Optimization Of Compliant Mechanisms Research Articles

Topology Optimization of Compliant Mechanisms Using Level Set Method without Re-Initialization

In this paper, a new level set method for topology optimization of compliant mechanisms is presented. A new formulation is developed and built in the traditional level set method to force the level set function to be close to a signed distance function during the optimal process. The validity of the method is illustrated by topology optimization of a widely studied compliant mechanism.

Topology optimization of compliant circular path mechanisms based on an aggregated linear system and singular value decomposition

SUMMARYThis paper proposes a topology optimization method for the design of compliant circular path mechanisms, or compliant mechanisms having a set of output displacement vectors with a constant norm, which is induced by a given set of input forces. To perform the optimization, a simple linear system composed of an input force vector, an output displacement vector and a matrix connecting them is constructed in the context of a discretized linear elasticity problem using FEM. By adding two constraints: 1, the dimensions of the input and the output vectors are equal; 2, the Euclidean norms of all local input force vectors are constant; from the singular value decomposition of the matrix connecting the input force vector and the output displacement vector, the optimization problem, which specifies and equalizes the norms of all output vectors, is formulated. It is a minimization problem of the weighted summation of the condition number of the matrix and the least square error of the second singular value and the specified value. This methodology is implemented as a topology optimization problem using the solid isotropic material with penalization method, sensitivity analysis and method of moving asymptotes. The numerical examples illustrate mechanically reasonable compliant circular path mechanisms and other mechanisms having multiple outputs with a constant norm. Copyright © 2011 John Wiley & Sons, Ltd.

Conceptual Design of Compliant Mechanisms for Flapping Wings with Topology Optimization

This work discusses the integration of two previously disparate research areas: topology optimization of compliant mechanisms and flapping wing vehicles. The efficient actuation of the latter is considerably challenging, with competing weight, energy, and authority requirements; intuitive design strategies are not typically available for the aeroelastic physics that define the flapping system. We discuss the incorporation of these physics into a gradient-based topological optimization scheme, to design thrust-optimal compliant flapping mechanisms. This is done with a nonlinear dynamical finite element model incorporating both the mechanism and the wing structure, coupling elastic, inertial, aerodynamic, and actuator forces. Several optimal mechanism topologies are presented, along with a detailed discussion of the relevant flapping physics driving the design process.

Multi-objective Topology Optimization of Thermo-mechanical Compliant Mechanisms

The material characteristics of a structure will change with temperature variation,and will induce stress within the structure.Currently,the optimal design for the topology of compliant mechanisms is mainly performed in single physical field.However,when compliant mechanisms work in high temperature environments,their displacement outputs are generated not only by mechanical load,but also by the temperature variation which may become the prominent factor.Therefore,the influence of temperature must be considered in the design.In this paper,a novel optimization method for multi-objective topology of thermo-mechanical compliant mechanisms is presented.First,the thermal field is analyzed with finite-element method,where the thermal strain is taken into account in the constitutive relation,and the equivalent nodal thermal load is derived with the principle of virtual work.Then the thermal load is converted into physical loads in elastic field,and the control equation of the thermo-mechanical compliant mechanism is obtained.Second,the mathematical model of the multi-objective topology optimization is built by incorporating both the flexibility and stiffness.Meanwhile,the coupling sensitivity function and the sensitivity analysis equations of thermal steady-state response are derived.Finally,optimality criteria algorithm is employed to obtain numerical solution of the multi-objective topology optimization.Numerical examples show that the compliant mechanisms have better performance and are more applicable if the temperature effect is taken into account in the design process.The presented modeling and analysis methods provide a new idea and an effective approach to topology optimization of compliant mechanisms in electrothermic coupling field and multiphysics fields.

Topology Optimization of Compliant Mechanisms with Geometrical Nonlinearities Using the Ground Structure Approach

