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

Barthold, Franz‐Joseph; Stein, Erwin

doi:10.1007/bf01279652

Cited by 34 publications

(21 citation statements)

References 47 publications

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“…Barthold and Stein [17] and the references cited therein. In addition to the mechanical body B that represents the current (optimized) design, we introduce a fixed reference configurationB that represents the initial design.…”

Section: Fictitious Energymentioning

confidence: 99%

A fictitious energy approach for shape optimization

Scherer

Denzer

Steinmann

2009

Numerical Meth Engineering

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SUMMARYThis paper deals with shape optimization of continuous structures. As in early works on shape optimization, coordinates of boundary nodes of the FE-domain are directly chosen as design variables. Convergence problems and problems with jagged shapes are eliminated by a new regularization technique: an artificial inequality constraint added to the optimization problem limits a fictitious total strain energy that measures the shape change of the design with respect to a reference design. The energy constraint defines a feasible design space whose size can be varied by one parameter, the upper energy limit. By construction, the proposed regularization is applicable to a wide range of problems; although in this paper, the application is restricted to linear elastostatic problems.

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Section: Fictitious Energymentioning

confidence: 99%

A fictitious energy approach for shape optimization

Scherer

Denzer

Steinmann

2009

Numerical Meth Engineering

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“…An enhancement of the above mentioned approach by Noll in the context of variational design sensitivity analysis was proposed by [3,6,8]. Following the intrinsic concept, a given manifold can be described locally using an intrinsic coordinate system defined on an independent continuous parameter space P with local coordinates .…”

Section: Enhanced Kinematicsmentioning

confidence: 99%

“…shape optimization or problems from configurational mechanics, the intrinsic formulation in local coordinates has advantages, because we deal with two independent placement mappings, see [3,6,8] for more details. The relationship of this formalism to the arbitrary Lagrangian-Eulerian (ALE) approach is discussed in [6].…”

Section: Remarkmentioning

confidence: 99%

On variational sensitivity analysis and configurational mechanics

Materna

Barthold

2007

Comput Mech

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This contribution is concerned with the application of variational design sensitivity analysis in the context of structural optimization and configurational mechanics. In both disciplines we consider variations of the material configuration and we use techniques from variational sensitivity analysis in order to solve these problems. We derive the physical and material residual problem in one step by using standard optimization procedures. Furthermore, we investigate the sensitivity of the physical as well as the material residual problem and obtain the coupled saddle point problem based on these sensitivities. Both problems are coupled by the pseudo load operator, which plays an important role by the solution of structural optimization problems. By means of computational examples from mesh optimization and shape optimization, we demonstrate the capability of the proposed theoretical framework.

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“…Its description is split into two parts: The approximation itself and an accompanying scheme for e cient treatment of so-called linearly explicit constraints (32). These constraints simply constitute a feasible domain in the parameter space with a piecewise linear boundary.…”

Section: Approximation Procedures For Iterative Design Updatesmentioning

confidence: 99%

“…The idea is the one behind the methods of feasible directions described by Zoutendijk [26] or Haftka and G urdal [27]. Any search direction in the design space R N of the cubic objective approximation algorithm that violates a constraint is projected into a feasible direction that satisÿes all constraints (32). According to Zoutendijk, an optimization problem with (linear) constraints on Y ∈ R N can be written in the form…”

Section: Treatment Of Explicit Linear Constraintsmentioning

confidence: 99%

A simple approach towards fully stressed design in hyperelasticity exploiting the isoparametric finite element concept

Kirchner¹,

Immel²

2000

Int. J. Numer. Meth. Engng.

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SUMMARYA novel approach towards fully stressed designs in hyperelasticity is discussed leading to closed-form expressions for the sensitivities of the objective and displacements with respect to design variations. The key idea is the modiÿcation of the classical approach coupled with a so-called design element method o ering a lot of parallelism to standard ÿnite element methods. We bypass implicit constraints on dependent quantities and derive an explicit linearly constrained optimization problem solved by means of ÿrst-order procedures. The results obtained with the proposed method are adequate from an engineering point of view though being computed with a simple method.

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

Cited by 34 publications

References 47 publications

A fictitious energy approach for shape optimization

A fictitious energy approach for shape optimization

On variational sensitivity analysis and configurational mechanics

A simple approach towards fully stressed design in hyperelasticity exploiting the isoparametric finite element concept

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