Geometric Optimization of Spatial Multimaterial Compliant Mechanisms and Structures Using Three-Dimensional Multilayer Wide Curves

2009 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Geometric Optimization ◽  
Programming Algorithm ◽  
Variable Cross ◽  
Multiple Materials

Three-dimensional multilayer wide curves are spatial curves with variable cross sections and multiple materials. This paper introduces a geometric optimization method for spatial multimaterial compliant mechanisms and structures by using three-dimensional multilayer wide curves. In this paper, every multimaterial connection is represented by a three-dimensional multilayer wide curve and the whole spatial multimaterial compliant mechanism or structure is modeled as a set of connected three-dimensional multilayer wide curves. The geometric optimization of a spatial multimaterial compliant mechanism or structure is considered as the optimal selection of control parameters of the corresponding three-dimensional multilayer wide curves. The deformation and performance of spatial multimaterial compliant mechanisms and structures are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm. The effectiveness of the proposed geometric optimization procedure is verified by the demonstrated examples.

Geometric Optimization of Spatial Compliant Mechanisms Using Three-Dimensional Wide Curves

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Three Dimensional ◽  
Optimization Method ◽  
Geometric Optimization ◽  
Programming Algorithm ◽  
Variable Cross ◽  
Finite Element Procedure ◽  
And Performance

A three-dimensional wide curve is a spatial curve with variable cross sections. This paper introduces a geometric optimization method for spatial compliant mechanisms by using three-dimensional wide curves. In this paper, every material connection in a spatial compliant mechanism is represented by a three-dimensional wide curve and the whole spatial compliant mechanism is modeled as a set of connected three-dimensional wide curves. The geometric optimization of a spatial compliant mechanism is considered as the generation and optimal selection of the control parameters of the corresponding three-dimensional parametric wide curves. The deformation and performance of spatial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm.

Geometric Synthesis of Spatial Compliant Mechanisms Using Three-Dimensional Wide Curves

2008 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Method ◽  
Three Dimensional ◽  
Programming Algorithm ◽  
Variable Cross ◽  
Finite Element Procedure ◽  
And Performance ◽  
Selection Of

A three-dimensional wide curve is a spatial curve with variable cross sections. This paper introduces a geometric synthesis method for spatial compliant mechanisms by using three-dimensional wide curves. In this paper, every connection in a spatial compliant mechanism is represented by a three-dimensional wide curve and the whole spatial compliant mechanism is modeled as a set of connected three-dimensional wide curves. The geometric synthesis of a spatial compliant mechanism is considered as the generation and optimal selection of control parameters of the corresponding three-dimensional parametric wide curves. The deformation and performance of spatial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The optimization problem is solved by the MATLAB constrained nonlinear programming algorithm. The effectiveness of the proposed geometric procedures is verified by the demonstrated examples.

Wide Curve Based Geometric Optimization of Compliant Mechanisms

2005 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Geometric Optimization ◽  
Programming Algorithm ◽  
Free Form ◽  
Control Parameters ◽  
Practical Constraints

A wide curve is a curve with width or cross-section. This paper presents a geometric optimization method of compliant mechanisms based on the free form wide curve theory. With the proposed method, geometric optimization can be performed to further improve the performance of a compliant mechanism after its topology is selected. Every connection in the topology is represented as a parametric wide curve in which variable shape and size are fully described and conveniently controlled by the limited number of parameters. The geometric optimization is formulated on the control parameters of the wide curves corresponding to all connections in the topology. Problem-dependent objectives are optimized and practical constraints are imposed during the optimization process. The optimization problem is solved by the constrained nonlinear programming algorithm in Matlab Optimization Toolbox. An example is presented to verify the effectiveness of the proposed optimization procedure.

Geometric Modeling and Optimization of Multi-Material Compliant Mechanisms Using Multi-Layer Wide Curves

2007 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Geometric Optimization ◽  
Optimization Approach ◽  
Variable Cross ◽  
Modeling And Optimization ◽  
Multiple Materials

Multi-material compliant mechanisms enhance the performance of regular single-material compliant mechanisms by adding a new design option, material type variation. This paper introduces a geometric modeling method for multimaterial compliant mechanisms by using multi-layer wide curves. Based on the introduced modeling method, a geometric optimization approach for multi-material compliant mechanisms is proposed. A multi-layer wide curve is a curve with variable cross-sections and multiple materials. In this paper, every connection in the multi-material compliant mechanism is represented by a multi-layer wide curve and the whole mechanism is modeled as a set of connected multi-layer wide curves. The geometric modeling and optimization of a multi-material compliant mechanism are considered as the generation and optimal selection of the control parameters of the corresponding multi-layer wide curves. The deformation and performance of multi-material compliant mechanisms is evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the optimization process. The effectiveness of the proposed geometric modeling and optimization procedures is verified by the demonstrated examples.

Geometric Modeling and Synthesis of Spatial Multimaterial Compliant Mechanisms and Structures Using Three-Dimensional Multilayer Wide Curves

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Three Dimensional ◽  
Modeling Method ◽  
Synthesis Process ◽  
Variable Cross ◽  
Finite Element Procedure ◽  
Multiple Materials

A 3D multilayer wide curve is a spatial curve with variable cross sections and multiple materials. The performance of multimaterial compliant mechanisms and structures is enhanced by integrating multiple materials into one-piece configurations. This paper introduces a geometric modeling method for spatial multimaterial compliant mechanisms and structures by using 3D multilayer wide curves. Based on the introduced modeling method, a geometric synthesis approach is proposed. In this paper, every connection in a spatial multimaterial compliant mechanism or structure is represented by a 3D multilayer wide curve and the whole compliant mechanism or structure is modeled as a set of connected wide curves. The geometric modeling and synthesis are considered as the generation and optimization of the control parameters of the corresponding 3D multilayer wide curves. The performance of spatial multimaterial compliant mechanisms and structures is evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized and the practical constraints are imposed during the synthesis process. The effectiveness of the proposed geometric modeling and synthesis procedures is verified by the demonstrated examples.

Geometric Modeling and Optimization of Multimaterial Compliant Mechanisms Using Multilayer Wide Curves

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Geometric Optimization ◽  
Optimization Approach ◽  
Variable Cross ◽  
Modeling And Optimization ◽  
Multiple Materials

Multimaterial compliant mechanisms enhance the performance of regular single-material compliant mechanisms by adding a new design option, material type variation. This paper introduces a geometric modeling method for multimaterial compliant mechanisms by using multilayer wide curves. Based on the introduced modeling method, a geometric optimization approach for multimaterial compliant mechanisms is proposed. A multilayer wide curve is a curve with variable cross sections and multiple materials. In this paper, every connection in the multimaterial compliant mechanism is represented by a multilayer wide curve, and the whole mechanism is modeled as a set of connected multilayer wide curves. The geometric modeling and the optimization of a multimaterial compliant mechanism are considered as the generation and the optimal selection of the control parameters of the corresponding multilayer wide curves. The deformation and performance of multimaterial compliant mechanisms are evaluated by the isoparametric degenerate-continuum nonlinear finite element procedure. The problem-dependent objectives are optimized, and the practical constraints are imposed during the optimization process. The effectiveness of the proposed geometric modeling and optimization procedures is verified by the demonstrated examples.

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.

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.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Hybrid Discretization

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 no matter 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 grey cell problem that is usually caused by intermediate material states. Von Mises 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 choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions require no postprocessing or interpretation, and have no point flexure, unsmooth boundary and zigzag member. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples in compliant mechanisms.

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