The majority of topology optimization of compliant mechanisms uses linear finite element models to find the structure responses.Because the displacements of compliant mechanisms are intrinsically large,the topological design can not provide quantitatively accurate result.Thus,topological design of these mechanisms considering geometrical nonlinearities is essential.A new methodology for geometrical nonlinear topology optimization of compliant mechanisms under displacement loading is presented.Frame elements are chosen to represent the design domain because they are capable of capturing the bending modes.Geometrically nonlinear structural response is obtained by using the co-rotational total Lagrange finite element formulation,and the equilibrium is solved by using the incremental scheme combined with Newton-Raphson iteration.The multi-objective function is developed by the minimum strain energy and maximum geometric advantage to design the mechanism which meets both stiffness and flexibility requirements, respectively.The adjoint method and the direct differentiation method are applied to obtain the sensitivities of the objective functions. The method of moving asymptotes(MMA) is employed as optimizer.The numerical example is simulated to show that the optimal mechanism based on geometrically nonlinear formulation not only has more flexibility and stiffness than that based on linear formulation,but also has better stress distribution than the one.It is necessary to design compliant mechanisms using geometrically nonlinear topology optimization.Compared with linear formulation,the formulation for geometrically nonlinear topology optimization of compliant mechanisms can give the compliant mechanism that has better mechanical performance.A new method is provided for topological design of large displacement compliant mechanisms.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

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.

An element addition strategy for thermally actuated compliant mechanism topology optimization

PurposeThe purpose of this paper is to describe an element addition strategy for topology optimization of thermally actuated compliant mechanisms under uniform temperature fields.Design/methodology/approachThe proposed procedure is based on the evolutionary structural optimization (ESO) method. In previous works, this group of authors has successfully applied the ESO method for compliant mechanism optimization under directly applied input loads. The present paper progresses on this work line developing an extension of this procedure, based on an additive version of the method, to approach the more complicated case of thermal actuators.FindingsThe adopted method has been tested in several numerical applications and benchmark examples to illustrate and validate the approach, and designs obtained with this method are compared favorably with the analytical solutions and results derived by other authors using different optimization methods, showing the viability of this technique for uniformly heated actuators optimization.Research limitations/implicationsAs a simple initial approach, this research considers only uniform heating of the system, while many thermal actuators are heated nonuniformly. Future works will be based on electrothermal actuation, and nonuniform Joule heating will be considered as well, which might lead to more elegant and efficient solutions.Practical implicationsCompliant micromechanisms that are responsible for movement play a crucial role in microelectromechanical systems (MEMS) design, which cannot be manufactured using typical assembly processes and may not make use of traditional hinges or bearings. The topology optimization method described in this paper enables the systematic design of these devices, which can result in reduced conception time and manufacturing cost.Originality/valueThe ESO method has been successfully applied to several optimum material distribution problems, but not for thermal compliant mechanisms. Even if most applications of this method have been oriented for maximum stiffness structure design, this paper shows that this computation method may be also useful in the design of thermal compliant mechanisms and provides engineers with a very simple and practical alternative design tool.

An Improved Material-Mask Overlay Strategy for Topology Optimization of Structures and Compliant Mechanisms

The honeycomb-based domain representation directly yields checkerboard and point flexure free optimal solutions to various topology design problems without requiring any supplementary suppression method. This is because the root cause behind the appearance of these pathologies, namely, the permitted single-point connectivity between contiguous subregions in rectangular-cell-based representation, is eliminated. The mesh-free material-mask overlay method further promises unadulterated “black and white” solutions in contrast to density interpolation schemes where the material is modeled between the “void” and “filled” states. Here, we propose improvements to the material-mask overlay method by judiciously increasing the number of material masks during a sequence of subsearches for the best solution. We used an alternative, mutation-based zero-order stochastic search, which, through a small population of solution vectors, can yield multiple solutions from a single search for nonconvex topology optimization formulations. Wachspress hexagonal cells are used as finite elements since they offer rich displacement interpolation functions. Singular solutions are penalized and filtered. With the improved material-mask overlay method, we showcase the synthesis using two classical small displacement problems each on optimal stiff structures and compliant mechanisms to illustrate the extraction of pathology-free, “black and white,” and multiple solutions.

Three-Dimensional Optimal Material Distributions for Micro-Gripper with Straight-Line Path and Parallel Movement Arms

Abstract The development of micro-electro-mechanical systems (MEMS) is a subject of intense research due to the significant impact of miniaturization. The assembly of micro-devices involves handling of parts that are extremely small. A micro-gripper compliant mechanism is one of the key elements in micro-robotics as well as micro-assembly technologies for handling and manipulating micro-objects without damage. Topology optimization has proven to be a power- ful method for the conceptual design of structures and mechanisms. This paper presents topology optimization of three-dimensional micro-gripper compliant mechanism with straight-line path and with parallel movement gripping arms. A three-dimensional finite element analysis model using ANSYS is constructed for the propose design domain. The optimal configuration micro-grippers, which can realize a straight-line path and parallel movement of the gripping arms, are demonstrated.

