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

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.

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

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 no matter 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 grey cell problem that is usually caused by intermediate material states. Von Mises 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 avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions require no postprocessing or interpretation, and have no point flexure, unsmooth boundary and zigzag member. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples in compliant mechanisms.

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is usually caused by intermediate material states. Local 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 avoid the need to select the initial guess solution and conduct sensitivity analysis. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

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.

Inspired by nature’s multi-material compliant designs and the capability of modern manufacturing methods to make multi-material components without assembly, and motivated by the versatility and enhanced functionality with multi-material designs, we formalize the notion and the design of heterogeneous compliant mechanisms. In the topology optimization of compliant mechanisms, a fictitious density function 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 optimality criteria method, we synthesize compliant mechanisms with multiple materials with and without the material resource constraint. The numerical examples include the two, three, and four material designs where void is treated as one material. This new design method enables us to optimally juxtapose stiff and flexible materials in heterogeneous compliant mechanisms that can be built using a variety of modern manufacturing methods.

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.

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.

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.

Structural Topology Optimization of Compliant Mechanisms Based on the Continuous Approximation Assumption of Material Distributions

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.

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

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.

Larger deformation and higher bearing capacity is a worthwhile goal for designing the compliant mechanism. By virtue of the anisotropy, variable stiffness and superior designability, fiber reinforced composite material is effective way to solve the contradictory problem. There are several reports to design compliant mechanism with composites and improve its performances. But adding directly stress constraints in topology optimization process is very complex and difficult to establish the explicit expression of stress constraints for compliant mechanism with composites. This paper investigated the topology optimization and performance prediction of compliant mechanism with composites by neural network. Topology configurations, output displacements and maximal stress in matrix materials of compliant mechanism under different fiber laying angles were firstly implemented. Subsequently, neutral network models were built to predict the output displacement and maximal stress. Examples of compliant inverter and gripper were used to verify the proposed method.

A method is developed to systematically remove and reintroduce low density elements from and into the finite element mesh on which the structural topology optimization problem is defined. The material density field which defines the topology and the local ‘stiffness’ of the structure is optimally distributed via non‐linear programming techniques. To prevent elements from having zero stiffness, an arbitrarily small lower bound on the material density is typically imposed to ensure that the global stiffness matrix does not become singular. While this approach works well for most minimum compliance problems, the presence of low density elements can cause computational problems, particularly in structures that exhibit geometric non‐linearities, e.g. in compliant mechanisms. To resolve this problem, a systematic approach for removing and reintroducing low density elements is presented, and the substantial performance improvements both in design and computational efficiency of the method over current methods are discussed. Several structures and compliant mechanisms are designed to demonstrate the method. Copyright © 2003 John Wiley & Sons, Ltd.