Topology Optimization Of Compliant Mechanisms Research Articles

A simple evolutionary topology optimization procedure for compliant mechanism design

This work presents a modified version of the evolutionary structural optimization (ESO) procedure for its application in topology optimization of compliant mechanisms. The proposed procedure is based in the ESO method, which has been successfully applied to several optimum material distribution problems, such us stiffness, frequency or buckling problems, but not for compliant mechanism optimization. It will be shown that an additive version of this method must be adopted in order to achieve the optimum design, since the traditional ESO method's element removal technique is not efficient in this case. The proposed method will apply the objective functions and restrictions suggested in previous works, as well as original formulations and alternative approaches derived in this investigation which improve the solutions obtained by other authors. The procedure has been implemented into a general optimization software and tested in several numerical applications and benchmark examples to illustrate and validate the approach.

Shape and topology optimization of compliant mechanisms using a parameterization level set method

In this paper, a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms. The structural shape boundary is implicitly embedded into a higher-dimensional scalar function as its zero level set, resultantly, establishing the level set model. By applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function, the temporal and spatial Hamilton–Jacobi equation from the conventional level set method is then discretized into a series of algebraic equations. Accordingly, the original shape and topology optimization is now fully transformed into a parameterization problem, namely, size optimization with the expansion coefficients of interpolants as a limited number of design variables. Design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints. The structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method. It is highlighted that the present method can not only inherit the merits of the implicit boundary representation, but also avoid some unfavorable features of the conventional discrete level set method, such as the CFL condition restriction, the re-initialization procedure and the velocity extension algorithm. Finally, an extensively investigated example is presented to demonstrate the benefits and advantages of the present method, especially, its capability of creating new holes inside the design domain.

Topology design of large displacement compliant mechanisms with multiple materials and multiple output ports

Topology optimization of compliant mechanisms is presented in this paper wherein the layout design problem is addressed in its original binary or discrete (0-1) form. Design variables are modeled as discrete variables and allowed to assume values pertaining only to their void (0) or solid (1) states. Due to this discrete nature, a genetic algorithm is employed as an optimization routine. Using the barrier assignment approach, the search algorithm is extended to use with multiple materials. The layout design of compliant mechanisms is performed wherein displacements at multiple points (ports) in the design region are maximized along the respective prescribed directions. With multiple output ports and multiple materials, additional freedom in motion and force transduction can be achieved with compliant mechanisms. Geometrically large deformation analysis is employed to compute the displacement-based multiple objectives that are extremized using Nondominated Sorting in Genetic Algorithms (or NSGA). With genetic algorithms, buckling or snap through like issues with nonconvergent solutions in the population when computing nonlinear deformations can be implicitly circumvented.

Topology optimization of channel flow problems

This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low-to-moderate Reynolds numbers. This makes the flow problem nonlinear and hence a nontrivial extension of the work of Borrvall and Petersson (2003).Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity-driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc.

Compliant mechanism design using multi-objective topology optimization scheme of continuum structures

Topology optimization problems for compliant mechanisms using a density interpolation scheme, the rational approximation of material properties (RAMP) method, and a globally convergent version of the method of moving asymptotes (GCMMA) are primarily discussed. First, a new multi-objective formulation is proposed for topology optimization of compliant mechanisms, in which the maximization of mutual energy (flexibility) and the minimization of mean compliance (stiffness) are considered simultaneously. The formulation of one-node connected hinges, as well as checkerboards and mesh-dependency, is typically encountered in the design of compliant mechanisms. A new hybrid-filtering scheme is proposed to solve numerical instabilities, which can not only eliminate checkerboards and mesh-dependency efficiently, but also prevent one-node connected hinges from occurring in the resulting mechanisms to some extent. Several numerical applications are performed to demonstrate the validity of the methods presented in this paper.

Dynamic Topology Optimization of Compliant Mechanisms and Piezoceramic Actuators

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 whether the piezoelectric actuator element is considered design or nondesign. At high driving frequencies, it was found that the dynamically optimized structure is very near resonance.

Topology Optimization of Compliant Mechanism with Geometrical Advantage

A compliant mechanism is a mechanism that produces its motion by the flexibility of some or all of its members when the input forces are applied. Because of its mobility resulted from flexibility, it is difficult to expect the configuration in prioi. In this work, the design method of a compliant mechanism with the specified geometrical advantage is proposed to control the motion. The multiobjective optimization problem is formulated to minimize the deviation of the specified geometrical advantage and structural compliance of a mechanism and topology optimization is applied to determine the configuration of a mechanism. The results of example problems including a displacement converter design and a gripper design are compared with a multi-criteria model and show that the design of an accurate compliant mechanism with specified geometrical advantage can be obtained.

