Topology Optimization Of Compliant Mechanisms Research Articles

Compliant Mechanism Synthesis Using Nonlinear Elastic Topology Optimization With Variable Boundary Conditions

ABSTRACTIn topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads and supports are often difficult to find manually. This substantially limits topology optimization's effectiveness for many mechanism design problems. We remove this limitation by developing a method which automatically determines optimal positioning of a prescribed input displacement and a set of supports simultaneously with an optimal material layout. Using nonlinear elastic physics, we synthesize a variety of compliant mechanisms with large output displacements, snap‐through responses, and prescribed output paths, producing designs with significantly improved performance in every case tested. Compared to optimal designs generated using manually designed boundary conditions used in previous studies, the mechanisms presented in this paper see performance increases ranging from 47% to 380%. The results show that nonlinear mechanism responses may be particularly sensitive to boundary condition locations and that effective placements can be difficult to find without an automated method.

Topology optimization of compliant mechanisms including links, supports and material distribution

This paper proposes a novel topology optimization method integrating the layout of the supports, links and material distribution to design partially compliant mechanisms. The potential supports and links are distributed in the design domain in initialization, each with an active or inactive state. The nonlinear spring model is implemented for the unified modeling of potential supports and links. The mechanical properties of springs are associated with the states of supports and links. Within the traditional density-based framework, a new group of design variables representing the states of supports and links is introduced into the topology optimization model. For obtaining a physically realizable mechanism, the design variables representing the element density of the structure and the states of supports or links are uniformly penalized for avoiding intermediate values. Sensitivity analysis is conducted by implementing the adjoint equation method. The versatility and flexibility of the proposed method are demonstrated via numerical examples and the accuracy of the nonlinear spring model is verified by comparison of results.

Topology Optimization of Compliant Mechanisms Considering Manufacturing Uncertainty, Fatigue, and Static Failure Constraints

This study presents a new robust formulation for the topology optimization of compliant mechanisms, addressing the design challenges while considering manufacturability, static strength, and fatigue failure. A three-field density projection is implemented to control the minimum size of both real-phase and null-phase material structures to meet the manufacturing process requirements. The static strength is evaluated via the sum of the amplitude and the mean absolute value of the signed von Mises stress. The fatigue failure is solved via the modified Goodman criterion. The real output displacement is optimized by adding artificial springs to the prescribed value. This approach is implemented based on an improved solid isotropic material with penalization (SIMP) interpolation method to describe and solve the optimization model and derive the shape sensitivity of the optimization problem. Finally, two numerical examples are applied to illustrate the effectiveness of the presented method.

Topology optimization of compliant mechanisms under transient thermal conditions

This work considers multi-material topology optimization of compliant mechanisms under transient thermal and quasi-static mechanical conditions wherein thermally actuated devices are optimized for different operating conditions. The materials are modeled using finite strain thermo-hyperelasticity and a two way coupling between the energy balance and equilibrium equations is investigated. The design updates are generated from the gradient-based method of moving asymptotes optimizer and the sensitivities are computed using the time dependent adjoint sensitivity analysis. Results show the impact of designing for short versus long actuation times.

HMPS法とCA-IESO法を用いたコンプライアントメカニズムの形態創生

In this paper, a topology optimization method of compliant mechanisms considering geometrical nonlinearity is proposed. In the method, the HMPS method, which is one of particle methods, is used for the analysis considering geometrical nonlinearity. The CA-IESO (Cellular Automaton - Improved Evolutionary Structural Optimization) method is used for the topology optimization. In the formulations, we show the objective function and the sensitivity those are adapted to the topology optimization of compliant mechanism using the CA-IESO method. Several numerical examples are provided to demonstrate the effectiveness of the proposed method for the topology optimization of compliant mechanisms.

Topology Optimization of Compliant Mechanisms Based on Rotation Constraint Strategy

Topology Optimization of Compliant Mechanisms Based on Rotation Constraint Strategy

Topology optimization of compliant mechanisms with distributed compliance (hinge-free compliant mechanisms) by using stiffness and adaptive volume constraints instead of stress constraints

Many approaches have been developed for the synthesis of compliant mechanisms via topology optimization. Most of these approaches produce mechanisms with lumped compliance if not extended appropriately, such as with stress constraints. With mechanisms with lumped compliance, the deformation is concentrated in regions of small dimensions (referred to as “de facto hinges” or “one-node connected hinges”) causing notch overstresses. Some extensions to these approaches overcome this by forcing mechanisms with distributed compliance (also referred to as “hinge-free compliant mechanisms”). However, the currently known extensions have a number of drawbacks. Stress constraints, for example, make the optimization formulation highly nonlinear and non-convex. In this paper, a new extension is presented that permits the synthesis of mechanisms with distributed compliance by combining a constraint for the allowed structural stiffness with an adaptive volume constraint. The presented optimization approach can be easily solved using linear optimization. The basis for the extension presented in this paper is the modal synthesis approach, which permits the synthesis of transverse-load-insensitive compliant mechanisms. The methodology developed is tested on suitable design examples.

