Auxetic structure design using compliant mechanisms: A topology optimization approach with polygonal finite elements

2019 ◽  
Vol 129 ◽  
pp. 69-80 ◽  
Author(s):  
Cícero R. de Lima ◽  
Glaucio H. Paulino
Keyword(s):  
Topology Optimization ◽  
Finite Elements ◽  
Compliant Mechanisms ◽  
Structure Design ◽  
Optimization Approach ◽  
Polygonal Finite Elements ◽  
Auxetic Structure

An Evolutionary Multi-Objective Optimization Approach to the Topology Optimization of Auxetic Structures

2002 ◽  
Author(s):  
Ashraf O. Nassef
Keyword(s):  
Topology Optimization ◽  
Elastic Modulus ◽  
Finite Elements ◽  
Multiobjective Optimization ◽  
Poisson Ratio ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Finite Elements Analysis ◽  
Multi Objective ◽  
Auxetic Structures

Auxetic structures are ones, which exhibit an in-plane negative Poisson ratio behavior. Such structures can be obtained by specially designed honeycombs or by specially designed composites. The design of such honeycombs and composites has been tackled using a combination of optimization and finite elements analysis. Since, there is a tradeoff between the Poisson ratio of such structures and their elastic modulus, it might not be possible to attain a desired value for both properties simultaneously. The presented work approaches the problem using evolutionary multiobjective optimization to produce several designs rather than one. The algorithm provides the designs that lie on the tradeoff frontier between both properties.

Design of Compliant Structural Mechanisms Using B-Spline Elements

2011 ◽  
Author(s):  
Ashok V. Kumar ◽  
Anand Parthasarathy
Keyword(s):  
Inverse Problem ◽  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Spline Approximation ◽  
Structural Response ◽  
Field Application ◽  
Optimization Approach ◽  
Objective Functions ◽  
B Spline ◽  
Spline Basis

Structural design is an inverse problem where the geometry that fits a specific design objective is found iteratively through repeated analysis or forward problem solving. In the case of compliant structures, the goal is to design the structure for a particular desired structural response that mimics traditional mechanisms and linkages. It is possible to state the inverse problem in many different ways depending on the choice of objective functions used and the method used to represent the shape. In this paper, some of the objective functions that have been used in the past, for the topology optimization approach to designing compliant mechanisms are compared and discussed. Topology optimization using traditional finite elements often do not yield well-defined smooth boundaries. The computed optimal material distributions have shape irregularities unless special techniques are used to suppress them. In this paper, shape is represented as the contours or level sets of a characteristic function that is defined using B-spline approximation to ensure that the contours, which represent the boundaries, are smooth. The analysis is also performed using B-spline elements which use B-spline basis functions to represent the displacement field. Application of this approach to design a few simple mechanisms is presented.

Topology Optimization of Three-Dimensional Woven Materials Using a Ground Structure Design Variable Representation

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Seung-Hyun Ha ◽  
Hak Yong Lee ◽  
Kevin J. Hemker ◽  
James K. Guest
Keyword(s):  
Topology Optimization ◽  
Design Variable ◽  
Three Dimensional ◽  
Structure Design ◽  
Optimization Approach ◽  
Ground Structure ◽  
Flow Equations ◽  
Combined Algorithm ◽  
Variable Representation ◽  
3D Weaving

Three-dimensional (3D) weaving has recently arisen as viable means for manufacturing metallic, architected microlattices. Herein, we describe a topology optimization approach for designing the architecture of such 3D woven lattices. A ground structure design variable representation is combined with linear manufacturing constraints and a projection mapping to realize lattices that satisfy the rather restrictive topological constraints associated with 3D weaving. The approach is demonstrated in the context of inverse homogenization to design lattices with maximized fluid permeability. Stokes flow equations with no-slip conditions governing unit cell flow fields are interpolated using the Darcy–Stokes finite element model, leveraging existing work in the topology optimization of fluids. The combined algorithm is demonstrated to design manufacturable lattices with maximized permeability whose properties have been experimentally measured in other published work.

scholarly journals Topology Optimization considering Nonsmooth Structural Boundaries in the Intersection Areas of the Components

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ruichao Lian ◽  
Shikai Jing ◽  
Zefang Shi ◽  
Zhijun He ◽  
Guohua Song
Keyword(s):  
Topology Optimization ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Optimization Approach ◽  
Structural Topology ◽  
Topology Description Function ◽  
Structural Responses ◽  
Structure Boundary ◽  
Compliance Problem ◽  
The Impact

