L-System-Generated Topology Optimization of Compliant Mechanisms Using Graph-Based Interpretation

2018 ◽  
Author(s):  
Brent R. Bielefeldt ◽  
Darren J. Hartl ◽  
Ergun Akleman
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Level Set Methods ◽  
Optimization Techniques ◽  
L System ◽  
Design Variables ◽  
System L ◽  
Reconfigurable Structures

Traditional topology optimization techniques, such as density-based and level set methods, have proven successful in identifying potential design configurations but suffer from rapidly increasing design space dimensionality and convergence to local minima. A heuristic alternative to these approaches couples a genetic algorithm with a Lindenmayer System (L-System), which encodes design variables and governs the development of the structure when coupled with some sort of interpreter. This work discusses the development of a graph-based interpretation scheme referred to as Spatial Interpretation for the Development of Reconfigurable Structures (SPIDRS). This framework allows for the effective exploration of the design space using a limited number of design variables. The theory and implementation of this method are detailed, and a compliant mechanism case study is presented to demonstrate the ability of SPIDRS to generate structures capable of achieving multiple design goals.

L-System-Generated Mechanism Topology Optimization Using Graph-Based Interpretation

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Brent R. Bielefeldt ◽  
Ergun Akleman ◽  
Gregory W. Reich ◽  
Philip S. Beran ◽  
Darren J. Hartl
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Level Set Methods ◽  
Optimization Techniques ◽  
L System ◽  
Design Variables ◽  
System L ◽  
Multiple Case ◽  
Multiple Case Studies ◽  
Reconfigurable Structures

Traditional topology optimization techniques, such as density-based and level set methods, have proven successful in identifying potential design configurations for structures and mechanisms but suffer from rapidly increasing design space dimensionality and the possibility of converging to local minima. A heuristic alternative to these approaches couples a genetic algorithm with a Lindenmayer system (L-system), which encodes design variables and governs the development of the structure when coupled with an interpreter to translate genomic information into structural topologies. This work discusses the development of a graph-based interpretation scheme referred to as spatial interpretation for the development of reconfigurable structures (SPIDRS). This framework allows for the effective exploration of mechanism design spaces using a limited number of design variables. The theory and implementation of this method are detailed, and multiple case studies are presented to demonstrate the ability of SPIDRS to generate adaptive structures capable of achieving multiple design goals.

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.

Graph-Based Interpretation of L-System Encodings Toward Aeroelastic Topology Optimization of a Morphing Airfoil in Supersonic Flow

2019 ◽  
Author(s):  
Brent R. Bielefeldt ◽  
Darren J. Hartl ◽  
Joshua D. Hodson ◽  
Gregory W. Reich ◽  
Philip S. Beran ◽  
...  
Keyword(s):  
Supersonic Flow ◽  
Performance Criteria ◽  
Preliminary Design ◽  
Structural Topology ◽  
L System ◽  
Design Variables ◽  
System L ◽  
Interpretation Algorithm ◽  
Actuation Systems ◽  
Reconfigurable Structures

Abstract This work details the preliminary design of a morphing airfoil in supersonic flow using evolutionary design principles. The structural topology of the airfoil includes a fixed outer mold line, fixed spars, and designable internal stiffeners and actuators. The designable components are generated using a bio-inspired model known as a Lindenmayer System (L-System), which encodes design variables and governs the development of a structural topology when coupled with an interpretation algorithm. Here, we utilize a graph-based interpretation scheme known as Spatial Interpretation for the Development of Reconfigurable Structures (SPIDRS), which has been shown to effectively explore the mechanism design space using a limited number of design variables. The optimization process behind this preliminary design problem is discussed, and optimal airfoil topologies capable of meeting specified aerodynamic performance criteria are presented in hopes of gaining a better understanding of how actuation systems could be integrated into the next generation of aircraft.

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.

Multiobjective Topology Extraction of the Compliant Mechanisms

2014 ◽  
Vol 971-973 ◽  
pp. 1941-1948
Author(s):  
Zhao Kun Li ◽  
Hua Mei Bian ◽  
Li Juan Shi ◽  
Xiao Tie Niu
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Threshold Value ◽  
Jump Discontinuity ◽  
Engineering Practice ◽  
Distribution Method ◽  
Black And White ◽  
Design Variables

Homogenization or material distribution method based topology optimization will create final topologies in grey level image and saw tooth jump discontinuity boundaries that are not suitable for direct engineering practice, so it is necessary to extract the topological diagram. And a new topology extraction method for compliant mechanisms is presented. In the fist stage, the grey image is transferred into the black-and white finite element topology optimization results. The threshold value meeting to objective function is obtained so that each element is either empty or solid; in the second stage, the density contour approach is used by redistributing nodal densities to generate the smooth boundaries; in the third stage, Smooth boundaries are represented by parameterized B-spline curves whose control points selected from the viewpoint of stiffness and flexibility constitute the parameters ready to undergo shape optimization; Then shape optimization is executed to improve stress-based local performance, The parameters that present the outer shape of the compliant mechanism are used as design variables; In the final stage, simulations of numerical examples are presented to show the validity of the proposed method.

scholarly journals Integrated Multi-Step Design Method for Practical and Sophisticated Compliant Mechanisms Combining Topology and Shape Optimizations

2007 ◽  
Vol 19 (2) ◽  
pp. 141-147
Author(s):  
Masakazu Kobayashi ◽  
◽  
Shinji Nishiwaki ◽  
Hiroshi Yamakawa ◽  
◽  
...  
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Traditional Methods ◽  
Second Stage ◽  
Spring Element ◽  
Design Variables ◽  
Additional Constraints

