Optimization criteria and algorithms for bar structures made of work-hardening elasto-plastic materials

Selyugin, Sergey

doi:10.1007/bf01742748

Cited by 6 publications

(10 citation statements)

References 14 publications

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“…Some results for the truss based on the use of AP2 and AP3 algorithms were obtained earlier [13], they are also presented here just for the comparison with new results.…”

Section: Five-member Trussmentioning

confidence: 94%

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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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“…Some results for the truss based on the use of AP2 and AP3 algorithms were obtained earlier [13], they are also presented here just for the comparison with new results.…”

Section: Five-member Trussmentioning

confidence: 94%

“…of (13) corresponds to members presented in the considered equally stressed structure, the second integral corresponds to other members. If the condition…”

Section: Theoretical Considerationmentioning

confidence: 99%

Optimization algorithms for physically non‐linear structures

Selyugin¹

2001

Numerical Meth Engineering

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“…The latter papers were based on the sensitivity analysis approach. Selyugin (1992Selyugin ( , 1994 proposed and developed an optimization approach for structures made of work-hardening elasto-plastic materials. This approach was based on the analysis of optimality conditions.…”

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confidence: 99%

“…The present paper is devoted to an extension of the approach (Selyugin 1992(Selyugin , 1994 to plane-stress structures (membranes) made of work-hardening elasto-plastic materials. Deformation plasticity theory (Kachanov 1969, Ilyushin 1948) is used for algorithm development.…”

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confidence: 99%

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Optimality criteria-based algorithms for plane-stress elastoplastic structures

Selyugin

1995

Structural Optimization

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Optimization problems for plane-stress structures made of work-hardening elasto-plastic materials are theoretically considered. The deformation theory of plasticity is used. Optimality conditions for mean structural compliance minimization problems are obtained and investigated, and it is shown that the conditions lead to fully-stressed design. On the basis of the theoretical results obtained several optimization algorithms for the structures are developed. Numerical test results for the alogrithms are presented and analysed. High convergence rates of the algorithms are demonstrated. Significant physical properties of the numerical results are discussed.

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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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Optimization criteria and algorithms for bar structures made of work-hardening elasto-plastic materials

Cited by 6 publications

References 14 publications

Optimization algorithms for physically non‐linear structures

Optimization algorithms for physically non‐linear structures

Optimality criteria-based algorithms for plane-stress elastoplastic structures

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

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