An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms

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 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.

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 :

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 new fuzzy strategy for size and topology optimization of truss structures

A multi-mesh strategy is employed to reduce the computational costs associated with incorporating correlated uncertainties into structural topology optimization problems. Uncertainty quantification is achieved through an existing perturbation-based method. This method transforms uncertainties in stiffness, such as geometric and material property randomness, into an augmented deterministic topology optimization problem. Although the approach has proven quite efficient in general, the uncertainty sources are tied to the finite element analysis mesh. Computational costs then rise significantly when refining the finite element mesh in the presence of correlated random variables. We therefore propose separating the analysis and uncertainty mesh. The technique is evaluated on problems of expected stiffness with uncertainties in elastic modulus and compared to solutions found using the standard perturbation and Monte Carlo topology optimization algorithms.

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.

The center of mass and the inertia tensor are important parameters characterizing the kinetic properties of many structural systems, e.g., the rotor, spacecraft, and aircraft. In these occasions, designs not consistent with the requirements on the center of mass and inertia tensor cannot be accepted. In this paper, mathematical models are established to carry out the topology optimization of continua considering the mass and inertia characteristics. Two numerical examples, one for minimizing the static compliance considering locations of the center of mass and the other for maximizing the fundamental eigenfrequency considering both locations of the center of mass and values of the inertia products, are presented to demonstrate that the requirements on mass and inertia characteristics could have a profound influence on the final optimized layouts in structural topology optimization problems. On the other hand, the mass and inertia characteristics can also be tuned by topology optimization methods. In the second numerical problem, the smooth minimum operator is used to approximate the fundamental eigenfrequency with the first 4 eigenfrequencies so that the possible non-differentiability of the repeated eigenfrequencies can be avoided. Due to its extreme importance in engineering practice, the work of this paper can be useful to carry out designs in accordance with the requirements on the mass and inertia characteristics under the framework of traditional density-based structural topology optimization methods.

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.

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.

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.

Robust topology optimization of multi-material structures under load uncertainty using the alternating active-phase method

The increasing structural flexibility of large aircraft leads to significant aeroelastic effects. More efficient topology optimization techniques are required for the design to further take advantage of aeroelasticity and obtain lightweight structures. This paper proposes a moving boundary meshfree topology optimization that combines the Galerkin method of weighted residuals and non-uniform rational B-splines (NURBS). The solution domain is described by the control points of NURBS and its property is calculated adaptively with an integration subtraction technique. The minimal compliance is searched for using the globally convergent method of moving asymptotes (GCMMA) by designing the locations of control points as subject to volume and flux constraints. The method is first applied to a typical two-dimensional design example with symmetric boundary conditions. The results show that the shape constraints can be conveniently applied, and smoother boundaries are obtained with fewer parameters. Then, a three-dimensional wing structure with asymmetric boundary conditions is optimized. A three-dimensional flight load that combines the high-order-panel and meshfree methods is employed to calculate the elastic loads and update asymmetric external loads during the optimization process. The designed wing satisfies engineering requirements and the presented method can solve the practical topology optimization problems of three-dimensional structures.

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

In this paper, design-dependent pressure loads are addressed for topology optimization problems of multiphase material structures. The modeling of unidirectional load distribution with respect to the material density is studied and mathematical formulations of exponential form are established for the first time to model unidirectional pressure loads on the moving surface and contact surface of fixed shape, respectively. In both load cases, sensitivity analysis scheme of the structural compliance is developed to show the effects of the design-dependent loads. By means of 2D and 3D numerical examples, comparative studies are performed in detail to show the effects of different load cases upon the optimal configurations. It is seen that the proposed design procedure is reliable to deal with the design-dependent load cases.