Evolutionary topological optimization of vibrating continuum structures for natural frequencies

Huang, Xiaodong; Zuo, Zhi Hao; Xie, Yi Min

doi:10.1016/j.compstruc.2009.11.011

Cited by 219 publications

(99 citation statements)

References 27 publications

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“…Again, even though our structure is enclosed to a fluid domain, our design domain will consist to a solid-void region. Thus, the sensitivity numbers to rank the elemental sensitivities are identical to the ones proposed by Huang et al [15] as…”

Section: Materials Interpolation Scheme and Sensitivity Numbersmentioning

confidence: 57%

“…It is important to point out that also when x min tends to 0, x i = x min for a void element, which indicates that the element is not completely eliminated from the design domain as proposed for the soft-kill BESO method [15,21].…”

Section: Materials Interpolation Scheme and Sensitivity Numbersmentioning

confidence: 99%

“…For the soft-kill BESO method developed by Huang et al [15], to keep the ratio between mass and stiffness constant when x i = x min it is required that…”

Section: Materials Interpolation Scheme and Sensitivity Numbersmentioning

confidence: 99%

“…In this case, the sensitivity number is a local index and represent the sensitivity of each element with respect to the objective function. Studies with the BESO method have recently been published presenting convergent and mesh independent solutions for stiffness maximization [14], for natural frequency maximization [15] and others. Critical analysis of ESO-based methods are found in [16], while a later review about the ESO/BESO methods is found in [17] and a book is also available [18].…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary Topology Optimization for Fluid-structure Interaction Problems and Natural Frequency Maximization

Picelli¹,

Vicente²,

Pavanello³

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. Multiphysics systems including dynamic fluid-structure interaction problems have hardly been studied in several fields of mechanical engineering. Among others, we can cite the researches in vibrations of submerged structures and the design of poroacoustic absorbing systems. Structural Topology Optimization can be applied in this class of problems in order to obtain new materials and structures. In this paper, it is presented the topology optimization based on volume constraints and natural frequency maximization of fluid-structure interaction problems. The method used in this work is the Bi-directional Evolutionary Structural Optimization (BESO), which consists in a successive elimination and replacement of elements in the design domain. This domain is defined initially and through a sensitivity analysis of the structure's eigenvalue solution, the evolutionary algorithm remove or add solid elements. The aim of this work is to propose a new version of the BESO method applied to fluid-structure interaction systems. We consider the case of free vibration of structures attached to a fixed fluid domain. Numerical results show that the BESO method can be applied to this kind of multiphysics problem.

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Section: Materials Interpolation Scheme and Sensitivity Numbersmentioning

confidence: 57%

Section: Materials Interpolation Scheme and Sensitivity Numbersmentioning

confidence: 99%

“…For the soft-kill BESO method developed by Huang et al [15], to keep the ratio between mass and stiffness constant when x i = x min it is required that…”

Section: Materials Interpolation Scheme and Sensitivity Numbersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evolutionary Topology Optimization for Fluid-structure Interaction Problems and Natural Frequency Maximization

Picelli¹,

Vicente²,

Pavanello³

2014

Proceedings of 10th World Congress on Computational Mechanics

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“…Beams, plates and 3D continua are treated and different numerical tools (penalization's) to obtain 1 -0 designs are applied. Among these papers are [2], [3], [4], [5], [6] and [7]. Note, that 1 -0 optimal designs is not the goal of the here presented research, that may be classified as traditional size optimization, where stiffness interpolation should be viewed instead from a physical point of view.…”

mentioning

confidence: 99%

Eigenfrequency optimized 3D continua, with possibility for cavities

Pedersen¹,

Pedersen²

2015

Journal of Sound and Vibration

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Eigenfrequency optimization for 3D continua is formulated and exemplified by the geometry and boundary conditions of a thick plate. Numerical finite element models are based on four node tetrahedra and results from subspace iterations give directly the basis for the continuum redesign. The 3D modeling with a large number of elements has the possibility in optimal design to obtain (as found) not only holes but also cavities in the continuum. Sensitivity analysis is presented on the element level with simple physical interpretation of the involved terms. This general result has general value for control of eigenfrequencies. It is found that in the combination of partial differentiation with the chain rule of differentiation, a specific notation is needed and a suggestion is presented.The optimization method is based on a derived optimality criterion, and as such the maximization problem change to a problem of determining a design with uniform values of this criterion. Non-linear stiffness interpolation may be a physical reality. A two parameter interpolation function is incorporated analytical, also in the sensitivity analysis and the optimality criterion, but without focusing on 1-0 optimal solutions. Two cases of boundary conditions, two cases of total amount of material, and cases of linear and non-linear stiffness interpolation are studied.

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A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

Munk

2018

Numerical Meth Engineering

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Summary A bidirectional evolutionary structural optimization algorithm is presented, which employs integer linear programming to compute optimal solutions to topology optimization problems with the objective of mass minimization. The objective and constraint functions are linearized using Taylor's first‐order approximation, thereby allowing the method to handle all types of constraints without using Lagrange multipliers or sensitivity thresholds. A relaxation of the constraint targets is performed such that only small changes in topology are allowed during a single update, thus ensuring the existence of feasible solutions. A variety of problems are solved, demonstrating the ability of the method to easily handle a number of structural constraints, including compliance, stress, buckling, frequency, and displacement. This is followed by an example with multiple structural constraints and, finally, the method is demonstrated on a wing‐box, showing that topology optimization for mass minimization of real‐world structures can be considered using the proposed methodology.

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Evolutionary topological optimization of vibrating continuum structures for natural frequencies

Cited by 219 publications

References 27 publications

Evolutionary Topology Optimization for Fluid-structure Interaction Problems and Natural Frequency Maximization

Evolutionary Topology Optimization for Fluid-structure Interaction Problems and Natural Frequency Maximization

Eigenfrequency optimized 3D continua, with possibility for cavities

A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

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