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Ole Sigmund - One of the best experts on this subject based on the ideXlab platform.

  • reanalysis techniques for robust Topology Optimization
    2012
    Co-Authors: Oded Amir, Ole Sigmund, Boyan Stefanov Lazarov, Mattias Schevenels
    Abstract:

    The article focuses on the reduction of the computational eort involved in robust Topology Optimization procedures. The performance of structures designed by means of Topology Optimization may be seriously degraded due to fabrication errors. Robust formulations of the Optimization problem were shown to yield optimized designs that are tolerant with respect to such manufacturing uncertainties. The main drawback of such procedures is the added compu- tational cost associated with the need to evaluate a set of designs by performing multiple finite element analyses. In this article, we propose ecient robust Topology Optimization procedures based on reanalysis techniques. The approach is demonstrated on two compliant mechanism design problems where robust design is achieved by employing either a worst case formulation or a stochastic formulation. It is shown that the time spent on finite element analysis within robust Topology Optimization can be reduced significantly, without aecting the outcome of the Optimization process.

  • Topology Optimization for nano photonics
    Laser & Photonics Reviews, 2011
    Co-Authors: Jakob Søndergaard Jensen, Ole Sigmund
    Abstract:

    Topology Optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics applications. Topology Optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion. The Optimization problem is efficiently solved using mathematical programming-based Optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind Topology Optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices, and lists some of the future challenges in non-linear applications.

  • Topology Optimization for nano‐photonics
    Laser & Photonics Reviews, 2010
    Co-Authors: Jakob Søndergaard Jensen, Ole Sigmund
    Abstract:

    Topology Optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics applications. Topology Optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion. The Optimization problem is efficiently solved using mathematical programming-based Optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind Topology Optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices, and lists some of the future challenges in non-linear applications.

  • manufacturing tolerant Topology Optimization
    Acta Mechanica Sinica, 2009
    Co-Authors: Ole Sigmund
    Abstract:

    In this paper we present an extension of the Topology Optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick (dilated) structures compared to the intended Topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust Topology Optimization approach, under- and over-etching is modelled by image processing-based “erode” and “dilate” operators and the Optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using Topology Optimization.

Piotr Breitkopf - One of the best experts on this subject based on the ideXlab platform.

  • Recent Advances on Topology Optimization of Multiscale Nonlinear Structures
    Archives of Computational Methods in Engineering, 2017
    Co-Authors: Piotr Breitkopf
    Abstract:

    Research on Topology Optimization mainly deals with the design of monoscale structures, which are usually made of homogeneous materials. Recent advances of multiscale structural modeling enables the consideration of microscale material heterogeneities and constituent nonlinearities when assessing the macroscale structural performance. However, due to the modeling complexity and the expensive computing requirement of multiscale modeling, there has been very limited research on Topology Optimization of multiscale nonlinear structures. This paper reviews firstly recent advances made by the authors on Topology Optimization of multiscale nonlinear structures, in particular techniques regarding to nonlinear Topology Optimization and computational homogenization (also known as FE^2) are summarized. Then the conventional concurrent material and structure Topology Optimization design approaches are reviewed and compared with a recently proposed FE^2-based design approach, which treats the microscale Topology Optimization process integrally as a generalized nonlinear constitutive behavior. In addition, discussions on the use of model reduction techniques is provided in regard to the prohibitive computational cost.

  • Topology Optimization of multiscale elastoviscoplastic structures: Topology Optimization OF MULTISCALE ELASTOVISCOPLASTIC STRUCTURES
    International Journal for Numerical Methods in Engineering, 2015
    Co-Authors: Felix Fritzen, Liang Xia, Matthias Leuschner, Piotr Breitkopf
    Abstract:

    In this chapter, we take a step further toward the design of multiscale elastoviscoplastic structures using the multiscale design framework discussed in Chapter 1. This subject is extremely challenging from both aspects of Topology Optimization and multiscale modeling . First, unlike linear designs, Topology Optimization of elastovisoplastic structures encounters instability issues during the iterative solution process and the evaluation of sensitivities is more demanding. Second, the consideration of path-dependent plastic behavior at the microscopic scale results in significantly augmented computational burden in terms of computing time and storage requirement when using the FE 2 method.

Jakob Søndergaard Jensen - One of the best experts on this subject based on the ideXlab platform.

  • Topology Optimization for nano photonics
    Laser & Photonics Reviews, 2011
    Co-Authors: Jakob Søndergaard Jensen, Ole Sigmund
    Abstract:

    Topology Optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics applications. Topology Optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion. The Optimization problem is efficiently solved using mathematical programming-based Optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind Topology Optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices, and lists some of the future challenges in non-linear applications.

  • Topology Optimization for nano‐photonics
    Laser & Photonics Reviews, 2010
    Co-Authors: Jakob Søndergaard Jensen, Ole Sigmund
    Abstract:

    Topology Optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics applications. Topology Optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion. The Optimization problem is efficiently solved using mathematical programming-based Optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind Topology Optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices, and lists some of the future challenges in non-linear applications.

Anders Klarbring - One of the best experts on this subject based on the ideXlab platform.

  • Fatigue constrained Topology Optimization
    Structural and Multidisciplinary Optimization, 2014
    Co-Authors: Erik Holmberg, Bo Torstenfelt, Anders Klarbring
    Abstract:

    We present a contribution to a relatively unexplored application of Topology Optimization: structural Topology Optimization with fatigue constraints. A probability based high-cycle fatigue analysis is combined with principal stress calculations in order to find the Topology with minimum mass that can withstand prescribed variable-amplitude loading conditions for a specific life time. This allows us to generate optimal conceptual designs of structural components where fatigue life is the dimensioning factor. We describe the fatigue analysis and present ideas that make it possible to separate the fatigue analysis from the Topology Optimization. The number of constraints is kept low as they are applied to stress clusters, which are created such that they give adequate representations of the local stresses. Optimized designs constrained by fatigue and static stresses are shown and a comparison is also made between stress constraints based on the von Mises criterion and the highest tensile principal stresses. The paper is written with focus on structural parts in the avionic industry, but the method applies to any load carrying structure, made of linear elastic isotropic material, subjected to repeated loading conditions.

  • Stress constrained Topology Optimization
    Structural and Multidisciplinary Optimization, 2013
    Co-Authors: Erik Holmberg, Bo Torstenfelt, Anders Klarbring
    Abstract:

    This paper develops and evaluates a method for handling stress constraints in Topology Optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements. The three formulations and different approaches to stress constraints are compared using two well known test examples in Topology Optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained Topology Optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications.

Claus B W Pedersen - One of the best experts on this subject based on the ideXlab platform.

  • crashworthiness design of transient frame structures using Topology Optimization
    Computer Methods in Applied Mechanics and Engineering, 2004
    Co-Authors: Claus B W Pedersen
    Abstract:

    Abstract The aim of this paper is to present Topology Optimization as a method to obtain conceptual designs for crashworthiness. The Topology Optimization formulation uses rigorously computed sensitivities. The large displacements and plasticity of the 2D beam elements are modelled with the co-rotational formulation and the plastic zone formulation, respectively. Three examples are presented to show the results of combining Topology Optimization and crashworthiness Optimization.