An Analytical Model to Predict Optimal Material Properties in the Context of Optimal Structural Design

Bendsøe, Martin P.; Guedes, J. M.; Haber, Robert B.; Pedersen, Pauli; Taylor, John E.

doi:10.1115/1.2901581

Cited by 204 publications

(112 citation statements)

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“…For instance, in free material optimization of structures for stiffness maximization, the problem is reduced to solving only one design variable per material sampling point, namely the norm or the trace of the elasticity tensor [12]. It is shown analytically in [13] that the elements of the elasticity tensor can then be fully recovered from the optimal norm and the related displacements.…”

Section: Condition For Uniqueness Of the Density Distributionmentioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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SUMMARYTopology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non-unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing nonuniqueness.

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Section: Condition For Uniqueness Of the Density Distributionmentioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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show abstract

“…where the weight factors for element e are chosen by the relative elastic energy density (u e ) n in load case n, and each [ C e ] n are derived by optimality criteria and expressed in principal strains, see [5]. The heuristic procedure rapidly converges towards a design with an optimized strength that is measured by the maximum elastic energy density over the specified load cases and over the full continuum space.…”

Section: Multiple Load Cases Fully Stressed For Strength Optimizationsmentioning

confidence: 99%

Optimized constitutive distributions visualized by lamina formulas

Pedersen

2016

Mechanics of Advanced Materials and Structures

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Abstract. For optimal design most parameters may be classified in size, shape and topology, such as simple density variables and parameters for surface description. Density and surface can be rather directly visualized. Extending the design to material design in sense of design of distributions of constitutive matrices, a practical visualization is more complicated but may be based on classical laminate analysis. In rotational transformation of constitutive matrices, some practical quantities are often termed invariants, but the invariance relates to an unchanged reference direction. Rotating this reference direction, the practical quantities do change and this point is clarified with derived rotational transformation for these practical quantities.

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“…In this article, we focus on Free Material Optimization, originally introduced for the optimal design of solid bodies by [3]. The design variable used in Free Material Optimization is the full material tensor at each point of the design domain.…”

Section: Introductionmentioning

confidence: 99%

Free Material Optimization for Plates and Shells

Gaile

Leugering

Stingl

2009

IFIP Advances in Information and Communication Technology

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Abstract. In this article, we present the Free Material Optimization (FMO) problem for plates and shells based on Naghdi's shell model. In FMO -a branch of structural optimization -we search for the ultimately best material properties in a given design domain loaded by a set of given forces. The optimization variable is the full material tensor at each point of the design domain. We give a basic formulation of the problem and prove existence of an optimal solution. Lagrange duality theory allows to identify the basic problem as the dual of an infinite-dimensional convex nonlinear semidefinite program. After discretization by the finite element method the latter problem can be solved using a nonlinear SDP code. The article is concluded by a few numerical studies.

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An Analytical Model to Predict Optimal Material Properties in the Context of Optimal Structural Design

Cited by 204 publications

References 0 publications

Bounds for decoupled design and analysis discretizations in topology optimization

Bounds for decoupled design and analysis discretizations in topology optimization

Optimized constitutive distributions visualized by lamina formulas

Free Material Optimization for Plates and Shells

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