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S. Schwarz, K. Maute, E. Ramm (2001)
Topology and shape optimization for elastoplastic structural responseComputer Methods in Applied Mechanics and Engineering, 190
Bingyang Chen, N. Kikuchi (2001)
Topology optimization with design-dependent loadsFinite Elements in Analysis and Design, 37
M. Bendsøe (2009)
Topology Optimization
A. Klarbring, J. Petersson, B. Torstenfelt, M. Karlsson (2003)
Topology optimization of flow networksComputer Methods in Applied Mechanics and Engineering, 192
S. Rahmatalla, C. Swan (2004)
A Q4/Q4 continuum structural topology optimization implementationStructural and Multidisciplinary Optimization, 27
O. Sigmund, P. Clausen (2007)
Topology optimization using a mixed formulation: An alternative way to solve pressure load problemsComputer Methods in Applied Mechanics and Engineering, 196
C. Cinquini, M. Bruggi (2006)
ON THE USE OF MIXED FINITE ELEMENTS IN TOPOLOGY OPTIMIZATIONFoundations of Civil and Environmental Engineering
Q. Liang, Y. Xie, G. Steven (2000)
Optimal Topology Design of Bracing Systems for Multistory Steel FramesJournal of Structural Engineering-asce, 126
O. Sigmund (2000)
A new class of extremal compositesJournal of The Mechanics and Physics of Solids, 48
Q. Liang, G. Steven (2002)
A performance-based optimization method for topology design of continuum structures with mean compliance constraintsComputer Methods in Applied Mechanics and Engineering, 191
(1998)
2004), where among the others a CST formulation is tested showing the arising of the undesired phenomenon. A mixed formulation using continuous linear
C. Fleury (1989)
CONLIN: An efficient dual optimizer based on convex approximation conceptsStructural optimization, 1
James Guest, J. Prévost, T. Belytschko (2004)
Achieving minimum length scale in topology optimization using nodal design variables and projection functionsInternational Journal for Numerical Methods in Engineering, 61
H. Leipholz (1983)
On direct methods in the calculus of variationsComputer Methods in Applied Mechanics and Engineering, 37
M. Bendsøe, O. Sigmund (1999)
Material interpolation schemes in topology optimizationArchive of Applied Mechanics, 69
Claes Johnson, B. Mercier (1978)
Some equilibrium finite element methods for two-dimensional elasticity problemsNumerische Mathematik, 30
M. Bendsøe, N. Kikuchi (1988)
Generating optimal topologies in structural design using a homogenization methodApplied Mechanics and Engineering, 71
J. Petersson (1999)
Some convergence results in perimeter-controlled topology optimizationComputer Methods in Applied Mechanics and Engineering, 171
H. Eschenauer, N. Olhoff (2001)
Topology optimization of continuum structures: A review*Applied Mechanics Reviews, 54
T. Bruns, D. Tortorelli (2001)
Topology optimization of non-linear elastic structures and compliant mechanismsComputer Methods in Applied Mechanics and Engineering, 190
O. Sigmund, J. Petersson (1998)
Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minimaStructural optimization, 16
K. Matsui, Kenjiro Terada (2004)
Continuous approximation of material distribution for topology optimizationInternational Journal for Numerical Methods in Engineering, 59
T. Bruns, O. Sigmund, D. Tortorelli (2002)
Numerical methods for the topology optimization of structures that exhibit snap‐throughInternational Journal for Numerical Methods in Engineering, 55
P. Duysinx, M. Bendsøe (1997)
Topology Optimization of Continuum Structures with Stress Constraints
K. Svanberg (1987)
The method of moving asymptotes—a new method for structural optimizationInternational Journal for Numerical Methods in Engineering, 24
Alejandro Díaaz, N. Kikuchi (1992)
Solutions to shape and topology eigenvalue optimization problems using a homogenization methodInternational Journal for Numerical Methods in Engineering, 35
F. Brezzi, M. Fortin (2011)
Mixed and Hybrid Finite Element Methods, 15
G. Jang, Je Jeong, Yoon Kim, D. Sheen, Chunjae Park, Myoungnyoun Kim (2003)
Checkerboard‐free topology optimization using non‐conforming finite elementsInternational Journal for Numerical Methods in Engineering, 57
The paper presents a topology optimization formulation that uses mixed-finite elements, here specialized for the design of multi-loaded structures. The discretization scheme adopts stresses as primary variables in addition to displacements which usually are the only variables considered. Two dual variational formulations based on the Hellinger-Reissner variational principle are presented in continuous and discrete form. The use of the mixed approach coupled with the choice of nodal densities as optimization variables of the topology problem lead to 0–1 checkerboard-free solutions even in the case of multi-loaded structures design. The method of moving asymptotes (MMA) by Svanberg (1984) is adopted as minimization algorithm. Numerical examples are provided to show the capabilities of the presented method to generate families of designs responding to different requirements depending on stiffness criteria for common structural multi-load problems. Finally the ongoing research concerning the presence of stress constraints and the optimization of incompressible media is outlined.
Advances in Structural Engineering – SAGE
Published: Dec 1, 2007
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