Shape design of pin-jointed multistable compliant mechanisms using snapthrough behavior

A general approach is presented for generating pin-jointed multistable compliant mechanisms using snapthrough behavior. An optimization problem is formulated for minimizing the total structural volume under constraints on the displacements at the specified nodes, stiffnesses at initial and final states, and load factors to lead to snapthrough behavior. The design variables are cross-sectional areas and the nodal coordinates. It is shown in the numerical examples that several mechanisms can be naturally found as a result of optimization starting from randomly selected initial solutions. It is also shown that no local bifurcation point exists along the equilibrium path, and the obtained mechanism is not sensitive to initial imperfections.     

Topology optimization of structures with integral compliant mechanisms for mid-frequency response

The purpose of this paper is to present a method for developing new truss-like sandwich structures that exhibit desirable mid-frequency vibratory characteristics. Specifically, a genetic algorithm optimization routine is used to determine candidate small scale structural topologies, i.e. unit cells, that may be used in the design of larger scale periodic sandwich structures. This multi-scale procedure is demonstrated starting with several unit cell topology optimization examples. From these examples a specific optimal unit cell is selected for further investigation and integration into a periodic sandwich beam. Computational results indicate that the proposed optimization approach is effective when used to design new structures for reduced mid-frequency vibratory response.     

Complex-shaped beam element and graph-based optimization of compliant mechanisms

Compliant mechanisms are designed to be intentionally flexible, providing hingeless mechanisms. This work contributes a complex-shaped beam element formulation in conjunction with the ground structure approach. We identify compliant mechanism design solutions by using evolutionary topology optimization and increase flexibility by using a parametrization concept based on graph theory. The new operators for evolutionary optimization are also explained and sample problems are used to address the question of how our contribution increases design solutions space.     

Topology design of large displacement compliant mechanisms with multiple materials and multiple output ports

Topology optimization of compliant mechanisms is presented in this paper wherein the layout design problem is addressed in its original binary or discrete (0-1) form. Design variables are modeled as discrete variables and allowed to assume values pertaining only to their void (0) or solid (1) states. Due to this discrete nature, a genetic algorithm is employed as an optimization routine. Using the barrier assignment approach, the search algorithm is extended to use with multiple materials. The layout design of compliant mechanisms is performed wherein displacements at multiple points (ports) in the design region are maximized along the respective prescribed directions. With multiple output ports and multiple materials, additional freedom in motion and force transduction can be achieved with compliant mechanisms. Geometrically large deformation analysis is employed to compute the displacement-based multiple objectives that are extremized using Nondominated Sorting in Genetic Algorithms (or NSGA). With genetic algorithms, buckling or snap through like issues with nonconvergent solutions in the population when computing nonlinear deformations can be implicitly circumvented.     

Six-DOF micro-manipulator based on compliant parallel mechanism with integrated force sensor

This paper describes the design of a micro-scale manipulator based on a six-DOF compliant parallel mechanism (CPM), which is featured by piezo-driven actuators and integrated force sensor capable of delivering six-DOF motions with high precision and providing real-time force information for feedback control. Particularly, the position and screw-based Jacobian analyses of the CPM are presented. Then, the compliance model and the workspace evaluation of the CPM are proposed in order to account for the compliance and obtain design guidelines. Finally, the integrated sensor is introduced. The static features of such a mechanism include high positioning accuracy, structural compactness and smooth and continuous displacements.     

A new level set method for systematic design of hinge-free compliant mechanisms

This paper presents a new level set-based method to realize shape and topology optimization of hinge-free compliant mechanisms. A quadratic energy functional used in image processing applications is introduced in the level set method to control the geometric width of structural components in the created mechanism. A semi-implicit scheme with an additive operator splitting (AOS) algorithm is employed to solve the Hamilton-Jacobi partial differential equation (PDE) in the level set method. The design of compliant mechanisms is mathematically represented as a general non-linear programming with a new objective function augmented by the high-order energy term. The structural optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints. In doing so, it is expected that numerical difficulties such as the Courant-Friedrichs-Lewy (CFL) condition and periodically applied re-initialization procedures in most conventional level set methods can be eliminated. In addition, new holes can be created inside the design domain. The final mechanism configurations consist of strip-like members suitable for generating distributed compliance, and solving the de-facto hinge problem in the design of compliant mechanisms. Two widely studied numerical examples are studied to demonstrate the effectiveness of the proposed method in the context of designing distributed compliant mechanisms.     

