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Journal ArticleDOI

Topology optimization approaches: A comparative review

21 Aug 2013-Structural and Multidisciplinary Optimization (Springer Berlin Heidelberg)-Vol. 48, Iss: 6, pp 1031-1055
TL;DR: An overview, comparison and critical review of the different approaches to topology optimization, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
Abstract: Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
Citations
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Journal ArticleDOI
TL;DR: A detailed survey of ongoing methodologies for soft actuators, highlighting approaches suitable for nanometer- to centimeter-scale robotic applications, including both the development of new materials and composites, as well as novel implementations leveraging the unique properties of soft materials.
Abstract: This review comprises a detailed survey of ongoing methodologies for soft actuators, highlighting approaches suitable for nanometer- to centimeter-scale robotic applications. Soft robots present a special design challenge in that their actuation and sensing mechanisms are often highly integrated with the robot body and overall functionality. When less than a centimeter, they belong to an even more special subcategory of robots or devices, in that they often lack on-board power, sensing, computation, and control. Soft, active materials are particularly well suited for this task, with a wide range of stimulants and a number of impressive examples, demonstrating large deformations, high motion complexities, and varied multifunctionality. Recent research includes both the development of new materials and composites, as well as novel implementations leveraging the unique properties of soft materials.

897 citations

Journal ArticleDOI
TL;DR: A comprehensive understanding of the interrelation between the various aspects of the subject, as this is essential to demonstrate credibility for industrial needs, is presented in this paper, which highlights some key topics requiring attention for further progression.

761 citations

Journal ArticleDOI
TL;DR: Bendsoe et al. as mentioned in this paper proposed a new computational framework for structural topology optimization based on the concept of moving morphable components, which can integrate the size, shape, and topological optimization in CAD modeling systems seamlessly.
Abstract: In the present work, we intend to demonstrate how to do topology optimization in an explicit and geometrical way. To this end, a new computational framework for structural topology optimization based on the concept of moving morphable components is proposed. Unlike in the traditional solution frameworks, where topology optimization is achieved by eliminating unnecessary materials from the design domain or evolving the structural boundaries, optimal structural topology is obtained by optimizing the layout of morphable structural components in the proposed approach. One of the advantages of the proposed approach, which may have great potential in engineering applications, is that it can integrate the size, shape, and topology optimization in CAD modeling systems seamlessly. The approach can combine both the advantages of explicit and implicit geometry descriptions for topology optimization. It also has the great potential to reduce the computational burden associated with topology optimization substantially. Some representative examples are presented to illustrate the effectiveness of the proposed approach. 1. M. P. Bendsoe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, 71:

701 citations

Journal ArticleDOI
TL;DR: A new computational framework for structural topology optimization based on the concept of moving morphable components is proposed, which can combine both the advantages of explicit and implicit geometry descriptions for topology Optimization.
Abstract: In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the proposed solution paradigm can incorporate more geometry and mechanical information into topology optimization directly and therefore render the solution process more flexible. It also has the great potential to reduce the computational burden associated with topology optimization substantially. Some representative examples are presented to illustrate the effectiveness of the proposed approach.

580 citations

Journal ArticleDOI
TL;DR: In this article, a survey of recent advances of topology optimization techniques applied in aircraft and aerospace structures design is presented, including standard material layout for airframe structures, layout design of stiffener ribs for aircraft panels, multi-component layout design for aerospace structural systems, and multi-fasteners design for assembled aircraft structures.
Abstract: Topology optimization has become an effective tool for least-weight and performance design, especially in aeronautics and aerospace engineering. The purpose of this paper is to survey recent advances of topology optimization techniques applied in aircraft and aerospace structures design. This paper firstly reviews several existing applications: (1) standard material layout design for airframe structures, (2) layout design of stiffener ribs for aircraft panels, (3) multi-component layout design for aerospace structural systems, (4) multi-fasteners design for assembled aircraft structures. Secondly, potential applications of topology optimization in dynamic responses design, shape preserving design, smart structures design, structural features design and additive manufacturing are introduced to provide a forward-looking perspective.

557 citations

References
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Journal ArticleDOI
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.

13,020 citations

Journal ArticleDOI
TL;DR: A comprehensive description of the primal-dual interior-point algorithm with a filter line-search method for nonlinear programming is provided, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix.
Abstract: We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlinear programming.

7,966 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a methodology for optimal shape design based on homogenization, which is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i.i.
Abstract: Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i~otropic material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements. The computation of effective material properties for the anisotropic material is carried out using the method of homogenization. Computational results are presented and compared with results obtained by boundary variations.

5,858 citations

Book
31 Oct 2002
TL;DR: A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.
Abstract: This book is an introduction to level set methods and dynamic implicit surfaces. These are powerful techniques for analyzing and computing moving fronts in a variety of different settings. While it gives many examples of the utility of the methods to a diverse set of applications, it also gives complete numerical analysis and recipes, which will enable users to quickly apply the techniques to real problems. The book begins with a description of implicit surfaces and their basic properties, then devises the level set geometry and calculus toolbox, including the construction of signed distance functions. Part II adds dynamics to this static calculus. Topics include the level set equation itself, Hamilton-Jacobi equations, motion of a surface normal to itself, re-initialization to a signed distance function, extrapolation in the normal direction, the particle level set method and the motion of co-dimension two (and higher) objects. Part III is concerned with topics taken from the fields of Image Processing and Computer Vision. These include the restoration of images degraded by noise and blur, image segmentation with active contours (snakes), and reconstruction of surfaces from unorganized data points. Part IV is dedicated to Computational Physics. It begins with one phase compressible fluid dynamics, then two-phase compressible flow involving possibly different equations of state, detonation and deflagration waves, and solid/fluid structure interaction. Next it discusses incompressible fluid dynamics, including a computer graphics simulation of smoke, free surface flows, including a computer graphics simulation of water, and fully two-phase incompressible flow. Additional related topics include incompressible flames with applications to computer graphics and coupling a compressible and incompressible fluid. Finally, heat flow and Stefan problems are discussed. A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.

5,526 citations

Book
17 Sep 2011
TL;DR: In this article, the authors proposed a topology optimization by distribution of isotropic material for truss structures with anisotropic materials, based on the topology design of truss structure.
Abstract: 1 Topology optimization by distribution of isotropic material- 2 Extensions and applications- 3 Design with anisotropic materials- 4 Topology design of truss structures- 5 Appendices- 6 Bibliographical notes- References- Author Index

4,881 citations