Compliant mechanisms designed by traditional topology optimization have a linear output response, and it is difficult for traditional methods to implement mechanisms having nonlinear output responses, such as nonlinear deformation or path. To design a compliant mechanism having a specified nonlinear output path, we propose a two-stage design method based on topology and shape optimizations. In the first stage, topology optimization generates an initial conceptual compliant mechanism based on ordinary design conditions, with “additional” constraints used to control the output path in the second stage. In the second stage, an initial model for the shape optimization is created, based on the result of the topology optimization, and additional constraints are replaced by spring elements. The shape optimization is then executed, to generate the detailed shape of the compliant mechanism having the desired output path. At this stage, parameters that represent the outer shape of the compliant mechanism and of spring element properties are used as design variables in the shape optimization. In addition to configuring the specified output path, executing the shape optimization after the topology optimization also makes it possible to consider the stress concentration and large displacement effects. This is an advantage offered by the proposed method, because it is difficult for traditional methods to consider these aspects, due to inherent limitations of topology optimization.

Design of Compliant Mechanisms of Distributed Compliance Using a Level-Set Based Topology Optimization Method

2011 ◽  
Vol 110-116 ◽  
pp. 2319-2323 ◽  
Author(s):  
Yu Wang ◽  
Zhen Luo
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Operator Splitting ◽  
Level Set Methods ◽  
Optimization Method ◽  
Energy Functional ◽  
Structural Shape ◽  
Geometric Size

This paper presents a level set-based structural shape and topology optimization for the design of compliant mechanisms. The design boundary of the compliant mechanism is implicitly represented as the zero level-set of a higher-dimensional level set surface. A quadratic energy functional is introduced to augment the objective function in order to control the structural geometric size of the resulting mechanism. The optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints. A semi-implicit scheme with an additive operator splitting (AOS) algorithm is used to solve the Hamilton-Jacobi partial differential equation (PDE) in the level set method. In doing so, it is expected that numerical difficulties in most conventional level set methods can be eliminated. The final mechanism is characterized with strip-like members able to generate distributed compliance, and so that to resolve the hinge problem long sought-after in the design of compliant mechanisms. Typical numerical case is used to evidence the effectiveness of this method in the design of monolithic compliant mechanisms.

scholarly journals A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

2021 ◽  
Vol 26 (2) ◽  
pp. 34
Author(s):  
Isaac Gibert Martínez ◽  
Frederico Afonso ◽  
Simão Rodrigues ◽  
Fernando Lau
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Volume Fraction ◽  
Optimization Techniques ◽  
Free Form ◽  
Aerodynamic Shape Optimization ◽  
Sequential Approach ◽  
Airfoil Surface ◽  
Aerodynamic Shape ◽  
Design Variables

The objective of this work is to study the coupling of two efficient optimization techniques, Aerodynamic Shape Optimization (ASO) and Topology Optimization (TO), in 2D airfoils. To achieve such goal two open-source codes, SU2 and Calculix, are employed for ASO and TO, respectively, using the Sequential Least SQuares Programming (SLSQP) and the Bi-directional Evolutionary Structural Optimization (BESO) algorithms; the latter is well-known for allowing the addition of material in the TO which constitutes, as far as our knowledge, a novelty for this kind of application. These codes are linked by means of a script capable of reading the geometry and pressure distribution obtained from the ASO and defining the boundary conditions to be applied in the TO. The Free-Form Deformation technique is chosen for the definition of the design variables to be used in the ASO, while the densities of the inner elements are defined as design variables of the TO. As a test case, a widely used benchmark transonic airfoil, the RAE2822, is chosen here with an internal geometric constraint to simulate the wing-box of a transonic wing. First, the two optimization procedures are tested separately to gain insight and then are run in a sequential way for two test cases with available experimental data: (i) Mach 0.729 at α=2.31°; and (ii) Mach 0.730 at α=2.79°. In the ASO problem, the lift is fixed and the drag is minimized; while in the TO problem, compliance minimization is set as the objective for a prescribed volume fraction. Improvements in both aerodynamic and structural performance are found, as expected: the ASO reduced the total pressure on the airfoil surface in order to minimize drag, which resulted in lower stress values experienced by the structure.

Structural Analysis and Optimal Design of Lightweight Skate for Loading and Unloading

2013 ◽  
Vol 785-786 ◽  
pp. 1258-1261
Author(s):  
In Pyo Cha ◽  
Hee Jae Shin ◽  
Neung Gu Lee ◽  
Lee Ku Kwac ◽  
Hong Gun Kim
Keyword(s):  
Topology Optimization ◽  
Structural Analysis ◽  
Optimal Design ◽  
Optimization Techniques ◽  
Normal Operation ◽  
Stress And Strain ◽  
Initial Model ◽  
Design Variables ◽  
Model Set ◽  
Main Frame

Topology optimization and shape optimization of structural optimization techniques are applied to transport skate the lightweight. Skate properties by varying the design variables and minimize the maximum stress and strain in the normal operation, while reducing the volume of the objective function of optimal design and Skate the static strength of the constraints that should not degrade compared to the performance of the initial model. The skates were used in this study consists of the main frame, sub frame, roll, pin main frame only structural analysis and optimal design was performed using the finite element method. Simplified initial model set design area and it compared to SM45C, AA7075, CFRP, GFRP was using the topology optimization. Strength does not degrade compared to the initial model, decreased volume while minimizing the stress and strain results, the optimum design was achieved efficient lightweight.

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