Plates, Laminates and Shells - Asymptotic Analysis and Homogenization

Lewiński, Tomasz; Telega, Józef Joachim

doi:10.1142/9789812813695

Cited by 70 publications

(79 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Detailed lecture on this topic is provided in the books by Cherkaev [4] and Allaire [5]. All details concerning the thin plate optimization can be found in Lewiński and Telega [77], Lewiński [78] and Dzierżanowski [79,80]. The relaxed 2D problem of minimal compliance for the linear elasticity case reduces to…”

Section: Applications In Civil Engineeringmentioning

confidence: 99%

“…Remark 3.3. The relaxation by homogenization method to make the problem (P 1,2 ) well-posed can also be applied for thin plate optimization [77][78][79]91], sandwich plates optimization [92], see also Studziński et al [93] and Díaz et al [94] and shallow shells [77][78][79]95], see also Krog and Olhoff [96]. Most of the homogenization formulae for plates and shells can be found in [77].…”

Section: Remark 32mentioning

confidence: 99%

See 1 more Smart Citation

Topology optimization in structural mechanics

Lewiński¹,

Czarnecki²,

Dzierżanowski³

et al. 2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

View full text Add to dashboard Cite

Abstract. Optimization of structural topology, called briefly: topology optimization, is a relatively new branch of structural optimization. Its aim is to create optimal structures, instead of correcting the dimensions or changing the shapes of initial designs. For being able to create the structure, one should have a possibility to handle the members of zero stiffness or admit the material of singular constitutive properties, i.e. void. In the present paper, four fundamental problems of topology optimization are discussed: Michell's structures, two-material layout problem in light of the relaxation by homogenization theory, optimal shape design and the free material design. Their features are disclosed by presenting results for selected problems concerning the same feasible domain, boundary conditions and applied loading. This discussion provides a short introduction into current topics of topology optimization.

show abstract

Section: Applications In Civil Engineeringmentioning

confidence: 99%

Section: Remark 32mentioning

confidence: 99%

Topology optimization in structural mechanics

Lewiński¹,

Czarnecki²,

Dzierżanowski³

et al. 2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

View full text Add to dashboard Cite

show abstract

“…Let us note that dependence of the solution on domain variations for classical boundary value problems is analyzed in [126]. For domain variations in free boundary crack problems we refer the reader to [67], [72] (see also [87]). Now, we are in a position to give the mixed formulation for the problem (6.25)-(6.29).…”

Section: Mixed Formulation Consider the Space Of Stressesmentioning

confidence: 99%

On the analysis of boundary value problems in nonsmooth domains

Fremiot

Horn

Laurain

et al. 2009

Dissertationes Math.

View full text Add to dashboard Cite

“…The mathematical foundation of such method, known as the homogenization theory, is being developed simultaneously with its mechanical applications from 1970s. Detailed exposition of this topic lays outside of scope of the paper, hence we refer the reader to Cherkaev (2000), Lewiński and Telega (2000), Milton (2002) and Tartar (2000) for further references.…”

Section: Introductionmentioning

confidence: 99%

On the comparison of material interpolation schemes and optimal composite properties in plane shape optimization

Dzierżanowski

2012

Struct Multidisc Optim

View full text Add to dashboard Cite

This paper deals with the classical problem of material distribution for minimal compliance of twodimensional structures loaded in-plane. The main objective of the research consists in investigating the properties of the exact solution to the minimal compliance problem and incorporating them into an approximate solid-void interpolation model. Consequently, a proposition of a constitutive relation for a porous material arise. The non-smoothness of stress energy functional known from the approach based on homogenization may be thus avoided which is beneficial for the numerical implementation of the scheme. It is next shown that the simplified variant of the proposed formula justifies and generalizes the RAMP (Rational Approximation of Material Properties) interpolation model of Stolpe and Svanberg (Struct Multidisc Optim 22:116-124). In the second part of the paper, explicit formulae for function θ : → [0, 1] describing the distribution of basic isotropic material in the design space ∈ R 2 are derived for various interpolation schemes by the requirement of optimality imposed at each x ∈ . Theoretical considerations are illustrated by a code written in MATLAB for typical optimization problems of a cantilever and MBB beam.

show abstract

Plates, Laminates and Shells - Asymptotic Analysis and Homogenization

Cited by 70 publications

References 0 publications

Topology optimization in structural mechanics

Topology optimization in structural mechanics

On the analysis of boundary value problems in nonsmooth domains

On the comparison of material interpolation schemes and optimal composite properties in plane shape optimization

Contact Info

Product

Resources

About