Topology Optimization and Performance Prediction for Compliant Mechanism with Composites by Neural Network

Random variable of thermo-mechanical coupling (TMC) structure is analyzed first, then the topology optimization model of TMC compliant mechanism is established. According to the uncertainty factors such as temperature, load, volume ratio and thermal expansion coefficient in the process of topology optimization, the robust reliability optimal design method is introduced into the topology optimization process. The various factors on the sensitivity of topology optimization process is analyzed, the best match between various factors is find out, which make the product has robust reliability for the change of the uncertainty. The residual analysis for the most sensitive factors is carried out. Finally the correctness and validity of the method is verified with an example. Introduction When we study the compliant mechanisms by adopting topological optimization method, we only need to give design domain and allocate input and output position, no need from the perspective of a known rigidity. The mechanism come from this method have a input and output relationship of optimized “force—displacement”, thus it attracts people’s attention. Topology optimization research is developing from certain topology optimization direction to reliable topology optimization direction. Jinqing Zhan proposed a reliable topology optimization method of compliant mechanism based on infrastructure method. KHARMANDA proposed a reliable topology optimization method. Zhaokun Li proposed a geometric nonlinear topology optimization research method based on reliable compliant mechanism. Their research turned out that the mechanism based on reliable topology optimization is more reasonable than the mechanism based on certain topology optimization. Yongcong Kuang build a level set function to design variable, stiffness minimization, and proposed corresponding optimization algorithm. Mingtao Cui established a monolithic compliant mechanism multi-target reliable topology optimization design dual mathematical model. This paper combines topology optimization process of compliant mechanism and robust reliability optimal design, analyzes the sensitivity of uncertainty random variables such as design domain’s size, external load and temperature in topology optimization process. Then get the best combination among these random variables. Random Variable Coupling Field Analysis Hot objects will produce thermal expansion, thus caused by the thermal deformation and displacement of combined action of mechanical load and temperature load structure called a hot solid coupling structure, the finite element balance equation :

Although compliant mechanism design is a thoroughly studied field, surprisingly little information can be found in literature regarding selection of optimal materials. This paper is intended to fill this gap. Density-based, geometrically robust, stress constrained topology optimization based on a total Lagrangian FEM formulation is used for investigation of a compliant inverter and a compliant gripper example. Changes in handling of the projection parameters and the stress constraints are proposed for improved algorithmic stability and accurate representation of the stresses and material stiffness in topology optimization. Large-scale optimization studies are carried out, varying elastic modulus and allowable stress in a wide range. A comparison with an Ashby chart shows the characteristics of the best suited material. It is shown, that an optimal Young’s modulus and a minimum required material strength (depending on the modulus) can be identified from the results. Altering critical optimization parameters, e.g. allowable volume fraction and the minimum length scale, their influence on the optimal material choice is investigated. Guidelines for compliant mechanism designers for efficient selection of suited materials are developed.

This paper describes the new way that using topology optimum compliant mechanism and PZT microactuator to design a large force and compliant amplifier mechanism. The common shorting of the microactuator devices is the relation of inverse ratio appears between the output force and output displacement. The mechanism uses the PZT microactuator to be the input and utilize the compliant mechanism to enhance the output displacement. This study uses the PZT microactuator that has 3000mum length, 2000mum width, 500mum thickness and analyses the different performance of microactuator with different applied voltages, width of beam and thickness. In the study, we define the compliant amplifier design domain as 4000mum times 5000mum, thickness as 500mum, and discuss the effect for different optimization parameters. The driving input is a PZT microactuator that can actuate about 6000muN output force to the displacement amplifier and consequently the device can generate about 28mum output displacement when two voltages are applied

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.

This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical nonlinearity together with a suitably chosen hypereleastic material model, wherein the mechanical equilibrium equations are solved using the total Lagrangian finite element formulation. An objective based on least-square error with respect to target strains is formulated and minimized with the given set of constraints and the appropriate surroundings of the tissues. To circumvent numerical instabilities arising due to large deformation in low stiffness design regions during topology optimization, a strain-energy based interpolation scheme is employed. The approach uses an extended robust formulation i.e. the eroded, intermediate and dilated projections for the design description as well as variation in tissue stiffness. Efficacy of the synthesis approach is demonstrated by designing various compliant mechanisms for providing different target strains in biological tissue constructs. Optimized compliant mechanisms are 3D-printed and their performances are recorded in a simplified experiment and compared with simulation results obtained by a commercial software.

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.

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.

This paper presents a topology optimization method of compliant grippers considering stress constraints. The proportional topology optimization (PTO) algorithm is applied to the design of compliant grippers, and it is improved by introducing weight factors into the objective function and adding stress conditions on the basis of constraints. In the current gradient modeling of topology optimization, the global maximum stress is measured by P-norm function, and its sensitivity analysis of stress constraints is derived by adjoint equations. It is worth noting that more rigorous gradient calculations are employed in stress problems and their computation brings an additional computational burden. By contrast, the non-gradient method using PTO algorithm allocates design variables to the element proportionally according to the values of stress. It can eliminate difficulties in the analytical derivation and calculation of gradient, and improve the calculation efficiency. Subsequently, performances of compliant grippers generated by these two methods are compared through finite element analysis. Finally, the optimized compliant gripper prototype is manufactured by three-dimensional (3D) printing using flexible thermoplastic urethane. Experimental results indicate that the non-gradient method is effective, and the optimized compliant gripper has excellent characteristics of low stress and high output performance.

