Topology Optimization of Compliant Mechanisms Using Evolutionary Algorithm With Design Geometry Encoded as a Graph

2002 ◽  
Author(s):  
Shamim Akhtar ◽  
Kang Tai ◽  
Jitendra Prasad
Keyword(s):  
Topology Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Evolutionary Process ◽  
Optimization Procedure ◽  
Structural Topology ◽  
Mutation Operators ◽  
Design Variables ◽  
Straight Line

This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using an evolutionary algorithm (EA). The geometry representation scheme works by defining a skeleton which represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any EA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a graph which reflects this underlying topology so that the genetic crossover and mutation operators of the EA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

scholarly journals Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yue Wu ◽  
Qingpeng Li ◽  
Qingjie Hu ◽  
Andrew Borgart
Keyword(s):  
Topology Optimization ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimization Method ◽  
Structural Topology ◽  
Discrete Variables ◽  
And Topology ◽  
Design Variables ◽  
Improved Firefly Algorithm ◽  
Discrete Design Variables

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Stress Constraint ◽  
Cell Problem ◽  
Design Variables ◽  
Design Cell

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical, or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary, and every design cell is either solid or void to prevent gray cell problem that is usually caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum. No postprocessing is required for topology uncertainty caused by either point connection or gray cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Conduct Sensitivity Analysis

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is usually caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and avoid the need to select the initial guess solution and conduct sensitivity analysis. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

scholarly journals A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

2020 ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

Abstract In this paper a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability of generating connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. Lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize firefly algorithm based section of the hybrid algorithm. Input parameters, number of fireflies and number function evaluations were determined before implementation of firefly algorithm to solve formulated problems. Since direct application of firefly algorithm cannot generate connected topologies, outputs from firefly algorithm were used as an initial input material distribution for OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using OC method. Weight percentage reduction, maximum stress induced, optimal material distribution and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies and generated topologies are free from interference of end users, which only dependence on boundary conditions or the design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to OC method.

scholarly journals A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

2020 ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

Abstract In this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and number function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies and generated topologies are free from the interference of end-users, which only dependence on boundary conditions or the design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to the OC method.

scholarly journals A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

2020 ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

Abstract In this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and the number of function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies which are free from the interference of end-users, and only depend on boundary conditions or design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to the OC method.

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.

scholarly journals CARMA—Cellular Automata with Refined Mesh Adaptation—The Easy Way of Generation of Structural Topologies

2020 ◽  
Vol 10 (11) ◽  
pp. 3691
Author(s):  
Katarzyna Tajs-Zielińska ◽  
Bogdan Bochenek
Keyword(s):  
Topology Optimization ◽  
Cellular Automata ◽  
Optimization Problems ◽  
Computational Cost ◽  
Mesh Adaptation ◽  
Structural Topology ◽  
Fine Grid ◽  
Fine Mesh ◽  
Design Variables ◽  
Resolution Level

This paper is focused on the development of a Cellular Automata algorithm with the refined mesh adaptation technique and the implementation of this algorithm in topology optimization problems. Traditionally, a Cellular Automaton is created based on regular discretization of the design domain into a lattice of cells, the states of which are updated by applying simple local rules. It is expected that during the topology optimization process the local rules responsible for the evaluation of cell states can drive the solution to solid/void resulting structures. In the proposed approach, the finite elements are equivalent to cells of an automaton and the states of cells are represented by design variables. While optimizing engineering structural elements, the important issue is to obtain well-defined solutions: in particular, topologies with smooth boundaries. The quality of the structural topology boundaries depends on the resolution level of mesh discretization: the greater the number of elements in the mesh, the better the representation of the optimized structure. However, the use of fine meshes implies a high computational cost. We propose, therefore, an adaptive way to refine the mesh. This allowed us to reduce the number of design variables without losing the accuracy of results and without an excessive increase in the number of elements caused by use of a fine mesh for a whole structure. In particular, it is not necessary to cover void regions with a very fine mesh. The implementation of a fine grid is expected mainly in the so-called grey regions where it has to be decided whether a cell becomes solid or void. The benefit of the proposed approach, besides the possibility of obtaining high-resolution, sharply resolved fine optimal topologies with a relatively low computational cost, is also that the checkerboard effect, mesh dependency, and the so-called grey areas can be eliminated without using any additional filtering. Moreover, the algorithm presented is versatile, which allows its easy combination with any structural analysis solver built on the finite element method.

scholarly journals A firefly algorithm based hybrid method for structural topology optimization

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

AbstractIn this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and the number of function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies which are free from the interference of end-users, and only depend on boundary conditions or design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5 to 15% compared to the OC method.

Sign in / Sign up

Export Citation Format

Share Document