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.

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.

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.

Multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition

2021 ◽  
pp. 095440622110361
Author(s):  
Jinqing Zhan ◽  
Yu Sun ◽  
Min Liu ◽  
Benliang Zhu ◽  
Xianmin Zhang
Keyword(s):  
Boundary Condition ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Impedance Matching ◽  
Large Displacement ◽  
Thermal Impedance ◽  
Output Displacement ◽  
Topology Optimization Problem

Multi-material compliant mechanisms design enables potential design possibilities by exploiting the advantages of different materials. To satisfy mechanical/thermal impedance matching requirements, a method for multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition is presented in this study. In the optimization model, the element stacking method is employed to describe the material distribution and handle material-dependent boundary condition. The maximization of the output displacement of the compliant mechanism is developed as the objective function and the structural volume of each material is the constraint. Fictitious domain approach is applied to circumvent the numerical instabilities in topology optimization problem with geometrical nonlinearities. The method of moving asymptotes is applied to solve the optimization problem. Several numerical examples are presented to demonstrate the validity of the proposed method. The optimal topologies of the compliant mechanisms obtained by the proposed method can satisfy the specified material-dependent boundary condition.

Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements

2006 ◽  
Vol 129 (10) ◽  
pp. 1056-1063 ◽  
Author(s):  
Ashok Kumar Rai ◽  
Anupam Saxena ◽  
Nilesh D. Mankame
Keyword(s):  
Objective Function ◽  
Mechanical Response ◽  
Compliant Mechanisms ◽  
Element Formulation ◽  
Mechanical Responses ◽  
Design Variables ◽  
Lagrangian Finite Element ◽  
Synthesis Procedure ◽  
Synthesis Approach ◽  
Good Agreement

Initially curved frame elements are used in this paper within an optimization-based framework for the systematic synthesis of compliant mechanisms (CMs) that can trace nonlinear paths. These elements exhibit a significantly wider range of mechanical responses to applied loads than the initially straight frame elements, which have been widely used in the past for the synthesis of CMs. As a consequence, fewer elements are required in the design discretization to obtain a CM with a desired mechanical response. The initial slopes at the two nodes of each element are treated as design variables that influence not only the shape of the members in a CM, but also the mechanical response of the latter. Building on our prior work, the proposed synthesis approach uses genetic algorithms with both binary (i.e., 0/1) and continuous design variables in conjunction with a co-rotational total Lagrangian finite element formulation and a Fourier shape descriptors-based objective function. This objective function is chosen for its ability to provide a robust comparison between the actual path traced by a candidate CM design and the desired path. Two synthesis examples are presented to demonstrate the synthesis procedure. The resulting designs are fabricated as is, without any postprocessing, and tested. The fabricated prototypes show good agreement with the design intent.

Optimal tuned direct adaptive controller for seismic protecting of structures

2021 ◽  
pp. 1045389X2098878
Author(s):  
Amin Hosseini ◽  
Touraj Taghikhany ◽  
Milad Jahangiri
Keyword(s):  
Sensitivity Analysis ◽  
Adaptive Control ◽  
Optimization Problem ◽  
Adaptive Controller ◽  
Sensitivity Analyses ◽  
Building Structures ◽  
Building Structure ◽  
The Past ◽  
Innovative Method ◽  
Story Building

In the past few years, many studies have proved the efficiency of Simple Adaptive Control (SAC) in mitigating earthquakes’ damages to building structures. Nevertheless, the weighting matrices of this controller should be selected after a large number of sensitivity analyses. This step is time-consuming and it will not necessarily yield a controller with optimum performance. In the current study, an innovative method is introduced to tuning the SAC’s weighting matrices, which dispenses with excessive sensitivity analysis. In this regard, we try to define an optimization problem using intelligent evolutionary algorithm and utilized control indices in an objective function. The efficiency of the introduced method is investigated in 6-story building structure equipped with magnetorheological dampers under different seismic actions with and without uncertainty in the model of the proposed structure. The results indicate that the controller designed by the introduced method has a desirable performance under different conditions of uncertainty in the model. Furthermore, it improves the seismic performance of structure as compared to controllers designed through sensitivity analysis.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Sensitivity Analysis of a Radiative-Convective Model by the Adjoint Method

1982 ◽  
Vol 39 (9) ◽  
pp. 2038-2050 ◽  
Author(s):  
Matthew C. G. Hall ◽  
Dan G. Cacuci ◽  
Michael E. Schlesinger
Keyword(s):  
Sensitivity Analysis ◽  
Adjoint Method ◽  
Convective Model
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