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Topology optimization in structural mechanics PDF Print E-mail
Tbiuletynpanopology optimization in structural mechanics
T.Lewiński, S. Czarnecki, G.Dzierżanowski and T. Sokół
BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. 61, No. 1, 2013

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.
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On minimum compliance problems of thin elastic plates of varying thickness PDF Print E-mail
On minimum compliance problems of thin elastic plates of varying thickness
S. Czarnecki, T. Lewiński
Structural and Multidisciplinary Optimization
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The paper deals with two minimum compliance problems of variable thickness plates subject to an in-plane loading or to a transverse loading. The first of this problem (called also the variable thickness sheet problem) is reduced to the locking material problem in its stress-based setting, thus interrelating the stress-based formulation by Allaire (2002) with the kinematic formulation of Golay and Seppecher (Eur J Mech A Solids 20:631–644, 2001). The second problem concerning the Kirchhoff plates of varying thickness is reduced to a non-convex problem in which the integrand of the minimized functional is the square root of the norm of the density energy expressed in terms of the bending moments. This proves that the problem cannot be interpreted as a problem of equilibrium of a locking material. Both formulations discussed need the numerical treatment in which stresses (bending moments) are the main unknowns.
 
Exact least-volume trusses for two symmetric point loads and unequal permissible stresses in tension and compression PDF Print E-mail
structural optimizationExact least-volume trusses for two symmetric point loads and unequal permissible stresses in tension and compression Tomasz Sokół · George I. N. Rozvany
Structural and Multidisciplinary Optimization
January 2013, Volume 47, Issue 1, pp 151-155,
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In this Authors' Reply previously presented solutions are extended to unequal permissible stresses in tension and compression, comments are made on the lack of adjoint displacement fields in so-called O-regions (memberless regions), and some computational details are explained.
 
Exact analytical solutions for some popular benchmark problems in topology optimization III: L-shaped domains revisited PDF Print E-mail
structural optimizationExact analytical solutions for some popular benchmark problems in topology optimization III: L-shaped domains revisited
T. Lewiński, G. I. N. Rozvany, T. Sokół, K. Bołbotowski
Structural and Multidisciplinary Optimization
June 2013, Volume 47, Issue 6, pp 937-942
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The paper provides the corrections and extensions of the paper of the same title, published in vol. 35, 2008, pp. 165–174 of the current journal. The analytical solutions of Michell trusses constructed within the L-shaped domains are confirmed by the ground structure method of the truss optimization, thus giving the upper bounds of the exact solutions.


 
New analytical benchmarks for topology optimization and their implications. Part I: bi-symmetric trusses with two point loads between supports PDF Print E-mail
structural optimizationNew analytical benchmarks for topology optimization and their implications. Part I: bi-symmetric trusses with two point loads between supports, Tomasz Sokół · George I. N. Rozvany
Structural and Multidisciplinary Optimization, vol. 46 (4) (2012), 477-486,
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Extending some results by Sokół and Lewiński (Struct Multidisc Optim 42:835–853, 2010), the optimal topology of bi-symmetric trusses with two symmetrically placed pointloads is determined analytically, and verified by highly accurate numerical calculations. It is rather remarkable that Michell’s best-known classical solution had to wait over hundred years for its generalization from one to two point loads. Some implications of these solutions, including properties of so-called O-regions, are also discussed.

 
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