Structural Topology Optimization of Compliant Mechanisms (In cases Where the Ratio of the Displacement at the Input Location to the Displacement at the Output Location is Included in an Objective Function)

Structural Topology Optimization of Compliant Mechanisms (In cases Where the Ratio of the Displacement at the Input Location to the Displacement at the Output Location is Included in an Objective Function)

Reliability-based design of MEMS mechanisms by topology optimization

This paper presents a methodology for the design of micro-electro-mechanical systems (MEMS) by topology optimization accounting for stochastic loading and boundary conditions as well as material properties. This methodology combines recent advances in material-based topology optimization for compliant mechanisms undergoing large displacements and design optimization under uncertainties using first order reliability analysis methods. The performance measure approach is applied to the formulation of the optimization problem. The structural response is predicted by a co-rotational finite element formulation and the design and imperfection sensitivities are evaluated by an adjoint method. The methodology is illustrated by the topology optimization of a compliant mechanism. The results show the importance of accounting for the stochastic nature of the micro-system in the topology optimization process.

939 荷重入力位置の変位と出力変位の比を考慮したコンプライアントメカニズムのトポロジー最適設計法

939 荷重入力位置の変位と出力変位の比を考慮したコンプライアントメカニズムのトポロジー最適設計法

Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme

In the topology optimization of structures, compliant mechanisms or materials, a density-like func- tion is often used for material interpolation to overcome the computational difficulties encountered in the large "0-1" type integer programming problem. In this paper, we illustrate that a gradually formed continuous peak function can be used for material interpolation. One of the advantages of introducing the peak function is that multiple materials can easily be incorporated into the topology optimization without increasing the number of design variables. By using the peak function and the op- timality criteria method, we synthesize compliant mech- anisms with multiple materials with and without the ma- terial resource constraint. The numerical examples in- clude the two-phase, three-phase, and four-phase materi- als where void is treated as one material. This newdesign method enables us to optimally juxtapose stiff and flex- ible materials in compliant mechanisms, which can be built using modern manufacturing methods.

Convex analysis for topology optimization of compliant mechanisms

This paper analyses the convexity of the problem formulations for topological optimization of compliant mechanisms. In this context, a ground structure is assumed to consist of membranes with variable thickness or trusses with variable cross-sectional area. It is proven that the objective function of maximum mechanical or geometrical advantage may not be convex even though the constraints for the problem formulations give rise to a convex set. The constraints include volumetric constraint and a bound on input displacement. The nonconvex objective functions are shown analytically with two examples using truss elements. Also, it is illustrated numerically with an example using bilinear quadrilateral elements. It is concluded that nonconvex objective functions also attribute to difficulties in arriving at the globally optimal topology of compliant mechanisms, in addition to the number of design variables and constraints. As the problem is more complicated, the solution of the problem requires robust and reliable optimization techniques.

Techniques to suppress intermediate density in topology optimization of compliant mechanisms

Discrete topological problems are often relaxed with continuous design variables so that they can be solved using continuous mathematical programming. Such practice prevails because large-scale discrete 0–1 mathematical programming is not generally available. Although the relaxed problems become tractable, they may cause the appearance of intermediate density in the optimum topologies, especially those of structures and compliant mechanisms. Various penalty schemes have been proposed to suppress the intermediate density. Most of the past works assumed that the same penalty schemes could be effectively applied to both problems of stiffest structure design and compliant mechanism design. Differences in nature between the problems are generally neglected. This work distinguished the two problems, and observed that complaint mechanism (CM) problem does not suffer intermediate density as seriously as minimum compliance (MC) problem does. Besides allocating more material, explicit and implicit penalties were pursued to suppress intermediate density. To ensure mesh-independence and not to complicate the nonconvex objective function in CM problem, a new technique using a constraint of explicit penalty with variable bound is proposed to suppress intermediate density in topology optimization of compliant mechanisms. Together with a perimeter constraint, the new technique is also applied to MC problem.

Topology optimization of compliant mechanisms with multiple outputs

A procedure for the topology design of compliant mechanisms with multiple output requirements is presented. Two methods for handling the multiple output requirements are developed, a combined virtual load method and a weighted sum of objectives method. The problem formulations and numerical solution procedures are discussed and illustrated by design examples. The examples illustrate the capabilities of the design procedure, the effect of the direction of the output deflection requirements on the solution, as well as computational issues such as the effect of the starting point and effect of the material resource constraint.

Topology optimization of compliant mechanisms with multiple outputs

A procedure for the topology design of compliant mechanisms with multiple output requirements is presented. Two methods for handling the multiple output requirements are developed, a combined virtual load method and a weighted sum of objectives method. The problem formulations and numerical solution procedures are discussed and illustrated by design examples. The examples illustrate the capabilities of the design procedure, the effect of the direction of the output deflection requirements on the solution, as well as computational issues such as the effect of the starting point and effect of the material resource constraint.

Topology optimization of compliant mechanisms using the homogenization method

A procedure to obtain a topology of an optimal structure considering flexibility is presented. The methodology is based on a mutual energy concept for formulation of flexibility and the homogenization method. A multi-objective optimization problem is formulated as an application of compliant mechanism design. Some examples of the design of compliant mechanisms for plane structures are presented. © 1998 John Wiley & Sons, Ltd.

Topology optimization of compliant mechanisms using the homogenization method

Topology optimization of compliant mechanisms using the homogenization method