Design of distributed compliant micromechanisms with an implicit free boundary representation

In this paper, a parameterization approach is presented for structural shape and topology optimization of compliant mechanisms using a moving boundary representation. A level set model is developed to implicitly describe the structural boundary by embedding into a scalar function of higher dimension as zero level set. The compactly supported radial basis function of favorable smoothness and accuracy is used to interpolate the level set function. Thus, the temporal and spatial initial value problem is now converted into a time-separable parameterization problem. Accordingly, the more difficult shape and topology optimization of the Hamilton–Jacobi equation is then transferred into a relatively easy size optimization with the expansion coefficients as design variables. The design boundary is therefore advanced by applying the optimality criteria method to iteratively evaluate the size optimization so as to update the level set function in accordance with expansion coefficients of the interpolation. The optimization problem of the compliant mechanism is established by including both the mechanical efficiency as the objective function and the prescribed material usage as the constraint. The design sensitivity analysis is performed by utilizing the shape derivative. It is noted that the present method is not only capable of simultaneously addressing shape fidelity and topology changes with a smooth structural boundary but also able to avoid some of the unfavorable numerical issues such as the Courant–Friedrich–Levy condition, the velocity extension algorithm, and the reinitialization procedure in the conventional level set method. In particular, the present method can generate new holes inside the material domain, which makes the final design less insensitive to the initial guess. The compliant inverter is applied to demonstrate the availability of the present method in the framework of the implicit free boundary representation.     

An optimization method for dynamics of structures with repetitive component patterns

The design obtained from a topology optimization problem can be sensitive to the type and details of the ground structure used. A new type of ground structure containing hinged beam elements is described that increases the types of elements in the ground structure available to the optimizer. In addition to the pin-ended truss and rigidly-connected beam elements that have traditionally been used, two new types of elements are introduced: (1) a beam with a hinge on one end and a solid connection on the other end, (2) a beam with hinges on both ends. These elements have different deflection characteristics than those of the typical truss or beam elements, and can be used in ground structure-based compliant mechanism design. Given a reduced ground structure, these new elements effectively increase the design space. Pin-ended members with lengths larger than those of the ground structure cell size are permitted to develop, reducing the sensitivity of solutions to the cell density of the reduced ground structure. Furthermore, because these longer members do not require intermediate lateral support to provide stability, as series connections of shorter pin-ended members do, fewer ancillary members are required. Two compliant mechanism problems are solved to demonstrate the effectiveness of these new elements.     

Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace

In recent years, nanotechnology has been developing rapidly due to its potential applications in various fields that new materials and products are produced. In this paper, a novel macro/micro 3-DOF parallel platform is proposed for micro positioning applications. The kinematics model of the dual parallel mechanism system is established by the stiffness model with individual wide-range flexure hinge and the vector-loop equation. The inverse solutions and parasitic rotations of the moving platform are obtained and analyzed, which are based on a parallel mechanism with real parameters. The reachable and usable workspace of the macro motion and micro motion of the mechanism are plotted and analyzed. Finally, based on the analysis of parasitic rotations and usable workspace of micro motion, an optimization for the parallel manipulator is presented. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for the dual parallel mechanism in order to achieve the features of both larger workspace and higher motion precision.     

Genetic algorithm with advanced mechanisms applied to the protein structure prediction in a hydrophobic-polar model and cubic lattice

This paper presents a genetic algorithm applied to the protein structure prediction in a hydrophobic-polar model on a cubic lattice. The proposed genetic algorithm is extended with crowding, clustering, repair, local search and opposition-based mechanisms. The crowding is responsible for maintaining the good solutions to the end of the evolutionary process while the clustering is used to divide a whole population into a number of subpopulations that can locate different good solutions. The repair mechanism transforms infeasible solutions to feasible solutions that do not occupy the lattice point for more than one monomer. In order to improve convergence speed the algorithm uses local search. This mechanism improves the quality of conformations with the local movement of one or two consecutive monomers through the entire conformation. The opposition-based mechanism is introduced to transform conformations to the opposite direction. In this way the algorithm easily improves good solutions on both sides of the sequence. The proposed algorithm was tested on a number of well-known hydrophobic-polar sequences. The obtained results show that the mechanisms employed improve the algorithm's performance and that our algorithm is superior to other state-of-the-art evolutionary and swarm algorithms.     

Design and robust optimal control of smart beams with application on vibrations suppression

This paper presents the design of a vibration control mechanism for a beam with bonded piezoelectric sensors and actuators and an application of the arising smart structure for vibrations suppression. The mechanical modeling of the structure and the subsequent finite element approximation are based on Hamilton's principle and classical engineering theory for bending of beams in connection with simplified modeling of piezoelectric sensors and actuators. Two control schemes LQR and H₂ are considered. The latter robust controller takes into account uncertainties of the dynamical system and moreover incompleteness of the measured information, it therefore leads to applicable design of smart structures. The numerical simulation shows that sufficient vibration suppression can be achieved by means of the proposed general methods.     

