Compliant Mechanism Design Through Topology Optimization Using Pseudo-Rigid-Body Models

2016 ◽  
Author(s):  
Venkatasubramanian Kalpathy Venkiteswaran ◽  
Omer Anil Turkkan ◽  
Hai-Jun Su
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Rigid Body ◽  
Finite Element Methods ◽  
Compliant Mechanism ◽  
Beam Theory ◽  
Deformation Analysis ◽  
Optimization Approach ◽  
Algebraic Equations ◽  
Kinematic Loops

The initial design of compliant mechanisms for a specific application can be a challenging task. This paper introduces a topology optimization approach for planar mechanisms based on graph theory. It utilizes pseudo-rigid-body models, which allow the kinetostatic equations to be represented as nonlinear algebraic equations. This reduces the complexity of the system compared to beam theory or finite element methods, and has the ability to incorporate large deformations. Integer variables are used for developing the adjacency matrix, which is optimized by a genetic algorithm. Dynamic penalty functions describe the general and case-specific constraints. A symmetric 3R model is used to represent the beams in the mechanism. The design space is divided into rectangular segments while kinematic and static equations are derived using kinematic loops. The effectiveness of the approach is demonstrated with the example of an inverter mechanism. The results are compared against finite element methods to prove the validity of the new model as well as the accuracy of the approach outlined here. Future implementations of this method will include stress and deformation analysis and also introduce multi-material designs using different pseudo-rigid-body models.

Speeding Up Topology Optimization of Compliant Mechanisms With a Pseudorigid-Body Model

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Venkatasubramanian Kalpathy Venkiteswaran ◽  
Omer Anil Turkkan ◽  
Hai-Jun Su
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Solution Process ◽  
Beam Theory ◽  
Algebraic Equations ◽  
Element Analysis ◽  
System Equations ◽  
Kinematic Loops

This paper seeks to speed up the topology optimization using a pseudorigid-body (PRB) model, which allows the kinetostatic equations to be explicitly represented in the form of nonlinear algebraic equations. PRB models can not only accommodate large deformations but more importantly reduce the number of variables compared to beam theory or finite element methods. A symmetric 3R model is developed and used to represent the beams in a compliant mechanism. The design space is divided into rectangular segments, while kinematic and static equations are derived using kinematic loops. The use of the gradient and hessian of the system equations leads to a faster solution process. Integer variables are used for developing the adjacency matrix, which is optimized by a genetic algorithm. Dynamic penalty functions describe the general and case-specific constraints. The effectiveness of the approach is demonstrated with the examples of a displacement inverter and a crimping mechanism. The approach outlined here is also capable of estimating the stress in the mechanism which was validated by comparing against finite element analysis. Future implementations of this method will incorporate other pseudorigid-body models for various types of compliant elements and also try to develop multimaterial designs.

A Compliant Bistable Mechanism Design Incorporating Elastica Buckling Beam Theory and Pseudo-Rigid-Body Model

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Ümit Sönmez ◽  
Cem C. Tutum
Keyword(s):  
Rigid Body ◽  
Mechanism Design ◽  
Kinematic Analysis ◽  
Compliant Mechanism ◽  
Beam Theory ◽  
Algebraic Equations ◽  
Body Model ◽  
Buckling Beam ◽  
Rigid Body Model ◽  
Bistable Mechanism

In this work, a new compliant bistable mechanism design is introduced. The combined use of pseudo-rigid-body model (PRBM) and the Elastica buckling theory is presented for the first time to analyze the new design. This mechanism consists of the large deflecting straight beams, buckling beams, and a slider. The kinematic analysis of this new mechanism is studied, using nonlinear Elastica buckling beam theory, the PRBM of a large deflecting cantilever beam, the vector loop closure equations, and numerically solving nonlinear algebraic equations. A design method of the bistable mechanism in microdimensions is investigated by changing the relative stiffness of the flexible beams. The actuation force versus displacement characteristics of several cases is explored and the full simulation results of one of the cases are presented. This paper demonstrates the united application of the PRBM and the buckling Elastica solution for an original compliant mechanism kinematic analysis. New compliant mechanism designs are presented to highlight where such combined kinematic analysis is required.

Solving Topology Optimization Problems Using Wavelet Approximations

1998 ◽  
Author(s):  
Giuseppe C. A. DeRose ◽  
Alejandro R. Díaz
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Finite Element Methods ◽  
Condition Number ◽  
Optimization Problems ◽  
Mesh Size ◽  
Elasticity Problem ◽  
New Method ◽  
Galerkin Scheme

Abstract A new method to solve topology optimization problems is discussed. This method is based on the use of a Wavelet-Galerkin scheme to solve the elasticity problem associated with each iteration of the topology optimization sequence. Typically, finite element methods are used for this analysis. However, as the mesh size grows, the computational requirements necessary to solve the finite element equations increase beyond the capacity of current desk top computers. This problem is inherent to finite element methods, as the condition number of finite element matrices increases with mesh size. Wavelet-Galerkin techniques are used to replace standard finite element methods in an attempt to alleviate this problem. Examples demonstrating the performance of the new methodology are presented.

