A symmetry reduction method for continuum structural topology optimization

Kosaka, Iku; Swan, Colby C.

doi:10.1016/s0045-7949(98)00158-8

Cited by 77 publications

(24 citation statements)

References 30 publications

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“…In order to overcome the above weakness, it is necessary to define a design variable such as a continuously distributed density variable that has been used in the previous studies [19] for topology optimization. Therefore, a MACO algorithm is suggested in order to remedy the weakness of the standard ACO algorithm.…”

Section: Modified Ant Colony Optimization Algorithmmentioning

confidence: 99%

Topology optimum design of compliant mechanisms using modified ant colony optimization

Yoo

Han

2015

J Mech Sci Technol

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A Modified ant colony optimization (MACO) algorithm was suggested for topology optimal design of compliant mechanisms since standard ACO cannot provide an appropriate optimal topology. In order to improve computational efficiency and suitability of standard ACO algorithm in topology optimization for compliant mechanisms, a continuous variable, called the "Element contribution significance (ECS)," is employed, which serves to replace the positions of ants in the standard ACO algorithm, and assess the importance of each element in the optimization process. MACO algorithm was applied to topology optimizations of both linear and geometrically nonlinear compliant mechanisms using three kinds of objective functions, and optimized topologies were compared each other. From the comparisons, it was concluded that MACO algorithm can effectively be applied to topology optimizations of linear and geometrically nonlinear compliant mechanisms, and the ratio of Mutual potential energy (MPE) to Strain energy (SE) type of objective function is the best for topology optimal design of compliant mechanisms.

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Section: Modified Ant Colony Optimization Algorithmmentioning

confidence: 99%

Topology optimum design of compliant mechanisms using modified ant colony optimization

Yoo

Han

2015

J Mech Sci Technol

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“…The optimization problem is thus stated to minimize the reciprocal of the rst (or minimum) critical buckling load as follows: ( 27) subject to the normal bound constraints on the design variables [Eq. (1)], the linear, structural equilibrium state equation…”

Section: B Optimization Problemmentioning

confidence: 99%

“…24;25 Frequently, though certainly not always, however, multiple eigenvalues occur in symmetrical structures and are actually attributableto the structural symmetry. 26 In such cases approachesthat reduce the design space in accordance with the symmetry 27 can render the repeated eigenvalues fully differentiable in the reduced design space.…”

Section: B Optimization Problemmentioning

confidence: 99%

Continuum Topology Optimization of Buckling-Sensitive Structures

Rahmatalla

Swan

2002

43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Two formulations for continuum topologyoptimizationof structures taking buckling considerations into account are developed, implemented, and compared. In the rst, the structure undergoing a speci ed loading is modeled as a hyperelastic continuum at nite deformations and is optimized to maximize the minimum critical buckling load. In the second, the structure under a similar loading is modeled as linear elastic, and the critical buckling load is computed with linearized buckling analysis. Speci c issues addressed include usage of suitable "mixing rules," a node-based design variable formulation, techniques for eliminating regions devoid of structural material from the analysis problem, and consistent design sensitivity analysis. The performance of the formulations is demonstrated on the design of different structures. When problems are solved with moderate loads and generous material usage constraints, designs using compression and tension members are realized. Alternatively, when fairly large loads together with very stringent material usage constraints are imposed, structures utilizing primarily tension members result. Issues that arise when designing very light structures with stringent material usage constraints are discussed along with the importance of considering potential geometrical instabilities in the concept design of structural systems.

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“…More recent attempts on the simultaneous shape and topology optimization of di!erent design objectives including frequency/dynamic response have achieved some success. The most notable advance is the homogenization method [9,10], the density function method [11,12] and the continuum formulations [13,14]. Also, repeated frequency as encountered in dynamic problems especially in the above-mentioned aircraft design has been investigated extensively [14}18].…”

Section: Introductionmentioning

confidence: 99%