Topology Optimization Of Compliant Mechanisms Research Articles

Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model

This paper presents a new robust topology optimization framework for hinge-free compliant mechanisms with spatially varying material uncertainties, which are described using a non-probabilistic bounded field model. Bounded field uncertainties are efficiently represented by a reduced set of uncertain-but-bounded coefficients on the basis of the series expansion method. Robust topology optimization of compliant mechanisms is then defined to minimize the variation in output displacement under constraints of the mean displacement and predefined material volume. The nest optimization problem is solved using a gradient-based optimization algorithm. Numerical examples are presented to illustrate the effectiveness of the proposed method for circumventing hinges in topology optimization of compliant mechanisms.

Motion error based robust topology optimization for compliant mechanisms under material dispersion and uncertain forces

Due to the inevitable phenomena that multi-source uncertainty factors in compliant mechanisms, which generally originate from material dispersion and uncertain external forces, severely affect the output motion accuracy, the robustness assessment and optimization with high confidence and efficiency is of great significance for scientists and engineers. In view of this, this study develops a novel approach of robust topology synthesis for compliant mechanisms with desired motion output by minimizing the expectation of Taguchi quantity loss function. The sensitivities of the robustness index with respect to design variables are calculated by the method of adjoint vector. Furthermore, the solution procedures of motion error based robust topology synthesis for geometrically linear and non-linear compliant mechanisms are elaborated. Two engineering examples are eventually presented to demonstrate the validity and applicability of the developed methodology.

Stress‐based multi‐material topology optimization of compliant mechanisms

AbstractIn this paper, a level‐set‐based method is presented to deal with the multi‐material topology optimization of compliant mechanisms with stress constraints. A novel stress‐based multi‐material topology optimization model of compliant mechanisms is proposed. In this model, the multi‐material level set topology description model and the separable stress interpolation scheme are adopted. The weighted sum method is used to deal with the multi‐objective optimization of the output displacement and compliance of compliant mechanisms. The penalty of stresses is also considered in the objective function to control the local stress level in different materials. To solve the optimization problem, the parametric level set method is employed, and the sensitivity analysis is conducted. Application of the method is demonstrated by 2 numerical examples. Results show that the multi‐material structures without undesirable de facto hinges can be obtained. The output displacement and compliance of the compliant mechanisms are optimized, and stress constraints in different materials are simultaneously satisfied.

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

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.

Topology optimization of compliant mechanisms with curvilinear fiber path laminated composites

An approach for designing compliant mechanisms with curvilinear fiber path laminated composites is presented to obtain the optimum topology structure in this paper. A laminated plate with curvilinear fiber path is built by using the shifted fiber path method. Meanwhile, an equivalent constitutive relationship of the laminated plate has been obtained based on the laminated plate theory. Taking the element relative density as design variable, minimizing the weighted linear combination of the mutual strain energy and the strain energy is considered as an objective function to achieve the desired deformation and enough load-carrying capacity of compliant mechanisms with the volume constraint. The topology optimization problem is solved via the optimality criteria and the sensitivity filtering technology. The numerical examples of designing compliant inverters are investigated to demonstrate the effectiveness of the proposed method. And furthermore, the displacements and the stress levels are also discussed for the compliant inverters with different curvilinear fiber laminated sequences.

Topology optimization of compliant mechanism and its support through a level set method

In the present paper, the task of designing a compliant mechanism is accomplished by solving a multi-objective topology optimization problem. The objective function includes a target displacement at the output port and compliances of two load cases. The design variables include two types of boundaries, i.e., the traction free boundary and the Dirichlet boundary. The topology optimization of compliant mechanism and its support is solved by using a level set method. Two level set functions are used to represent a compliant mechanism and the two types of boundaries. Each of the two boundaries is represented by a part of the zero level set of one level set function. Evolution of the two boundaries is modeled by two independent Hamilton–Jacobi equations, thus the shape and topology of the two boundaries change independently. The shape derivatives are derived by using a Lagrangian function and the adjoint method. The finite element analysis is done by modifying a fixed background mesh, and the artificial weak material is not used. Numerical examples in two dimensions are investigated.

Mechanical Behaviour of Auxetic Microstructures Using Contact Mechanics and Elastoplasticity

The design of novel mechanical microstructures having auxetic behaviour is proposed in this paper using techniques of topology optimization for compliant mechanisms. The resulting microstructure can be modified in order to cover additional needs, not included in the topology optimization formulation. Classical structural optimization, contact mechanics, homogenization and nonlinear finite element analysis are used for this step. Thus, the modified microstructure or composite is studied with numerical homogenization in order to verify that it still has the wished auxetic behaviour. Finally, nonlinear finite element analysis shows how the auxetic behaviour is influenced by unilateral contact between the constituent materials, large displacements and elastoplasticity.