Design of compliant mechanisms: An explicit topology optimization method using end-constrained spline curves with variable width

In this study, an approach using moving end-constrained spline (ECS) curves with variable widths is presented for the explicit topology optimization of compliant mechanisms. The proposed approach uses a series of spline curves to represent the topology of the compliant mechanism. Instead of using a fixed width, we let the width of such spline curves vary along the curve. The optimized design is obtained by optimizing the width of the spline curves and the position of the control points. To avoid infeasible solutions in the design process, the end points of several specific spline curves are constrained according to the design region. The validity of the proposed method is demonstrated using different types of splines, such as the Bézier curve and B-spline curve, for the design of a force inverter, a compliant gripper and a compliant orthogonal displacement amplification mechanism.

Topology optimization of compliant mechanisms and structures subjected to design-dependent pressure loadings

This article presents an extended algorithm for topology optimization of compliant mechanisms and structures with design-dependent pressure loadings using the moving iso-surface threshold (MIST) method. In this algorithm, the fluid-structure interface is modeled using the finite element method via considering equivalent virtual strain energy and work and is tracked by an element-based searching scheme. Design-dependent pressure loads are directly applied on interface boundary and are calculated as virtual work equivalent nodal forces in the interface elements based on the finite element formulation. Several numerical examples are presented for topology optimization of mean compliance and compliant mechanisms. The present algorithm is validated through benchmarking with the results in literature and/or full finite element analysis (FEA) results of the optimum compliant mechanism and structure designs.

Multi-material topology optimization of compliant mechanisms using regularized projected gradient approach

In this article, the identification of optimal topologies for multi-material compliant mechanisms based on the regularized projected gradient approach is presented and analyzed. The monolithic structure of compliant mechanisms makes them suitable to be used in microelectromechanical systems to transfer load and force. The use of additive manufacturing technologies makes it possible to build multi-material structures. However, a proper design optimization approach must be considered to design multi-material mechanisms as well. In this article, the solid isotropic material with a penalization (SIMP) material interpolation scheme is used to parameterize the continuum design domain. The perimeter penalization approach is utilized to remove the checkerboard patterns and scatters in optimal designs. To handle the volume equality constraint, the regularized constraint projection strategy is utilized. Some benchmark problems are considered to analyze the performance of the method.

Design of a Continuum Mechanism That Matches the Movement of an Eight-Bar Linkage

Abstract This paper presents a design methodology for mechanisms consisting of a single continuous structure, continuum mechanisms, that blends the kinematic synthesis of rigid-body mechanisms with topology optimization for compliant mechanisms. Rather than start with a generic structure that is shaped to achieve a required force-deflection task for a compliant mechanism, our approach shapes the initial structure based on the kinematic synthesis of a rigid-body mechanism for the required movement, then the structure is shaped using finite element analysis to achieve the required force-deflection relationship. The result of this approach is a continuum mechanism with the same workpiece movement as the rigid link mechanism when actuated. An example illustrates the design process to obtain an eight-bar linkage that guides its workpiece in straight-line rectilinear movement. We show that the resulting continuum mechanism provides the desired rectilinear movement. A 210 mm physical model machined from Nylon-6 is shown to achieve 21.5 mm rectilinear movement with no perceived deviation from a straight-line.

Experimental verification of robust topology optimization for compliant mechanism

Purpose This paper is to present an experiment to verify that the motion errors of robust topology optimization results of compliant mechanisms are insensitive to load dispersion. Design/methodology/approach First, the test pieces of deterministic optimization and robust optimization results are manufactured by the combination of three-dimensional (3D) printing and casting techniques. To measure the displacement of the test piece of compliant mechanism, a displacement measurement method based on the image recognition technique is proposed in this paper. Findings According to the experimental data analysis, the robust topology optimization results of compliant mechanisms are less sensitive to uncertainties, comparing with the deterministic optimization results. Originality/value An experiment is presented to verify the effectiveness of robust topology optimization for compliant mechanisms. The test pieces of deterministic optimization and robust optimization results are manufactured by the combination of 3D printing and casting techniques. By comparing the experimental data, it is found that the motion errors of robust topology optimization results of compliant mechanisms are insensitive to load dispersion.

