Topology optimization using a mixed formulation: An alternative way to solve pressure load problems

Sigmund, Ole; Clausen, Peter M.

doi:10.1016/j.cma.2006.09.021

Cited by 178 publications

(146 citation statements)

References 26 publications

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“…Recently, it has also been demonstrated that by varying the shear modulus G and the bulk modulus K, the acoustic domain and the structural domain can be described simultaneously [22,23,28]; see Table 1 or reference [7]. Compared to a segregated analysis procedure, a disadvantage of the mixed displacement/pressure formulation is the increased system size due to the additional primary variables, which is significant especially for three dimensional problems.…”

Section: Basic Principles Of the Mixed Finite Element Formulationmentioning

confidence: 99%

“…In [7], a mixed formulation was used to solve topology optimization problems with pressure loads, however, to our knowledge, this paper is the first to employ the mixed displacement/pressure formulation for topology optimization of acoustic-structure interaction problems.…”

Section: A Mixed Finite Element Formulation For Acoustic-structure Inmentioning

confidence: 99%

“…Hence, we propose a simpler method without the need for explicit boundary representation. The method is based on density based material interpolation schemes, by adopting a mixed displacement/pressure finite element procedure [7,22].…”

Section: A Mixed Finite Element Formulation For Acoustic-structure Inmentioning

confidence: 99%

“…This mixed formulation has previously been suggested for efficient and accurate acoustic-structure interaction analysis [22,23,24]. Our idea to use the mixed formulation in connection with topology optimization comes from previous work on topology optimization of pressure loaded structures [7]. Instead of defining separate and distinct equilibrium equations for the two physical domains, we define a mixed displacement/pressure finite element formulation on the whole domain with both displacements and pressure as primary variables.…”

Section: Introductionmentioning

confidence: 99%

“…These applications, however, have mostly been restricted to problems where the multi-physics behavior is limited to the material-part of the design. The problems become much more complex if the governing equations for the "void" regions are different from those of the material regions, as seen for pressure loads [7,8] or electrostatic actuation [9]. The main problem here is to define a parameterization of the interface between the solid and void regions that allows for topology changes.…”

Section: Introductionmentioning

confidence: 99%

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

Yoon

Jensen

Sigmund

2006

Numerical Meth Engineering

184

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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.

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Section: Basic Principles Of the Mixed Finite Element Formulationmentioning

confidence: 99%

Section: A Mixed Finite Element Formulation For Acoustic-structure Inmentioning

confidence: 99%

Section: A Mixed Finite Element Formulation For Acoustic-structure Inmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Yoon

Jensen

Sigmund

2006

Numerical Meth Engineering

184

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Topology Optimization

Maute

2017

Encyclopedia of Computational Mechanics Second Edition

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Topology optimization is a computational approach to systematically optimize the conceptual layout and the geometry of a body on the basis of a basic description of a design problem. In contrast to other design optimization methods, the outer shape of the body and the geometry of the material interfaces within the body may undergo radical changes in the optimization process, including both shape and topological changes. This unique feature reduces significantly the dependence of the optimized design on the initial guess from which the optimization process is started and allows finding nonintuitive solutions for complex design problems. Formulating optimization problems that yield meaningful, practical designs requires a solid understanding of the physical phenomena that dominate the body's functionality, as well as insight into the mathematical characteristics of the high‐dimensional design spaces used in topology optimization. Topology optimization methods involve a broad variety of computational techniques for describing the geometry of the body, predicting the physical phenomena of interest, and searching for the optimum design. This chapter provides an introduction to modern topology optimization. Instead of providing a comprehensive overview, the most important and widely used approaches are discussed in sufficient detail to provide the reader with a basic understanding of the state of the art of topology optimization.

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From Bioinspiration to Computer Generation: Developments in Autonomous Soft Robot Design

Pinskier

Howard

2021

Advanced Intelligent Systems

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The emerging field of soft robotics presents a new paradigm for robot design in which “precision through rigidity” is replaced by “cognition through compliance.” Lightweight and flexible, soft robots have vast potential to interact with fragile objects and navigate unstructured environments. Like octopuses and worms in nature, soft robots’ flexible bodies conform to hard objects and reconfigure for different tasks, delegating the burden of control from brain to body through embodied cognition. However, because of the lack of efficient modeling and simulation tools, soft robots are primarily designed by hand. Typically, hard components from rigid robots or living creatures are heuristically substituted for comparable soft ones. Autonomous design and manufacturing methodologies are urgently required to produce bespoke, high‐performing robots. Currently, design methodologies exist between simple but realistic parametric optimizations, and evolutionary algorithms which simulate morphology and control coevolution. To find high‐performing designs, novel high‐fidelity simulators and high‐throughput manufacturing and testing processes are required to explore the complex soft material, morphology and control landscape, blending simulation, and experimental data. This article reviews the state of the art in autonomous soft robotic design. Existing manual and automated designs are surveyed and future directions to automate soft robot design and manufacturing are presented.

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Topology optimization using a mixed formulation: An alternative way to solve pressure load problems

Cited by 178 publications

References 26 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

Topology Optimization

From Bioinspiration to Computer Generation: Developments in Autonomous Soft Robot Design

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