Lagrangian Description Based Topology Optimization—A Revival of Shape Optimization

2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Weisheng Zhang ◽  
Jian Zhang ◽  
Xu Guo
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Structural Design ◽  
Previous Treatment ◽  
Lagrangian Description ◽  
Design And Optimization ◽  
Lagrangian Framework ◽  
And Topology ◽  
Moving Morphable Components ◽  
Classical Shape

Unlike in the previous treatment where shape and topology optimization were carried out essentially in an Eulerian framework, the aim of the present work is to show how to perform topology optimization based on a Lagrangian framework, which is seamlessly consistent with classical shape optimization approaches, with use of a set of moving morphable components (MMCs). It is hoped that the present work may light up the revival of classical shape optimization in structural design and optimization and inspire some subsequent works along this direction. Some representative examples are also provided to illustrate the effectiveness of the proposed solution framework.

scholarly journals A Level Set Method in Shape and Topology Optimization for Variational Inequalities

2007 ◽  
Vol 17 (3) ◽  
pp. 413-430 ◽  
Author(s):  
Piotr Fulmański ◽  
Antoine Laurain ◽  
Jean-Francois Scheid ◽  
Jan Sokołowski
Keyword(s):  
Topology Optimization ◽  
Variational Inequalities ◽  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Energy Functional ◽  
Optimization Techniques ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Topological Derivatives

A Level Set Method in Shape and Topology Optimization for Variational InequalitiesThe level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

A Computational Framework for Design and Optimization of Flexoelectric Materials

2019 ◽  
Vol 17 (01) ◽  
pp. 1850097 ◽  
Author(s):  
Hamid Ghasemi ◽  
Harold S. Park ◽  
Naif Alajlan ◽  
Timon Rabczuk
Keyword(s):  
Topology Optimization ◽  
Electromechanical Coupling ◽  
Electromechanical Coupling Coefficient ◽  
Multiple Constraints ◽  
Computational Framework ◽  
Design And Optimization ◽  
Density Mapping ◽  
And Topology ◽  
Mapping Techniques ◽  
Continuous Approximations

We combine isogeometric analysis (IGA), level set (LS) and pointwise density-mapping techniques for design and topology optimization of piezoelectric/flexoelectric materials. We use B-spline elements to discretize the fourth-order partial differential equations of flexoelectricity, which require at least [Formula: see text] continuous approximations. We adopt the multiphase vector LS model which easily copes with various numbers of material phases and multiple constraints. In case studies, we first confirm the accuracy of the IGA model and then provide numerical examples for both pure and composite flexoelectric structures. The results demonstrate the significant enhancement in electromechanical coupling coefficient that can be obtained using topology optimization and particularly by multi-material topology optimization for flexoelectric composites.

Structural Topology Optimization Through Explicit Boundary Evolution

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Weisheng Zhang ◽  
Wanying Yang ◽  
Jianhua Zhou ◽  
Dong Li ◽  
Xu Guo
Keyword(s):  
Topology Optimization ◽  
Optimal Designs ◽  
Structural Topology ◽  
B Spline ◽  
Numerical Examples ◽  
Optimization Framework ◽  
And Topology ◽  
Spline Curves ◽  
Structural Boundary ◽  
Moving Morphable Components

Traditional topology optimization is usually carried out with approaches where structural boundaries are represented in an implicit way. The aim of the present paper is to develop a topology optimization framework where both the shape and topology of a structure can be obtained simultaneously through an explicit boundary description and evolution. To this end, B-spline curves are used to describe the boundaries of moving morphable components (MMCs) or moving morphable voids (MMVs) in the structure and some special techniques are developed to preserve the smoothness of the structural boundary when topological change occurs. Numerical examples show that optimal designs with smooth structural boundaries can be obtained successfully with the use of the proposed approach.

Analysis and topology optimization structural design excavator bucket tooth using finite element method

2020 ◽  
Author(s):  
Sumar Hadi Suryo ◽  
Wijdan Muhammad Fawwaz ◽  
Yogi Adi Wijaya ◽  
Eko Wahyu Saputro ◽  
Harto
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Structural Design ◽  
Excavator Bucket ◽  
And Topology ◽  
Element Method

scholarly journals Sequentially coupled shape and topology optimization for 2.5D and 3D beam models

2021 ◽  
Author(s):  
Zhijun Wang ◽  
Akke S. J. Suiker ◽  
Hèrm Hofmeyer ◽  
Twan van Hooff ◽  
Bert Blocken
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Cantilever Beam ◽  
Computational Efficiency ◽  
Optimization Approach ◽  
Beam Model ◽  
Shape And Topology Optimization ◽  
Beam Elements ◽  
And Topology ◽  
Beam Type

