On optimal physically nonlinear trusses

Selyugin, Sergey

doi:10.1007/bf01742587

Cited by 9 publications

(1 citation statement)

References 7 publications

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“…It means that when the element design parameter (rod cross-sectional area, membrane thickness value, etc.) is varied we assume internal forces within the structural element to be ÿxed or, in other words, keeping in mind the above-mentioned stress ÿeld uniformity assumption, the following equality to be valid: kl = const; k;l= 1; 2; 3 (16) where the stress tensor kl may depend on the element internal co-ordinates. It follows from (16) that the imaginary forces applied to element nodes are constants.…”

Section: Optimization Algorithmsmentioning

confidence: 99%

Optimization algorithms for physically non‐linear structures

Selyugin¹

2001

Numerical Meth Engineering

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SUMMARYA family of numerical methods and algorithms targeted to the optimization of physically non-linear structures is proposed. The structures are described using ÿnite element approach, they are supposed to be loaded by single static loading. It is assumed that various types of ÿnite elements are used for the description. Buckling e ects are neglected. Sizing design variables with prescribed lower limits are considered. The numerical approach is based on the use of physically non-linear hyperelastic (PNH) model for the description of active loading process for the physically non-linear structures. Three optimization sub-problems for the PNH structures are considered. Variational principles for the structures as well as optimality conditions and particular solutions of the sub-problems are used for the development of algorithms intended for numerical solution of the sub-problems. Geometrical interpretation of the algorithms is presented. Monotonicity properties of the algorithms are proved under some assumptions. It is indicated how the algorithms may be used for the general case of optimization of physically non-linear structure under single loading. Numerical examples are presented. Monotonicity of the algorithms is demonstrated. It is noted that no numerical problems arise when some structural members degenerate during numerical process.

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Section: Optimization Algorithmsmentioning

confidence: 99%

Optimization algorithms for physically non‐linear structures

Selyugin¹

2001

Numerical Meth Engineering

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On Topology Aspects of Optimal BI-Material Physically Non-Linear Structures

Selyugin¹

2000

Topology Optimization of Structures and Composite Continua

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Some general optimal design results using anisotropic, power law nonlinear elasticity

Podersen

1998

Structural Optimization

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Recent results on optimal design with anisotropic materials and optimal design of the materials themselves are in most cases based on the assumption of linear elasticity. We shall extend these results to the nonlinear model classified as powerlaw elasticity. These models return proportionality between elastic strain energy density and elastic stress energy density. This is shown to imply localized sensitivity analysis for the total elastic energy, and for a number of optimal design problems this immediately gives practical, general results.For two-and three-dimensional problems the effective strain and the effective stress are defined from an energy consistent point of view, and it is shown that a definition generalizing the von Mises stress must be used. The optimization criterion of uniform energy density also holds for nonlinear materials, and several general conclusions can be based on this fact. Applications to size design illustrate this.For stiffness optimization the ultimate optimal material design problem is addressed. The validity of recent results are extended to nonlinear materials, and a simple proof based on constraint on the Frobenius norm is given. We note that the optimal material is orthotropic, that principal directions of material, strain and stress are aligned, and that there is no shear stiffness. In reality, the constitutive matrix only has one nonzero eigenvalue and the material therefore has stiffness only in relation to the specified strain condition. Results related to orientational design with.orthotropic materials are also focused on.With respect to strength optimization, i.e. the more difficult problem with local constraints, we shall comment on the influence of the different strength criteria.

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On optimal physically nonlinear trusses

Cited by 9 publications

References 7 publications

Optimization algorithms for physically non‐linear structures

Optimization algorithms for physically non‐linear structures

On Topology Aspects of Optimal BI-Material Physically Non-Linear Structures

Some general optimal design results using anisotropic, power law nonlinear elasticity

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