Topology optimization of compliant mechanisms considering strain variance

In this work, compliant mechanisms are designed by using multi-objective topology optimization, where maximization of the output displacement and minimization of the strain are considered simultaneously. To quantify the strain, we consider typical measures of strain, which are based on the p-norm, and a new class of strain quantifying functions, which are based on the variance of the strain. The topology optimization problem is formulated using the Solid Isotropic Material with Penalization (SIMP) method, and the sensitivities with respect to design changes are derived using the adjoint method. Since nearly void regions may be highly strained, these regions are excluded in the objective function by a projection method. In the numerical examples, compliant grippers and inverters are designed, and the tradeoff between the output displacement and the strain function is investigated. The numerical results show that distributed compliant mechanisms without lumped hinges can be obtained when including the variance of the strain in the objective function.

Topology optimization of compliant mechanisms considering stress constraints, manufacturing uncertainty and geometric nonlinearity

This paper proposes and investigates two formulations to topology optimization of compliant mechanisms considering stress constraints, manufacturing uncertainty and geometric nonlinearity. The first formulation extends the maximum output displacement robust approach with stress constraints to incorporate the effects of geometric nonlinear behavior during the optimization process. The second formulation relies on the concept of path-generating mechanisms, where not only the final configuration is important, but also the load–displacement equilibrium path. A novel path-generating formulation is thus proposed, not only to achieve the prescribed equilibrium path, but also to take stress constraints and manufacturing uncertainty into account during the optimization process. Although both formulations have different goals, the same main techniques are employed: density approach to topology optimization, augmented Lagrangian method to handle the large number of stress constraints, three-field robust approach to handle the manufacturing uncertainty, and the energy interpolation scheme to handle convergence issues due to large deformation in void regions. Several numerical examples are addressed to demonstrate applicability of the proposed approaches. The optimized results are post-processed with body-fitted finite element meshes. Obtained results demonstrate that: (1) the proposed nonlinear analysis based maximum output displacement approach is able to provide solutions with good performance in situations of large displacements, with stress and manufacturing requirements satisfied; (2) the linear analysis based maximum output displacement approach provides optimized topologies that show large stress constraint violations and rapidly varying stress behavior under uniform boundary variation, when these are post-processed with full nonlinear analysis; (3) the proposed path-generating formulation is able to provide solutions that follow the prescribed control points, including stress robustness.

Multi-material topology optimization of compliant mechanisms via solid isotropic material with penalization approach and alternating active phase algorithm

The present study aims at providing a topology optimization of multi-material compliant mechanisms using solid isotropic material with penalization (SIMP) approach. In this respect, three multi-material gripper, invertor, and cruncher compliant mechanisms are considered that consist of three solid phases, including polyamide, polyethylene terephthalate, and polypropylene. The alternating active-phase algorithm is employed to find the distribution of the materials in the mechanism. In this case, the multiphase topology optimization problem is divided into a series of binary phase topology optimization sub-problems to be solved partially in a sequential manner. Finally, the maximum displacement of the multi-material compliant mechanisms was validated against the results obtained from the finite element simulations by the ANSYS Workbench software, and a close agreement between the results was observed. The results reveal the capability of the SIMP method to accurately conduct the topology optimization of multi-material compliant mechanisms.

Stress-constrained level set topology optimization for compliant mechanisms

This work presents a level set-based topology optimization procedure to design compliant mechanisms subject to local stress constraints. A classical technical difficulty related to the design of compliant mechanisms is the emergence of non-realistic flexible joints (hinges) subject to unfeasible strain and stresses. A natural way to overcome this occurrence is the inclusion of stress constraints within the formulation. This approach brings, on the other hand, particular difficulties associated with the local nature of stress constraints. To deal with this issue, stress constraints are included in the present work using an augmented Lagrangian mathematical programming technique. A level set approach defines the design of the mechanical part and a reaction–diffusion equation is used to update the level set function towards the optimized state. A natural extension of the velocity field provided for the reaction–diffusion equation allows for hole nucleation during the design updating. The joining of an augmented Lagrangian approach and level set implicit boundaries to handle local stress constraints in order to obtain hinge-free compliant mechanisms is the novelty of this paper. Several two-dimensional numerical examples show the efficacy of the proposed procedure. In particular, an example analyzes the influence of the weak material in the design of compliant mechanisms. Level set designs enable that final solutions are validated in commercial finite element codes without any post-processing procedure.

