Structure topology optimization: fully coupled level set method via FEMLAB

Liu, Z.; Korvink, Jan G.; Huang, Ru

doi:10.1007/s00158-004-0503-z

Cited by 86 publications

(55 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Matlab based script FE-package is useful in implementing the finite element formulation and optimization since it allows easy implementation of different analysis domains and change of element types, etc. as well as for the possibility for semi-automated analytical sensitivity analysis, see [35,36,37].…”

Section: Implementation Of the U/p Mixed Finite Element Formulationmentioning

confidence: 99%

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

Yoon

Jensen

Sigmund

2006

Numerical Meth Engineering

179

View full text Add to dashboard Cite

SUMMARYThe paper presents a gradient based topology optimization formulation that allows to solve acousticstructure (vibro-acoustic) interaction problems without explicit boundary interface representation. In acoustic-structure interaction problems, the pressure and displacement fields are governed by Helmholtz equation and the elasticity equation, respectively. Normally, the two separate fields are coupled by surface-coupling integrals, however, such a formulation does not allow for free material redistribution in connection with topology optimization schemes since the boundaries are not explicitly given during the optimization process. In this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables (a u/p-formulation). The Helmholtz equation is obtained as a special case of the mixed formulation for the elastic shear modulus equating zero. Hence, by spatial variation of the mass density, shear and bulk moduli we are able to solve the coupled problem by the mixed formulation. Using this modeling approach, the topology optimization procedure is simply implemented as a standard density approach.Several two-dimensional acoustic-structure problems are optimized in order to verify the proposed method.

show abstract

Section: Implementation Of the U/p Mixed Finite Element Formulationmentioning

confidence: 99%

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

Yoon

Jensen

Sigmund

2006

Numerical Meth Engineering

179

View full text Add to dashboard Cite

show abstract

“…Refs. 18,19). However, in this paper we use the level set method proposed by van Dijk et al 14 in which the exact Heaviside function is used.…”

Section: Level Set Methods Using a Consistent Sensitivity Analysismentioning

confidence: 99%

Level Set Based Topology Optimization with Stress Constraints and Consistent Sensitivity Analysis

Verbart¹,

Langelaar²,

Dijk³

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

9
0
3
0

View full text Add to dashboard Cite

For aeronautical applications of topology optimization, it is of importance to develop topology optimization techniques, that can handle stress constraints in an efficient and accurate manner. The development of such topology optimization techniques is a challenging task due to the local nature of the stress constraints, their highly non-linear behaviour with respect to the design variables and the so-called singularity phenomenon. An accurate sensitivity analysis is essential for these type of problems with multiple constraints.In this paper, we propose a methodology of dealing with stress constraints in a level set based framework. In this framework, the level set function nodal values are related to element densities by an exact Heaviside projection. Stress relaxation and constraint aggregation techniques are used to deal with the singularity phenomenon and the local nature of the stress, respectively. A constrained optimization problem is then solved, in which the design variables (the level set nodal values) are updated in the projected steepest-descent direction, which is determined using a consistent sensitivity analysis.We demonstrate the effectiveness of this technique on two numerical examples. The results show that the level set method with a consistent sensitivity analysis allows for the treatment of multiple constraints by using constrained optimization techniques.

show abstract

“…In many shape optimization problems the topology of the optimal shape is not given a priori. One approach to allow the topology to adapt during a relaxation of the cost functional is to formulate the optimization problem in terms of shapes described by level sets -let us in particular refer to the approach by Allaire and coworkers [3,4,5,8] and to [28,38,55]. Explicitly, we assume the elastic body O to be represented by a level set function φ, that is O = {φ < 0}:={x ∈ D | φ(x) < 0}.…”

Section: Description Of Two Different Classes Of Admissible Shapesmentioning
confidence: 99%

On Shape Optimization with Stochastic Loadings
Atwal
¹
,
Conti
²
,
Geihe
³

et al. 2011
International Series of Numerical Mathematics
6
0
4
0
View full text Add to dashboard Cite

Abstract. This article is concerned with different approaches to elastic shape optimization under stochastic loading. The underlying stochastic optimization strategy builds upon the methodology of two-stage stochastic programming. In fact, in the case of linear elasticity and quadratic objective functional our strategy leads to a computational cost which scales linearly in the number of linearly independent applied forces, even for a large set of realization of the random loading. We consider, besides minimization of the expectation value of suitable objective functionals, also two different risk-averse approaches, namely the expected excess and the excess probability. Numerical computations are performed using either a level-set approach representing implicit shapes of general topology in combination with composite finite elements to resolve elasticity in two and three dimensions, or a collocation boundary element approach, where polygonal shapes represent geometric details attached to a lattice and describing a perforated elastic domain. Topology optimization is performed using the concept of topological derivatives. We generalize this concept, and derive an analytical expression which takes into account the interaction between neighboring holes. This is expected to allow efficient and reliable optimization strategies of elastic objects with a large number of geometries details on a fine scale. Mathematics Subject Classification (2000). 90C15, 74B05, 65N30, 65N38, 34E08, 49K45.Keywords. shape optimization in elasticity, two-stage stochastic programming, risk averse optimization, level set method, boundary element method, topological derivative.

show abstract

Structure topology optimization: fully coupled level set method via FEMLAB

Cited by 86 publications

References 16 publications

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

Level Set Based Topology Optimization with Stress Constraints and Consistent Sensitivity Analysis

On Shape Optimization with Stochastic Loadings

Contact Info

Product

Resources

About