多目的最適設計法を用いたコンプライアントメカニズムのロバストトポロジー最適設計

多目的最適設計法を用いたコンプライアントメカニズムのロバストトポロジー最適設計

Topology optimization of compliant structures and mechanisms using constructive solid geometry for 2-d and 3-d applications

This research focuses on the establishment of a constructive solid geometry-based topology optimization (CSG-TOM) technique for the design of compliant structure and mechanism. The novelty of the method lies in handling voids, non-design constraints, and irregular boundary shapes of the design domain, which are critical for any structural optimization. One of the most popular models of multi-objective genetic algorithm, non-dominated sorting genetic algorithm is used as the optimization tool due to its ample applicability in a wide variety of problems and flexibility in providing non-dominated solutions. The CSG-TOM technique has been successfully applied for 2-D topology optimization of compliant mechanisms and subsequently extended to 3-D cases. For handling these cases, a new software framework involving optimization routine for geometry and mesh generation with FEA solver has been developed. The efficacy of the approach has been demonstrated for 2-D and 3-D geometries and also compared with state of the art techniques.

Topology optimum design of compliant mechanisms using modified ant colony optimization

A Modified ant colony optimization (MACO) algorithm was suggested for topology optimal design of compliant mechanisms since standard ACO cannot provide an appropriate optimal topology. In order to improve computational efficiency and suitability of standard ACO algorithm in topology optimization for compliant mechanisms, a continuous variable, called the “Element contribution significance (ECS),” is employed, which serves to replace the positions of ants in the standard ACO algorithm, and assess the importance of each element in the optimization process. MACO algorithm was applied to topology optimizations of both linear and geometrically nonlinear compliant mechanisms using three kinds of objective functions, and optimized topologies were compared each other. From the comparisons, it was concluded that MACO algorithm can effectively be applied to topology optimizations of linear and geometrically nonlinear compliant mechanisms, and the ratio of Mutual potential energy (MPE) to Strain energy (SE) type of objective function is the best for topology optimal design of compliant mechanisms.

Topology optimization of compliant mechanisms using element-free Galerkin method

This paper will propose a topology optimization approach for the design of large displacement compliant mechanisms with geometrical non-linearity by using the element-free Galerkin (EFG) method. In this method, the Shepard function is applied to construct a physically meaningful density approximant, to account for its non-negative and range-bounded property. Firstly, in terms of the original nodal density field, the Shepard function method functionally similar to a density filter is used to generate a non-local nodal density field with enriched smoothness over the design domain. The density of any node can be evaluated according to the nodal density variables located inside the influence domain of the interested node. Secondly, in the numerical implementation the Shepard function method is again employed to construct a point-wise density interpolant. Gauss quadrature is used to calculate the integration of background cells numerically, and the artificial densities over all Gauss points can be determined by the surrounding nodal densities within the influence domain of the concerned computational point. Finally, the moving least squares (MLS) method is applied to construct the shape functions using the weight functions with compact support for assembling the meshless approximations of state equations. Since MLS shape functions are lack of the Kronecker delta function property, the penalty method is applied to enforce the essential boundary conditions. A typical large-deformation compliant mechanism is used as the numerical example to demonstrate the effectiveness of the proposed method.

Design and verification of auxetic microstructures using topology optimization and homogenization

The design of mechanical microstructures having auxetic behaviour is proposed in this paper using techniques of topology optimization for compliant mechanisms. A robust hybrid algorithm based on evolutionary algorithms and local search steps is used. The result may need verification in order to accommodate needs not taken into account in the topology optimization. Therefore, a numerical homogenization scheme is used in order to show that the final design still has the wished negative Poisson’s property.

Topology optimization of compliant mechanisms using pairs of curves

The structural topology optimization approach can be used to generate compliant mechanisms for some desired input–output requirements. The success of the optimization depends on the structural geometry representation scheme used. In this paper, a novel representation scheme is proposed. The representation scheme is characterized by pairs of curves that are used to connect Input/Ouput (I/O) regions of the structure. Each pair of curves includes a normal curve and a fat curve. The areas bounded by the pair of curves define the material distribution between them. All I/O regions are connected to one another (either directly or indirectly) by pairs of curves in order to form one single connected load-bearing structure. A genetic algorithm for constrained and multiobjective optimization is then applied with the representation scheme of the structure in the form of a graph. Simulation results from a displacement inverter and a displacement redirector indicate that the presented representation scheme is appropriate.