Compliant mechanisms use the flexibility of the limbs for movement and are produced monolithic, without any conventional joint. These flexible mechanisms have wide applications in several fields such as sensors, grippers, parallel mechanisms, micro-electro-mechanical systems, high-precision devices, and biomedical and surgery robots. Topology optimization is regarded as one of the most frequently used approaches for designing compliant mechanisms. The present study aimed to develop the ground structure approach by meshing the design domain using curved beam elements. Moreover, it seeks to implement three different metaheuristic algorithms, including the genetic algorithm, the imperialist competition algorithm, and the equilibrium optimizer for the topology optimization problem. The structural analysis of the compliant mechanism is necessary for determining the values of the objective functions for the optimization process. In the present study, the finite element method was used to analyze the obtained compliant mechanism. Based on the results, an optimum compliant mechanism with both straight and curved beam elements had better performance compared with a compliant mechanism with only straight beams.

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.

This paper presents a microgripper design and utilizes the topology optimum method to obtain larger output force and displacement. The goal of this study is to obtain the sharpest topology layout by simulation and computing. The difference between compliant mechanisms and traditional mechanisms is that compliant mechanisms have flexible pieces to transmit force or deliver motion. When we apply different forces, we use the flexibility to generate expectably related effects to fulfil our special functional purposes. In addition, the shape obtained from topology optimal design can be further refined by shape optimization. This research combines insights from the topology optimum compliant mechanism and the piezoelectric microactuator to design a microgripper and to analyze the effects with different parameters in topology optimization

Compliant mechanisms have been designed for various types of applications to transmit desired forces and motions. In this paper, we explore an application of compliant mechanisms for passive vibration isolation systems. For this, a compliant isolator is used to cancel undesired disturbances, resulting in attenuated output amplitude. A compliant mechanism is equipped with an isolator, while a compliant mechanism also functions as a transmission of force and controls the amount of displacement that is transmitted from it. It can be used as passive vibration isolation. Here, by introducing compliance into the connection, the transmission of applied forces is reduced at some frequencies at the expense of increasing transmission at other frequencies. While transmitted force is the key parameter from the receiver’s perspective, motion at the isolated machine is uninteresting. The force transmissibility is numerically identical to the motion transmissibility. The structural optimization approach is focused on the determination of the topology, shape, and size of the mechanism. The building blocks are used to optimize a structure for force transmission. The flexible building blocks method is used for the optimal design of compliant mechanisms. This approach is used to establish the actuator model of the block and its validation by commercial finite element software. A library of compliant elements is proposed in FlexIn. These blocks are limited in number, and the basis is composed of 36 elements. The force transmitted to the rigid foundation through the isolator is reduced in order to avoid the transmission of vibration to other machines. The preliminary results of FEA from ANSYS demonstrate that compliant mechanism can be effectively used to reduce the amount of force transmitted to the surface.

Compliant mechanisms utilize the elastic deformation of their constituent members to transfer forces or displacements. Compliant mechanisms are advantageous in robotic applications because of their simplified manufacturing, monolithic structure, high precision, low wear and backlash, and flexibility to accommodate a wide range of actuation schemes. Despite these significant advantages, modeling these mechanisms is challenging because of their complex and large nonlinear deformations. Currently, most modeling methods for compliant mechanisms are either kinematic or kinetostatic, such as the pseudo-rigid body method (PRBM), beam constraint model (BCM), and load-flow-based method. These methods are mostly limited to bending deformation and do not consider shear or stretch strain. Furthermore, they are not conducive to modeling compliant mechanisms with embedded actuators in the geometry of the mechanism. To overcome these limitations, here we adopt Cosserat rod modeling, which captures the generalized deformations of the constituent members of compliant mechanisms. Furthermore, it allows the modeling of compliant mechanisms with actuation members. Several compliant mechanism experimental prototypes, including compliant inverters and a compliant gripper, were presented to validate and depict the effectiveness of the Cosserat rod modeling. This modeling approach enables large-scale and efficient modeling of the complaint mechanisms with actuators and sensors.

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 compliant gripper with nearly parallel gripping motion is developed by a topology synthesis and a dimensional synthesis approach. The topology synthesis process can generate linkage-type compliant mechanisms. Suitable boundary conditions of the topology synthesis process are selected to achieve the desired functions of the device. The dimensional synthesis is based on an evolutionary optimal design process. To meet various design goals, a nondominated multi-objective genetic algorithm is selected for the optimal design process. A kinetostaic model based on the chained beam constraint model is developed for force–displacement analysis of the designs. Efficiency and accuracy of the design approach are proved by experiments. Appropriate linkage types of compliant mechanisms may be discovered by the topology optimization process before moving on to the dimensional synthesis to obtain final designs.