Stress-based topology optimization of compliant mechanisms using nonlinear mechanics

The present work demonstrates how a light structure can be easily designed through Topology Optimization even including complex analysis and sizing criteria such as hyperelastic Neo-Hookean materials for nonlinear analysis and aggregated stress constraints. The SIMP approach was adopted and two different strategies were analysed using an in house versatile MATLAB code. MMA was used as reference optimizer (in structural optimization) whereas a unified aggregation and relaxation method was adopted to deal with stress constraints. Feasibility was analyzed from the viewpoint of allowable stress verification. Two test cases are then studied: a morphing airfoil (for aeronautical applications) and a geometric inverter (for mechanics and bio-medical applications). For both, a hyperelastic Neo-Hookean material was chosen. Finally a complementary study on the effects of constraints and the input force intensity is also presented.

Topology optimization of compliant mechanism considering actual output displacement using adaptive output spring stiffness

This paper presents a new method for topology optimization of compliant mechanisms considering actual output displacement. The optimization problem is reformulated by maximizing the output displacement with artificial springs meanwhile optimizing the actual output displacement without artificial springs to the prescribed value. A method of adaptive output spring stiffness is developed for automatic adjustment of output spring stiffness according to the prescribed actual output displacement. The multi-objective design problem is converted into a single-objective problem using the weighted-sum method and a weighting factor with adaptive adjustment is presented. This method is implemented based on the SIMP (Solid Isotropic Material with Penalization) formulation and the design problem is solved by the MMA (Method of Moving Asymptotes) optimization algorithm on the basis of the sensitivity analysis. Numerous numerical examples are applied to illustrate the effectiveness of the presented method.

Topology optimization of compliant mechanisms with stress constraints and manufacturing error robustness

This work proposes a robust formulation to address the compliant mechanism design problem subject to both stress constraints and manufacturing uncertainty. The proposed formulation is an extension of the robust approach for compliant mechanism design based on eroded, intermediate and dilated projections. The novelty in this proposal comes from inclusion of a stress failure criterion in each projected field, in order to ensure compliant mechanisms that satisfy the stress failure criterion even in the presence of uniform manufacturing variations. The objective of the optimization problem is the minimization of the maximum displacement at the output port of the mechanism, given eroded, intermediate and dilated designs, subjected to upper and lower volume constraints and one stress constraint per finite element on each of the three projected fields. The objective function is weighted by the volume of the dilated topology, in order to avoid possible numerical instabilities that may occur when the upper volume constraint is not active. Several examples are solved and the optimized results are post-processed with body-fitted finite element meshes. Numerical results demonstrate that: 1) the proposed stress-constrained robust approach provides results in which both maximum stress and output displacements are robust with respect to uniform boundary variations; however, while the maximum stress is almost insensitive to manufacturing variations, the output displacement does show some degradation when compared with the traditional robust approach; 2) the traditional robust approach, i.e., without the stress considerations, provides results in which the maximum stress has unpredictable and non-smooth behavior after uniform boundary variation; and 3) the stress-constrained deterministic approach, i.e., without considering the manufacturing uncertainty, provides results in which both maximum stress and output displacements are non-robust with respect to uniform boundary variations.

Robust topology optimization of compliant mechanisms with uncertainties in output stiffness

SummaryThis work addresses the topology optimization approach to design robust compliant mechanisms with respect to uncertainties in the output stiffness, when compared to the traditional deterministic approach. To this end, two formulations are proposed: probabilistic and nonprobabilistic. The probabilistic formulation minimizes a joint objective function of expected output displacement plus a measure of its standard deviations, for given statistical distribution of the output stiffness. The nonprobabilistic formulation is written as minimization of a joint function of the median of output displacements, plus the width of the intervals that contains the extreme values of the output displacements, for a given interval of output stiffness. The Monte Carlo simulation method is used to evaluate expected values and standard deviations of output displacements in the probabilistic formulation and to assess results obtained with the deterministic approach. It is shown that both formulations lead to designs where output displacements are less sensitive to variations of output stiffness when compared to the traditional deterministic approach. Furthermore, as an additional benefit, it is observed that large variations of output stiffness can hinder the appearance of one‐node connected hinges, usually found in the deterministic design of compliant mechanisms.