Multiple-Material Topology Optimization of Compliant Mechanisms Created Via PolyJet Three-Dimensional Printing

Compliant mechanisms are able to transfer motion, force, and energy using a monolithic structure without discrete hinge elements. The geometric design freedoms and multimaterial capability offered by the PolyJet 3D printing process enables the fabrication of compliant mechanisms with optimized topology. The inclusion of multiple materials in the topology optimization process has the potential to eliminate the narrow, weak, hingelike sections that are often present in single-material compliant mechanisms and also allow for greater magnitude deflections. In this paper, the authors propose a design and fabrication process for the realization of 3-phase, multiple-material compliant mechanisms. The process is tested on a 2D compliant force inverter. Experimental and numerical performance of the resulting 3-phase inverter is compared against a standard 2-phase design.

Topology optimization of compliant mechanisms with desired structural stiffness

This paper develops a bi-directional evolutionary structural optimization (BESO) method for topological design of compliant mechanisms. The design problem is reformulated as maximizing the flexibility of the compliant mechanism subject to the mean compliance and volume constraints. Based on the finite element analysis, a new BESO algorithm is established for solving such an optimization problem by gradually updating design variables until a convergent solution is obtained. Several 2D and 3D examples are presented to demonstrate the effectiveness of the proposed BESO method. A series of optimized mechanism designs with or without hinge regions are obtained. Numerical results also indicate that the flexibility and hinge-related property of the optimized compliant mechanisms can be controlled by the desired structural stiffness.

Reliability-Based Topology Optimization of Compliant Mechanisms with Geometrically Nonlinearity

A new reliability-based topology optimization method for compliant mechanisms with geometrical nonlinearity is presented. The aim of this paper is to integrate reliability and geometrical nonlinear analysis into the topology optimization problems. Firstly, geometrical nonlinear response analysis method of the compliant mechanisms is developed based on the Total-Lagrange finite element formulation, the incremental scheme and the Newton-Raphson iteration method. Secondly, a multi-objective topology optimal model of compliant mechanisms considering the uncertainties of the applied loads and the geometry descriptions is established. The objective function is defined by minimum the compliance and maximum the geometric advantage to meet both the stiffness and the flexibility requirements, and the reliabilities of the compliant mechanisms are evaluated by using the first order reliability method. Thirdly, the computation of the sensitivities is developed with the adjoint method and the optimization problem is solved by using the Method of Moving Asymptotes. Finally, through numerical calculations, reliability-based topology designs with geometric nonlinearity of a typical compliant micro-gripper and a multi-input and multi-output compliant sage are obtained. The importance of considering uncertainties and geometric nonlinearity is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs, which shows that the reliability-based topology optimization yields mechanisms that are more reliable than those produced by deterministic topology optimization.

Hinge-Free Compliant Mechanism Design Via the Topological Level-Set

The objective of this paper is to introduce and demonstrate a new method for the topology optimization of compliant mechanisms. The proposed method relies on exploiting the topological derivative, and exhibits numerous desirable properties including: (1) the mechanisms are hinge-free; (2) mechanisms with different geometric and mechanical advantages (GA and MA) can be generated by varying a single control parameter; (3) a target volume fraction need not be specified, instead numerous designs, of decreasing volume fractions, are generated in a single optimization run; and (4) the underlying finite element stiffness matrices are well-conditioned. The proposed method and implementation are illustrated through numerical experiments in 2D and 3D.

Level Set-Based Topology Optimization of Hinge-Free Compliant Mechanisms Using a Two-Step Elastic Modeling Method

This paper presents a two-step elastic modeling (TsEM) method for the topology optimization of compliant mechanisms aimed at eliminating de facto hinges. Based on the TsEM method, an alternative formulation is developed and incorporated with the level set method. An efficient algorithm is developed to solve the level set-based optimization problem for improving the computational efficiency. Two widely studied numerical examples are performed to demonstrate the validity of the proposed method. The proposed formulation can prevent hinges from occurring in the resulting mechanisms. Further, the proposed optimization algorithm can yield fewer design iterations and thus it can improve the overall computational efficiency.

Topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method

A method for topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method is presented in this paper. The focus of this paper is on how to prevent generating the flexible hinges during the process of topology optimization of compliant mechanisms. In the proposed method, two types of mean compliances are introduced and built in the proposed multi-objective function for topology optimization of hinge-free compliant mechanisms with multiple outputs, therefore, the spring model widely used for topology optimization of compliant mechanisms is no longer needed. Some numerical examples are presented to illustrate the validity of the proposed method.

A new level set method for topology optimization of distributed compliant mechanisms

SUMMARYA new level set method for topology optimization of distributed compliant mechanism is presented in this study. By taking two types of mean compliance into consideration, several new objective functions are developed and built in the conventional level set method to avoid generating the de facto hinges in the created mechanisms. Aimed at eliminating the costly reinitialization procedure during the evolution of the level set function, an accelerated level set evolution algorithm is developed by adding an extra energy function, which can force the level set function to close to a signed distance function during the evolution. Two widely studied numerical examples in topology optimization of compliant mechanisms are studied to demonstrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.