A scaled boundary finite element based explicit topology optimization approach for three‐dimensional structures

2020 ◽  
Vol 121 (21) ◽  
pp. 4878-4900
Author(s):  
Weisheng Zhang ◽  
Zhe Xiao ◽  
Chang Liu ◽  
Yue Mei ◽  
Sung‐kie Youn ◽  
...  
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Three Dimensional ◽  
Optimization Approach ◽  
Scaled Boundary Finite Element

Topology Optimization of Compliant Mechanisms Based on Interpolation Meshless Method and Geometric Nonlinearity

2019 ◽  
Author(s):  
Yonghong Zhang ◽  
Zhenfei Zhao ◽  
Yaqing Zhang ◽  
Wenjie Ge
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Galerkin Method ◽  
Meshless Method ◽  
Geometric Nonlinearity ◽  
Compliant Mechanism ◽  
Linear Convergence ◽  
The Finite Element Method ◽  
Element Method

Abstract In order to prevent mesh distortion problem arising in topology optimization of compliant mechanism with massive displacement, a meshless Galerkin method was proposed and studied in this paper. The element-free Galerkin method (EFG) is more accurate than the finite element method, and it does not need grids. However, it is difficult to impose complex boundaries. This paper presents a topology optimization method based on interpolation meshless method, which retains the advantages of the finite element method (FEM) that is easy to impose boundary conditions and high accuracy of the meshless method. At the same time, a method of gradually reducing step is proposed to solve the problem of non-linear convergence caused by low-density points in topology optimization. Numerical example shows that these techniques are valid in topology optimization of compliant mechanism considering the geometric nonlinearity, and simultaneously these techniques can also improve the convergence of nonlinearity.

Replacement of brake master cylinder spring by compliant mechanism – A topology optimization approach

2020 ◽  
Author(s):  
Yuvaraja Subramani ◽  
Arunkumar Gopal ◽  
K. Vijay ◽  
S. Vignesh
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanism ◽  
Optimization Approach ◽  
Master Cylinder

Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates

1990 ◽  
Vol 57 (3) ◽  
pp. 707-718 ◽  
Author(s):  
Bilin Chang ◽  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Coordinate System ◽  
Deformable Body ◽  
Finite Element Formulation ◽  
Deformation Analysis ◽  
Element Formulation ◽  
Rectangular Plates ◽  
Shape Functions ◽  
Intermediate Element

In this investigation a nonlinear total Lagrangian finite element formulation is developed for the dynamic analysis of plates that undergo large rigid body displacements. In this formulation shape functions are required to include rigid body modes that describe only large translational displacements. This does not represent any limitation on the technique presented in this study, since most of commonly used shape functions satisfy this requirement. For each finite plate element an intermediate element coordinate system, whose axes are initially parallel to the axes of the element coordinate system, is introduced. This intermediate element coordinate system, which has an origin which is rigidly attached to the origin of the deformable body, is used for the convenience of describing the configuration of the element with respect to the deformable body coordinate system in the undeformed state. The nonlinear dynamic equations developed in this investigation for the large rigid body displacement and small elastic deformation analysis of the rectangular plates are expressed in terms of a unique set of time invariant element matrices that depend on the assumed displacement field. The invariants of motion of the deformable body discretized using the plate elements are obtained by assembling the invariants of its elements using a standard finite element procedure.

Modelling the Axis Drift of Short Wire Flexures and Increasing Their Support Stiffness Using Polymers

2021 ◽  
Author(s):  
Boris Daan ◽  
Jelle Rommers ◽  
Just L. Herder
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Finite Element Methods ◽  
Complex Geometries ◽  
Lower Error ◽  
Material Stiffness ◽  
Physical Tests ◽  
Novel Method ◽  
High Support ◽  
Modelling Approach

Abstract For steel flexures, complex geometries are required to reach high support stiffness and limit axis drift over large ranges of motion. These complex flexures are expensive and difficult to manufacture. This paper presents a method of designing short, polymer wire flexures with high support stiffness and modelling their axis drift using a novel method, the arc method. The arc method is validated against finite element methods (FEM) and physical tests, showing at least a factor 10 lower error than existing pseudo-rigid-body models (PRBM) at 70° deflection, while maintaining a simple modelling approach. The use of polymers increases support stiffness of wire flexures by a factor 7800 with respect to steel at 70° deflection, even though the material stiffness is substantially lower. This is due to the large allowed strain of polymers increasing the possible diameter by a factor 110.

B-Spline Based Robust Topology Optimization

2015 ◽  
Author(s):  
Yu Gu ◽  
Xiaoping Qian
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Analytical Description ◽  
Minimal Length ◽  
Optimization Approach ◽  
Material Density ◽  
B Spline ◽  
B Splines ◽  
Robust Formulation

In this paper, we present an extension of the B-spline based density representation to a robust formulation of topology optimization. In our B-spline based topology optimization approach, we use separate representations for material density distribution and analysis. B-splines are used as a representation of density and the usual finite elements are used for analysis. The density undergoes a Heaviside projection to reduce the grayness in the optimized structures. To ensure minimal length control so the resulting designs are robust with respect to manufacturing imprecision, we adopt a three-structure formulation during the optimization. That is, dilated, intermediate and eroded designs are used in the optimization formulation. We give an analytical description of minimal length of features in optimized designs. Numerical examples have been implemented on three common topology optimization problems: minimal compliance, heat conduction and compliant mechanism. They demonstrate that the proposed approach is effective in generating designs with crisp black/white transition and is accurate in minimal length control.

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