On optimization of beams and frames made of work-hardening elasto-plastic materials

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.

Section: Optimal Design For Strengthmentioning

confidence: 99%

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

Podersen

1998

“…Papers by BendsCe and Sokolowski (1987), Cinquini and Contro (1987), Dems and Mr6z (1978), Kaneko and Maier (1981), Mr6z el al. (1985), Nakamura and Takewaki (1989), and Selyugin (1991) deal with physical nonlinearity only. In most of the above-mentioned papers the optimization algorithms are developed on the basis of the sensitivity analysis of optimization problems.…”

Section: Introductionmentioning

confidence: 98%

“…At the same time, Dems and Mr6z (1978), Nakamura and Wakewaki (1989) and Selyugin (1991) use assumptions of the deformation theory of plasticity (that is, displacements and strains are small) and replace the complicated constraint systern and objective function by some energy optimization criteria based on the concept of structural compliance. Actually this formulation of the problem takes into account physical nonlinearity only.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, it is natural to hope that this approach will also be fruitful in nonlinear problems. Dems and Mr6z (1978) proposed the total complementary energy minimum criterion with prescribed volume of material as an optimization criterion, and Selyugin (1991) proposed the total elasto-plastic strain potential energy minimum criterion with prescribed volume of material. It was supposed that these criteria led to a minimum of structural compliance.…”

Section: Introductionmentioning

confidence: 99%

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

Selyugin

1992

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The problems of the optimization of bar structures made of work-hardening elasto-plastic materials are investigated on the basis of the deformation theory of plasticity. Two optimization criteria are discussed -the minimum of the total complementary energy and the minimum of the total elasto-plastic strain potential energy. It is proved that these criteria are equivalent and lead to equally-stressed structures, if the structures are statically determinate. Furthermore, a problem of the minimization of the integral over the structural volume of an arbitraxy monotonously increasing strictly convex smooth function of the absolute value of a strain or a stress with prescribed volume of material for statically determinate bar structures also proves to lead to equally-stressed structures. On the basis of the results obtained, two algorithms for the optimization of statically indeterminate trusses are proposed and illustrated. It is noted that the example structure degenerates to a statically determinate one as a result of the optimization process.

“…(1985), Saka (1988), and Selyugin (1992Selyugin ( , 1994. Membranes and plates were investigated to a minor extent (see Arora and Cardoso 1989;Mr6z el al.…”

mentioning

confidence: 99%

Optimality criteria-based algorithms for plane-stress elastoplastic structures

Selyugin

1995

Self Cite

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.