Reliability-based Topology Optimization of Compliant Mechanisms by Using Foundation Structure Approach

In order to avoid the degradation of mechanism performance caused by uncertainties in the process of manufacture and use,a new reliability-based topology optimization method for compliant mechanisms using the foundation structure approach is presented.Frame elements are chosen to represent the design domain because they are capable of capturing the bending modes.The applied load and the structural geometry size are considered as random variables,and the failure model of the mechanism is regarded as the series system of strain energy and mutual potential energy.The first-order reliability method is adopted to calculate the failure probability of the series system.The dual mathematical model of reliability-based topology optimization for compliant mechanisms is established,the dual algorithm is used for the optimization problem.The numerical example is simulated to show that the proposed method is correct and effective because it helps to obtain mechanisms with higher reliability than those obtained by the deterministic topology optimization.

Topology optimization of pressure-actuated compliant mechanisms

Topology optimization of a compliant mechanism under pressure input is presented by treating void regions with incompressible hydrostatic fluid. Since an input force is not imposed on one point, existing problem formulations such as attaching a spring on the node under the input force or constraining the input displacement are not valid for the present problem. Instead, to obtain the structural stiffness of a compliant mechanism, the mean compliance by the input pressure is considered. To deal with incompressibility, as an alternative to the mixed displacement–pressure formulation, displacement-based nonconforming finite elements are employed for both two- and three-dimensional problems. The effectiveness of the proposed approach is verified by designing grippers and stretchers.

Design Optimization of Compliant Mechanisms Consisting of Standardized Elements

We developed a design method to configure optimal compliant mechanisms consisting of standardized elements such as semirigid beams, hubs, and joints. In the proposed design approach, mechanism compliance is based upon elastic deformations of joint elements made of short elastic beams. To set up the design problem as an optimization problem, a standard ground beam-based topology optimization method is modified to handle compliant mechanisms comprised of design variable-independent semirigid beams and design variable-dependent elastic joints. In the proposed method, unlike structural stiffness maximization problems, intermediate values should appear to allow elastic deformations in the joints. With our approach, reconfiguration design from one existing compliant mechanism to another can be formulated wherein the number of beam element relocation operations is also minimized. This formulation can be useful in minimizing the time and effort required to convert one mechanism to another.

Mechanical and geometric advantages in compliant mechanism optimization

This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formulations of compliant mechanisms posed as a topology optimization problem. With a linear elastic structural analysis, we quantify mechanical (and geometric) advantage in terms of the stiffness elements of the mechanism’s structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formulations.

Compliant Mechanism Optimization: Analysis and Design with Intrinsic Characteristic Stiffness#

This article focuses on design formulation of compliant mechanisms posed as a topology optimization problem. With the use of linear elasticity theory, a single-input, single-output compliant mechanism is represented by the stiffness matrix of its structure with respect to the input–output ports. It is shown that the stiffness model captures the intrinsic stiffness properties of the mechanism. Furthermore, in order for the optimization problem to be properly defined, it is necessary that the stiffness matrix of the mechanism's structure must be guaranteed to be always positive definite. An exploratory design formulation is then presented based on this necessary condition. Numerical examples are provided to illustrate the potential benefits of using the intrinsic stiffness properties for compliant mechanism design with topology optimization techniques.

Geometric Optimization of Spatial Compliant Mechanisms Using Three-Dimensional Wide Curves

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.

A new multi-objective programming scheme for topology optimization of compliant mechanisms

This paper presents an alternative method in implementing multi-objective optimization of compliant mechanisms in the field of continuum-type topology optimization. The method is designated as “SIMP-PP” and it achieves multi-objective topology optimization by merging what is already a mature topology optimization method—solid isotropic material with penalization (SIMP) with a variation of the robust multi-objective optimization method—physical programming (PP). By taking advantages of both sides, the combination causes minimal variation in computation algorithm and numerical scheme, yet yields improvements in the multi-objective handling capability of topology optimization. The SIMP-PP multi-objective scheme is introduced into the systematic design of compliant mechanisms. The final optimization problem is formulated mathematically using the aggregate objective function which is derived from the original individual design objectives with PP, subjected to the specified constraints. A sequential convex programming method, the method of moving asymptotes (MMA) is then utilized to process the optimization evolvement based on the design sensitivity analysis. The main findings in this study include distinct advantages of the SIMP-PP method in various aspects such as computation efficiency, adaptability in convex and non-convex multi-criteria environment, and flexibility in problem formulation. Observations are made regarding its performance and the effect of multi-objective optimization on the final topologies. In general, the proposed SIMP-PP method is an appealing multi-objective topology optimization scheme suitable for “real world” problems, and it bridges the gap between standard topological design and multi-criteria optimization. The feasibility of the proposed topology optimization method is exhibited by benchmark examples.

