Multiobjective Topology Optimization of Compliant Microgripper With Geometrically Nonlinearity

2007 ◽  
Author(s):  
Zhaokun Li ◽  
Xianmin Zhang
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Structural Response ◽  
Decision Function ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Conflicting Objectives ◽  
Incremental Scheme ◽  
Moving Asymptotes

Since compliant mechanism is usually required to perform in more than one environment, the ability to consider multiple objectives has to be included within the framework of topology optimization. And the topology optimization of micro-compliant mechanisms is actually a geometrically nonlinear problem. This paper deals with multiobjective topology optimization of micro-compliant mechanisms undergoing large deformation. The objective function is defined by the minimum compliance and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements. The weighted sum of conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear structural response is calculated using a Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material with penalization approach is used in design of compliant mechanisms. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. These methods are further investigated and realized with the numerical example of compliant microgripper, which is simulated to show the availability of this approach proposed in this paper.

Multiobjective Topology Optimization of Multi-Input and Multi-Output Compliant Mechanisms with Geometrically Nonlinearity

2013 ◽  
Vol 706-708 ◽  
pp. 864-877
Author(s):  
Zhao Kun Li ◽  
Xian Min Zhang ◽  
Hua Mei Bian ◽  
Xiao Tie Niu
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Decision Function ◽  
Output Coupling ◽  
Element Formulation ◽  
Conflicting Objectives ◽  
Incremental Scheme ◽  
Coupling Terms ◽  
Suppression Strategy ◽  
Moving Asymptotes

Multiple degree-of-freedom compliant mechanisms are widely used in the fields of micro-positioning and micro-manipulation. This paper deals with multiobjective topology optimization of multi-input and multi-output compliant mechanisms undergoing large deformation. The objective function is defined by the minimum compliance and maximum geometric advantage to meet both stiffness and flexibility requirements. The suppression strategy of input and output coupling terms is studied and the expression of the output coupling terms is further developed. The weighted sum of the conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear mechanism response is calculated using the Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material with penalization approach is used in design of compliant mechanisms. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. Numerical examples of multiple inputs and outputs are presented to show the validity of the new method. Simulation results show that the compliant mechanisms can be deformed in the desirable manner and the coupling output displacements are suppressed significantly by using the presented method.

Topology Optimization of Large-Displacement Flexure Hinges

2015 ◽  
Author(s):  
Min Liu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Large Displacement ◽  
Element Formulation ◽  
Nonlinear Behaviour ◽  
Geometrically Nonlinear ◽  
Flexure Hinges ◽  
Lagrangian Finite Element ◽  
Moving Asymptotes

Research on topology optimization of compliant mechanisms is extensive but the design of flexure hinges using topology optimization method is comparatively rare. This paper deals with topology optimization of flexure hinges undergoing large-displacement. The basic optimization model is developed for topology optimization of the revolute hinge. The objective function for the synthesis of large-displacement flexure hinges are proposed together with constraints function. The geometrically nonlinear behaviour of flexure hinge is modelled using the total Lagrangian finite element formulation. The equilibrium is found by using a Newton-Raphson iterative scheme. The sensitivity analysis of the objective functions are calculated by the adjoint method and the optimization problem is solved using the method of moving asymptotes (MMA). Numerical examples are used to show the validity of the proposed method and the differences between the results obtained by linear and nonlinear modelling are large.

scholarly journals Topology Optimization of Multi-Materials Compliant Mechanisms

2021 ◽  
Vol 11 (9) ◽  
pp. 3828
Author(s):  
Wenjie Ge ◽  
Xin Kou
Keyword(s):  
Topology Optimization ◽  
Elastic Modulus ◽  
Optimization Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Least Square ◽  
Convergent Method ◽  
Material Conditions ◽  
Moving Asymptotes

In this article, a design method of multi-material compliant mechanism is studied. Material distribution with different elastic modulus is used to meet the rigid and flexible requirements of compliant mechanism at the same time. The solid isotropic material with penalization (SIMP) model is used to parameterize the design domain. The expressions for the stiffness matrix and equivalent elastic modulus under multi-material conditions are proposed. The least square error (LSE) between the deformed and target displacement of the control points is defined as the objective function, and the topology optimization design model of multi-material compliant mechanism is established. The oversaturation problem in the volume constraint is solved by pre-setting the priority of each material, and the globally convergent method of moving asymptotes (GCMMA) is used to solve the problem. Widely studied numerical examples are conducted, which demonstrate the effectiveness of the proposed method.