In the structural topology optimization approaches, the Moving Morphable Component (MMC) is a new method to obtain the optimized structural topologies by optimizing shapes, sizes, and locations of components. However, the optimized structure boundary usually generates local nonsmooth areas due to incomplete connection between components. In the present paper, a topology optimization approach considering nonsmooth structural boundaries in the intersection areas of the components based on the MMC is proposed. The variability of components’ shape can be obtained by constructing the topology description function (TDF) with multiple thickness and length variables. The shape of components can be modified according to the structural responses during the optimization process, and the relatively smooth structural boundaries are generated in the intersection areas of the components. To reduce the impact of the initial layout on the rate of convergence, this method is implemented in a hierarchical variable calling strategy. Compared with the original MMC method, the advantage of the proposed approach is that the smoothness of the structural boundaries can be effectively improved and the geometric modeling ability can be enhanced in a concise way. The effectiveness of the proposed method is demonstrated for topology optimization of the minimum compliance problem and compliant mechanisms.

Polygonal finite elements for topology optimization: A unifying paradigm

2009 ◽  
Vol 82 (6) ◽  
pp. 671-698 ◽  
Author(s):  
Cameron Talischi ◽  
Glaucio H. Paulino ◽  
Anderson Pereira ◽  
Ivan F. M. Menezes
Keyword(s):  
Topology Optimization ◽  
Finite Elements ◽  
Polygonal Finite Elements

Auxetic Structure Design: A Multi-material Topology Optimization with Energy-Based Homogenization Approach

2021 ◽  
pp. 1018-1032
Author(s):  
T. M. Tran ◽  
Q. H. Nguyen ◽  
T. T. Truong ◽  
T. N. Nguyen ◽  
N. M. Nguyen
Keyword(s):  
Topology Optimization ◽  
Structure Design ◽  
Homogenization Approach ◽  
Auxetic Structure

A Global Constraint on Relative Rotation to Avoid Lumped Compliant Mechanisms in Topology Optimization

2008 ◽  
Author(s):  
Sangamesh R. Deepak
Keyword(s):  
Topology Optimization ◽  
Finite Elements ◽  
Elastic Deformation ◽  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Compliant Mechanisms ◽  
Benchmark Problems ◽  
Global Constraint ◽  
Relative Rotation ◽  
Local Constraint

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However, it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint on the following benchmark problems — displacement inverter and gripper.

Design of Compliant Mechanisms for Amplification of Induced Strain Actuators

1999 ◽  
Author(s):  
Shawn Canfield ◽  
Mary I. Frecker
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Procedure ◽  
Computation Time ◽  
Mechanical Efficiency ◽  
Optimality Criteria ◽  
Optimization Approach ◽  
Detail Design ◽  
Problem Formulations

Abstract The focus of this paper is on designing compliant mechanism amplifiers for piezoelectric actuators using a topology optimization approach. Two optimization formulations are developed: one in which the overall stroke amplification or geometric advantage (GA) is maximized, and another where the mechanical efficiency (ME) of the amplifier is maximized. Two solution strategies are used, Sequential Linear Programming (SLP) and an Optimality Criteria method, and results are compared with respect to computation time and mechanism performance. Design examples illustrate the characteristics of both problem formulations, and physical prototypes have been fabricated as proof of concept. An automated detail design procedure has also been developed which allows the topology optimization results obtained in MATLAB to be directly translated into a neutral 3-D solid geometry format for import into other CAE programs.

Design of Grip-and-Move Manipulators Using Symmetric Path Generating Compliant Mechanisms

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
N. F. Wang ◽  
K. Tai
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Optimization Procedure ◽  
Problem Formulation ◽  
Optimization Approach ◽  
Structural Topology ◽  
Graph Theoretic ◽  
Mutation Operators ◽  
Future Work ◽  
Crossover And Mutation

This paper presents the problem formulation and design of compliant grip-and-move manipulators. Each manipulator is composed of two identical path generating compliant mechanisms such that it can grip an object and convey it from one point to another. The integration of both gripping and moving behaviors within a simple mechanism is accomplished by the use of compliant mechanisms, which generate paths that are symmetric. The automated synthesis of these symmetric path generating mechanisms is by a structural topology optimization approach. The problem of topology optimization of continuum structures is solved using a multiobjective genetic algorithm coupled with a morphological representation of geometry that efficiently defines the variable structural geometry upon a finite element grid. A graph-theoretic chromosome encoding together with compatible crossover and mutation operators are then applied to form an effective evolutionary optimization procedure. Two designs have been created and are presented in this paper, and some concluding remarks and future work are put forward.

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