AbstractA sequentially coupled shape and topology optimization framework is presented in which the outer geometry and the internal topological layout of beam-type structures are optimized simultaneously. The outer geometry of the beam-type structures is parametrically described by non-uniform rational B-splines (NURBS), which guarantees a highly accurate description of the structural shape and enable an efficient control of the design domain with only a few control points. The computational efficiency of the coupled optimization approach is assured by applying a gradient-based optimization algorithm, for which the sensitivities are derived in closed form. The formulation of the coupled optimization approach is tailored toward 2.5D and full 3D representations of beam structures used in engineering applications. The 2.5D beam model, which has been taken from the literature, uses standard beam elements to simulate the beam response in the longitudinal direction, whereby the cross-sectional properties of the beam elements are calculated from additional 2D finite element method (FEM) analyses. A comparison study of a cantilever beam problem subjected to pure shape optimization and pure topology optimization illustrates that the 2.5D and 3D beam models lead to similar shape and topology designs, but that the 2.5D beam model has a significantly higher computational efficiency. Specifically, the computational times for the 2.5D model are about a factor 70 (shape optimization) and 1.4 (topology optimization) lower than for the 3D model, which indicates that in the coupled optimization approach the optimization of the shape provides the largest contribution to the higher computational efficiency of the 2.5D model. The coupled shape and topology optimization analysis subsequently performed on the 2.5D cantilever beam model demonstrates that the specific order at which the alternating shape and topology optimization increments are performed in the staggered update procedure turns out to have some influence on the computational speed and the value of the minimal compliance computed. Despite these differences, the final beam structures following from the different staggered update procedures illustrate how shape and topology can be efficiently optimized in an integrated, coupled fashion.

Generating Constructal Networks for Area-to-Point Conduction Problems Via Moving Morphable Components Approach

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Baotong Li ◽  
Chengbin Xuan ◽  
Guoguang Liu ◽  
Jun Hong
Keyword(s):  
Finite Element Method ◽  
Arbitrary Direction ◽  
Electromagnetic Bandgap ◽  
Design Algorithm ◽  
Flexible Modeling ◽  
Lagrangian Framework ◽  
Design Variables ◽  
Simulation And Experiment ◽  
Moving Morphable Components ◽  
Classical Shape

In this article, we focus on a generative design algorithm for area-to-point (AP) conduction problems in a Lagrangian framework. A physically meaningful continuous area to point path solution is generated through an adaptive growth procedure, which starts from the source point and extends spreading the whole conduction domain. This is achieved by using a set of special moving morphable components (MMCs) whose contour and skeleton are described explicitly by parameterized level-set surfaces. Unlike in the conventional methods where topology optimization was carried out in an Eulerian framework, the proposed optimizer is Lagrangian in nature, which is consistent with classical shape optimization approaches, giving great potential to reduce the total number of design variables significantly and also yielding more flexible modeling capability to control the structural feature sizes. By doing this, the growth elements are separated from the underlying finite element method (FEM) grids so that they can grow toward an arbitrary direction to form an optimized area-to-point path solution. The method is tested on an electromagnetic bandgap (EBG) power plane design example; both simulation and experiment verified the effectiveness of the proposed method.

Truss Design and Optimization Using Stress Analysis and NURBS Curves

2018 ◽  
Author(s):  
Antonio Caputi ◽  
Miri Weiss Cohen ◽  
Caterina Rizzi ◽  
Davide Russo
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Elastic Energy ◽  
Solid Material ◽  
Parametric Representation ◽  
Optimization Method ◽  
Design And Optimization ◽  
Spline Curves ◽  
Topology And Shape Optimization ◽  
Gradient Based

This paper presents a novel design methodology, which combines topology and shape optimization to define material distribution in the structural design of a truss. Firstly, in order to identify the best layout, the topology optimization process in the design domain is carried out by applying the BESO (Bidirectional Evolutionary Structural Optimization) method. In this approach, the low energy elements are eliminated from an initial mesh, and a new geometry is constructed. This new geometry consists of a set of elements with a higher elastic energy. This results in a new division of material providing different zones, some subjected to higher stress and others containing less elastic energy. Moreover, the elements of the final mesh are re-arranged and modified, considering the distribution of tension. This new arrangement is constructed by aligning and rotating the original mesh elements coherently to the principal directions. In the Shape Optimization stage, the resulting TO (Topology Optimization) geometry is refined. A process of replacing the tabular mesh is performed by rearranging the remaining elements. The vertices of the mesh are set as control polygon vertices and used as reference to define the NURBS (Non-Uniform Rational B-Spline) curves. This provides a parametric representation of the boundaries, outlining the high elastic energy zones. The final stage is the optimization of the continuous and analytically defined NURBS curve outlining the solid material domain. The Shape Optimization is carried out applying a gradient-based optimization method.

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