Computerized tolerance analysis of disk cam mechanisms with a roller follower

The tolerance analysis is one of the key elements of design and manufacturing of cam mechanisms. This paper presents a computerized method for analyzing the tolerances in disk cam mechanisms with a roller follower. By employing the concept of simulated higher-pair contact analysis, the kinematic deviation of the follower motion arising from the tolerance amount of each design parameter can be determined numerically. The offset translating roller follower and the oscillating roller follower cases are given to illustrate the proposed method. The tolerance analysis results show that, owing to the combined effects of various design parameters, the position accuracy of the follower motion may degrade considerably. But, the tolerance amounts of the design parameters may also have a compensating effect to enhance the relative accuracy of the follower motion between its high and low dwell positions. Hence, it is possible to find the optimal tolerance combination for balancing the kinematic accuracy and the tolerance amounts of disk cam mechanisms with a roller follower.     

A hierarchical genetic algorithm with age structure for multimodal optimal design of hybrid composites

A genetic algorithm aiming the optimal design of composite structures under non-linear behaviour is presented. The approach addresses the optimal material/stacking sequence in laminate construction and material distribution topology in composite structures as a multimodal optimization problem. The proposed evolutionary process is based on a sequential hierarchical relation between subpopulations evolving in separated isolation stages followed by migration. Improvements based on the species conservation paradigm are performed to avoid genetic tendencies due to elitist strategies used in the hierarchical subpopulations. The concept of species is associated with material distribution topology in composite structures, and an enlarged master population with age structure is considered concurrently with the hierarchical topology. Rules based on species concept are imposed on either isolation or migration stages to overcome the predominance of a species and to guarantee the diversity. A mutation process controlled by the stress field is implemented, improving the local genetic search. The proposed model allows multiple solutions for the optimal design problem.     

Type synthesis of a class of spatial lower-mobility parallel mechanisms with orthogonal arrangement based on Lie group enumeration

Type synthesis of lower-mobility parallel mechanisms (PMs) has drawn extensive interests, particularly two main approaches were established by using the reciprocal screw system theory and Lie group theory, respectively. Although every above approach provides a universal framework for structural design of general lower-mobility PMs, type synthesis is still a comparably difficult task for the PMs with particular geometry or required to fulfill some specified tasks. This paper aims at exploring a simple and ef...     

A complete development process of finite element software for body-in-white structure with semi-rigid beams in .NET framework

At the conceptual design stage, simplified finite element (FE) model of body-in-white (BIW) structure focuses on its specific merit to provide early-stage predictions for detailed FE model of that. This paper exploits a semi-rigid beam element (SRBE) that consists of a beam element with two semi-rigid connections at the ends to simulate the flexibility of joint. Guyan reduction method condenses the SRBE as a super element. A special finite element software for structural modeling and analysis of BIW (SMAB) is developed in .NET framework. The Unified Modeling Language is employed to depict the classes and their relationship. The design patterns are identified and applied in the framework design to facilitate communication and system expansion. Microsoft DirectX and GDI+ implement graphics display of spatial BIW frame and planar thin-walled cross section. Based on multi-threaded technology in .NET, subspace iteration method is paralleled to speed up the mode analysis. As a result, the efficiency of the SRBE is demonstrated by a benchmarking automotive body. Multi-threaded parallel is effective and useful, especially for frequency optimization.     

Proportional derivative and strain (PDS) boundary feedback control of a flexible space structure with a closed-loop chain mechanism

A simple space truss structure, a rigid connection of two flexible beams, is modeled as a distributed parameter system subject to holonomic constraints. Boundary feedback control synthesis is developed for this structure. The synthesis is carried out in the infinite-dimensional setting, mathematical features of which give rise to a stabilizing PDS control algorithm. Due to simplicity of the implementation, the algorithm becomes extremely attractive under limitations on the computer power in the space. The effectiveness of the control strategy proposed is supported by experimental tests.     

BH2+与H2S反应机理的量子化学及电子密度拓扑研究

采用密度泛函方法B3LYP和耦合簇方法CCSD在6-311 G(d,p)条件中,研究BH_2~ 与H_2S的气相离子-分子反应的微观反应机理。优化反应势能面上各驻点的几何构型,通过振动分析和IRC计算证实中间体和过渡态的真实性和相互连接关系。采用电子密度拓扑分析反应(1)进程中的若干关键点,讨论反应进程中化学键的断裂、生成和变化规律,找到了该反应的结构过渡区(结构过渡态)和能量过渡态。