, such as crashworthiness design, a continuumbased con"guration design sensitivity analysis (DSA) and optimization methods are developed. The same transient dynamic analysis method used in Part I of this paper is employed here. The elastic}plastic material and "nite strain and rotation e!ect are considered. The "rst-order variations of the energy forms, load form and kinematic and structural responses with respect to con"guration design variables are derived. For the con"guration design, both the shape and orientation variations contribute to the "rst-order variation of the equations of motion. The angular design velocity "eld associated with Euler angles is used to represent the orientation variation to obtain accurate design sensitivity results. Like Part I of the paper, the updated Lagrangian formulation and direct di!erentiation method are used for DSA for the path-dependent problem. For the updated Lagrangian formulation, the design velocity "eld that de"nes the mapping between the initial and perturbed designs should also be updated at each con"guration. Numerical implementation of con"guration DSA and optimization is carried out for "xed time steps using DYNA3D and the modi"ed feasible direction (MFD) method. It is observed that the proposed DSA method yields better sensitivity results than the "nite di!erence method for the highly non-linear problem. Design optimization is carried out using the design sensitivity information

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Variational method for design sensitivity analysis in nonlinear structural mechanics

Cited by 113 publications

References 22 publications

A continuum mechanical-based formulation of the variational sensitivity analysis in structural optimization. Part I: analysis

A continuum mechanical-based formulation of the variational sensitivity analysis in structural optimization. Part I: analysis

Sensitivity Analysis of Cylindrical Shell

Design sensitivity analysis and optimization of non-linear transient dynamics. Part II?configuration design

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