Spanning Tree Based Topological Optimization of Compliant Mechanisms

2005 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Compliant Mechanisms ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Topological Optimization ◽  
Deformation Analysis ◽  
Discrete Optimization Problem ◽  
Minimum Number ◽  
And Performance

In graph theory, spanning trees connect all the vertices together using minimum number of edges. A topological optimization method of compliant mechanisms is presented based on spanning tree theory. A valid topology is regarded as a network connecting input, output, support and intermediate nodes, which contains at least one spanning tree among the introduced nodes. Invalid disconnected topologies can be weeded out if no spanning tree is included. No further deformation analysis and performance evaluation is needed for invalid disconnected topologies. Problem-dependent objectives are optimized for topological optimization of compliant mechanisms. Constraints about maximum input displacement and input force, maximum stress and overlapping connections are directly imposed during the optimization process. The discrete optimization problem is solved by genetic algorithm with penalty function handling constraints. An example is presented to verify the effectiveness of the proposed optimization procedure.

Topological Synthesis of Compliant Mechanisms Using Spanning Tree Theory

2004 ◽  
Vol 127 (4) ◽  
pp. 753-759 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Spanning Tree ◽  
Maximum Stress ◽  
Spanning Trees ◽  
Compliant Mechanisms ◽  
Deformation Analysis ◽  
Discrete Optimization Problem ◽  
Minimum Number ◽  
Synthesis Procedure ◽  
And Performance ◽  
Topological Synthesis

This paper introduces the spanning tree theory to the topological synthesis of compliant mechanisms, in which spanning trees connect all the vertices together using a minimum number of edges. A valid topology is regarded as a network connecting input, output, support, and intermediate nodes, which contains at least one spanning tree among the introduced nodes. Invalid disconnected topologies can be weeded out if no spanning tree is included. No further deformation analysis and performance evaluation is needed to invalidate disconnected topologies. Problem-dependent objectives are optimized for topological synthesis of compliant mechanisms. Constraints about maximum input displacement and force, maximum stress and overlapping connections are directly imposed during optimization process. The discrete optimization problem is solved by genetic algorithm with penalty function handling constraints. Two examples are given to verify the effectiveness of the proposed synthesis procedure.

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 A location optimization method for aircraft weakly-rigid structures

2014 ◽  
Vol 5 ◽  
pp. A18
Author(s):  
Zhong-Qi Wang ◽  
Yuan Yang ◽  
Yong-Gang Kang ◽  
Zheng-Ping Chang
Keyword(s):  
Optimization Procedure ◽  
Optimization Method ◽  
Optimal Number ◽  
Deformation Analysis ◽  
Element Analysis ◽  
Application Study ◽  
Location Optimization ◽  
Large Size ◽  
Analysis Theory ◽  
Nonlinear Programming Methods

Since aircraft weakly-rigid structure has large size and weak stiffness, there has serious deformation during assembly process. The current deformation analysis theory of rigid assembly is not applicable. Based on the N-2-1 (N > 3) locating principle, this paper presents a methodology for weakly-rigid parts. An optimization algorithm combines finite element analysis and nonlinear programming methods to find the optimal number and position of the locating points in order to minimize the assembly deformation. An example application study is presented to demonstrate the optimization procedure and its effectiveness by using the software of ABAQUS.

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.

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.

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.

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.

An Optimization Procedure for the Aerodynamic Model Tuning of Centrifugal Compressor Stages

2011 ◽  
Author(s):  
Susanne Svensdotter ◽  
Omar El Shamy ◽  
Nidal Ghizawi ◽  
Vittorio Michelassi ◽  
Sivasubramaniyan Sankaran
Keyword(s):  
Experimental Data ◽  
Centrifugal Compressor ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Design Flow ◽  
Flow Coefficient ◽  
Prediction Tool ◽  
Tuning Parameters ◽  
Model Tuning ◽  
And Performance

This paper presents an automated optimization procedure for tuning and optimizing the performance parameters of centrifugal compressor stages in order to improve the accuracy of a 1D performance prediction tool and performance database. An in-house, well-validated 1D tool is used to predict the performance of centrifugal compressor stages. The stages are usually tested under similitude conditions in order to verify the predicted performance with the experimental data. Continuous improvements have been done on the tool to improve its accuracy, but the tuning to test data is still done manually and separately for each tested design flow coefficient. As a further leap in this activity, an in-house developed optimization code (PEZ) is interfaced with the 1D prediction tool to provide the best possible solution within the given tuning limits. This provides the possibility to use an extended number of tuning parameters and to tune the entire design family simultaneously, thereby ensuring a smooth evolution of the tuning parameters within the database. The optimization plan consists of a Differential Evolution (DE) genetic algorithm followed by a simplex-based optimization method (AMOEBA) with an objective of reducing the Root Mean Square (RMS) value of the error with the specified constraints. The procedure was successfully challenged with several families of similar stages but with various design corrected mass flows, by setting different objective/constraints combinations. The Optimizer was able to reduce the total RMS value of the error by approximately 80% with respect to the baseline for one of the recently tuned families. The result is a minimal deviation between predicted and experimental data for entire families, as well as a significant time reduction compared to the previous tuning methodology.

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.

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.

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