Topology optimization of compliant mechanisms with geometrically nonlinear

2006 ◽  
Author(s):  
Li Zhaokun ◽  
Zhang Xianmin
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Geometrically Nonlinear

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.

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 Shape preserving design of geometrically nonlinear structures using topology optimization

2019 ◽  
Vol 59 (4) ◽  
pp. 1033-1051 ◽  
Author(s):  
Yu Li ◽  
Jihong Zhu ◽  
Fengwen Wang ◽  
Weihong Zhang ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Shape Preserving

Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications

1999 ◽  
Vol 123 (1) ◽  
pp. 33-42 ◽  
Author(s):  
A. Saxena ◽  
G. K. Ananthasuresh
Keyword(s):  
Finite Element ◽  
Linear Models ◽  
Compliant Mechanisms ◽  
Synthesis Method ◽  
Design Sensitivity ◽  
Finite Element Models ◽  
Geometrically Nonlinear ◽  
Linear Elastic ◽  
Nonlinear Design ◽  
Nonlinear Force

Optimal design methods that use continuum mechanics models are capable of generating suitable topology, shape, and dimensions of compliant mechanisms for desired specifications. Synthesis procedures that use linear elastic finite element models are not quantitatively accurate for large displacement situations. Also, design specifications involving nonlinear force-deflection characteristics and generation of a curved path for the output port cannot be realized with linear models. In this paper, the synthesis of compliant mechanisms is performed using geometrically nonlinear finite element models that appropriately account for large displacements. Frame elements are chosen because of ease of implementation of the general approach and their ability to capture bending deformations. A method for nonlinear design sensitivity analysis is described. Examples are included to illustrate the usefulness of the synthesis 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.

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