A Kinetoelastic Formulation of Compliant Mechanism Optimization

The current design algorithms for compliant mechanisms often generate solutions that imitate rigid-body linkages by means of point flexures or flexure pivots, by using the popular spring model formulation. This paper presents a kinetoelastic formulation for compliant mechanism optimization. With a state equation of the mechanism defined by the elasticity theory, the model incorporates not only the kinematic function requirements of the mechanism but, more importantly, the necessary conditions on the compliance characteristics of the mechanism’s structure. The kinematics of the compliant mechanism is defined on rigid bodies of input/output ports and is related to a set of kinetoelastic factors of the mechanism’s compliance matrix. The kinetoelastic formulation is applied to the problem of optimizing a compliant translational joint, producing compliant designs with compliance properties such as the leaf spring type sliding joint as opposed to the notch-type joint. This paper represents an initial development toward a more general methodology for compliant mechanism optimization.

Topology Optimization of Multiple Inputs and Outputs Compliant Mechanisms with Geometrically Nonlinearity

Multiple degree-of-freedom compliant mechanisms are widely used in the fields of micro-positioning and micro-manipulation, and the topology optimization of compliant mechanisms is actually a geometrically nonlinear problem.So it is very necessary to study the topology optimization of multiple inputs and outputs compliant mechanisms undergoing large deformation.A new topology optimization method of multiple inputs and multiple outputs compliant mechanisms with geometrical nonlinearity is presented.The multi-objective function is developed by the minimum compliance and maximum geometric advantage to design a mechanism which meets both stiffness and flexibility requirements,respectively.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 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 by using a total Lagrange finite element formulation and the equilibrium is found by using an incremental scheme combined with Newton-Raphson iterations.The solid isotropic material interpolation method is used in design of compliant mechanisms.The sensitivity of objective functions is analyzed by using the adjoint solution technique and the optimization problem is solved by using the method of moving approximation algorithm.These methods are further investigated and realized with the numerical examples,which are simulated to show the availability of this approach.

Shape Optimization of Compliant Mechanism for Planar Path Generation

A two-degree-of-freedom planar compliant mechanism possesses a workspace that is able to serve as a micromanipulator carrier to generate programmed planar path by controlling two independent inputs.To improve the manufacturability of the compliant mechanism design,shape optimization is investigated on the basis of extracted profile after topology optimization.The profile is abstracted into lined links and crunodes.Based on the principle of connectivity in topology,a condition is set up for judging the connectivity of link domain,and then a translational scanning algorithm using windows is constructed to search the crunodes of the required compliant mechanism in the design domain.On this basis,a link searching algorithm is built in order to locate the lined links for the abstraction of the contour of the compliant mechanism.The contour is reconstructed for the abstracted compliant mechanism.The contour is represented as linked simple curves whose parameters serve as optimized variables.Among these variables key dimensions are determined on the basis of sensitivity analysis.The error between the real output and the desired output of the compliant mechanism is used as objective function to form the optimization model of the contour dimension and then generate optimum contour of the compliant mechanism.This optimization improves the manufacturability of the designs without lowering the motion performance of the compliant mechanism.Case studies are given to demonstrate the effectiveness of the presented shape optimization method for compliant mechanism.

A new level set method for systematic design of hinge-free compliant mechanisms

This paper presents a new level set-based method to realize shape and topology optimization of hinge-free compliant mechanisms. A quadratic energy functional used in image processing applications is introduced in the level set method to control the geometric width of structural components in the created mechanism. A semi-implicit scheme with an additive operator splitting (AOS) algorithm is employed to solve the Hamilton–Jacobi partial differential equation (PDE) in the level set method. The design of compliant mechanisms is mathematically represented as a general non-linear programming with a new objective function augmented by the high-order energy term. The structural optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints. In doing so, it is expected that numerical difficulties such as the Courant–Friedrichs–Lewy (CFL) condition and periodically applied re-initialization procedures in most conventional level set methods can be eliminated. In addition, new holes can be created inside the design domain. The final mechanism configurations consist of strip-like members suitable for generating distributed compliance, and solving the de-facto hinge problem in the design of compliant mechanisms. Two widely studied numerical examples are studied to demonstrate the effectiveness of the proposed method in the context of designing distributed compliant mechanisms.