Piezoelectric Actuator Performance Metrics and Relation to Compliant Mechanism Design

2001 ◽  
Author(s):  
Hima Maddisetty ◽  
Mary Frecker
Keyword(s):  
Topology Optimization ◽  
Performance Metrics ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanical Efficiency ◽  
High Energy ◽  
High Energy Density ◽  
High Bandwidth ◽  
Compliant Mechanism Design ◽  
Actuator Performance

Abstract Piezoceramic actuators have gained widespread use due to their desirable qualities of high force, high bandwidth, and high energy density. Compliant mechanisms can be designed for maximum stroke amplification of piezoceramic actuators using topology optimization. In this paper, the mechanical efficiency and other performance metrics of such compliant mechanism/actuator systems are studied. Various definitions of efficiency and other performance metrics of actuators with amplification mechanisms from the literature are reviewed. These metrics are then applied to two compliant mechanism example problems and the effect of the stiffness of the external load is investigated.

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.

Topology Synthesis of Large-Displacement Compliant Mechanisms

1999 ◽  
Author(s):  
Claus B. W. Pedersen ◽  
Thomas Buhl ◽  
Ole Sigmund
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Problem ◽  
Adjoint Method ◽  
Compliant Mechanisms ◽  
Large Displacement ◽  
Element Formulation ◽  
Method Of Moving Asymptotes ◽  
Synthesis Tool ◽  
Lagrangian Finite Element ◽  
Moving Asymptotes

Abstract This paper describes the use of topology optimization as a synthesis tool for the design of large-displacement compliant mechanisms. An objective function for the synthesis of large-displacement mechanisms is proposed together with a formulation for synthesis of path-generating compliant mechanisms. The responses of the compliant mechanisms are modelled using a Total Lagrangian finite element formulation, the sensitivity analysis is performed using the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. Procedures to circumvent some numerical problems are discussed.

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.

The Comparision of Hybrid and Quadrilateral Discretization Models for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Author(s):  
Hong Zhou ◽  
Nitin M. Dhembare
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Search Space ◽  
Structural Members ◽  
Constraint Violation ◽  
Local Connection ◽  
Hybrid Discretization ◽  
Local Topology ◽  
Design Cell

The design domain of a synthesized compliant mechanism is discretized into quadrilateral design cells in both hybrid and quadrilateral discretization models. However, quadrilateral discretization model allows for point connection between two diagonal design cells. Hybrid discretization model completely eliminates point connection by subdividing each quadrilateral design cell into triangular analysis cells and connecting any two contiguous quadrilateral design cells using four triangular analysis cells. When point connection is detected and suppressed in quadrilateral discretization, the local topology search space is dramatically reduced and slant structural members are serrated. In hybrid discretization, all potential local connection directions are utilized for topology optimization and any structural members can be smooth whether they are in the horizontal, vertical or diagonal direction. To compare the performance of hybrid and quadrilateral discretizations, the same design and analysis cells, genetic algorithm parameters, constraint violation penalties are employed for both discretization models. The advantages of hybrid discretization over quadrilateral discretization are obvious from the results of two classical synthesis examples of compliant mechanisms.

Dynamic Topology Optimization of Compliant Mechanisms and Piezoceramic Actuators

2002 ◽  
Author(s):  
Hima Maddisetty ◽  
Mary Frecker
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Method ◽  
Mechanical Efficiency ◽  
Optimal Topology ◽  
Driving Frequency ◽  
Spring Stiffness ◽  
Piezoceramic Actuator ◽  
Near Resonance

A topology optimization method is developed to design a piezoelectric ceramic actuator together with a compliant mechanism coupling structure for dynamic applications. The objective is to maximize the mechanical efficiency with a constraint on the capacitance of the piezoceramic actuator. Examples are presented to demonstrate the effect of considering dynamic behavior compared to static behavior, and the effect of sizing the piezoceramic actuator on the optimal topology and the capacitance of the actuator element. Comparison studies are also presented to illustrate the effect of damping, external spring stiffness, and driving frequency. The optimal topology of the compliant mechanism is shown to be dependent on the driving frequency, the external spring stiffness, and if the piezoelectric actuator element is considered as design or non-design. At high driving frequencies, it was found that the dynamically optimized structure is very near resonance.

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