Minimum-weight design of flexible arms for specified fundamental frequency

The problem of designing a minimum-weight one-link flexible arm for a specified fundamental frequency of vibration has been investigated. The optimum design problem is formulated as a nonlinear eigenvalue problem using the variational method. Two iteration schemes are developed to find the optimum solution in the normal and degenerated cases. Numerical results have indicated that a significant reduction in link weight can be achieved by the proposed method. For example, for a geometrically similar cross section and a specified fundamental frequency ranging from 1 Hz to 10 Hz, the weight of an optimum link is 400% to 600% lighter than that of an uniform link. © 1997 John Wiley & Sons, Inc.     

Optimum design of frames with multiple constraints using an evolutionary method

This paper presents a simple evolutionary method for the optimum design of structures with stress, stiffness and stability constraints. The evolutionary structural optimization method is based on the concept of slowly removing the inefficient material and/or gradually shifting the material from the strongest part of the structure to the weakest part until the structure evolves towards the desired optimum. The iterative method presented here involves two steps. In the first step, the design variables are scaled uniformly to satisfy the most critical constraint. In the second step, a sensitivity number is calculated for each element depending on its influence on the strength, stiffness and buckling load of the structure. Based on the element sensitivity number, material is shifted from the strongest to the weakest part of the structure. These two steps are repeated in cycles until the desired optimum design is obtained. Illustrative examples are given to show the applicability of the method to the optimum design of frames and trusses with a large number of design variables.     

On the coupled dynamics of small spacecraft and elastic deployable appendages

A thorough investigation of the dynamics of finite-mass satellites with a deployable elastic arm is presented. This work is focused on the interaction between spacecraft rigid body motion and its flexible arm dynamics during the deployment process. The classical Newton–Euler formulation and the Lagrangian approach are applied to the study of the dynamics of spacecraft and its deploying arm. Utilizing a non-Newtonian floating frame to define the arm elastic deformation field, the interactions between the spacecraft and its moving arm have been simulated. Complete equations of motion show that the spacecraft motion induces dynamical stiffness on the arm; in addition, axial and lateral motions of the deploying elastic arm change the spacecraft mass-characteristics and thus influence the spacecraft’s rigid body motions. The overall dynamic behavior is highly dependent on spacecraft mass characteristics in addition to the “arm deployment time (ADT)”. The results of case studies clearly indicate that some assumptions previously applied in appendage dynamic analysis are not conservative and produce erroneous results. This study realistically investigates the dynamics of elastic deploying appendages by considering finite-mass characteristics for small and massy spacecraft. The results reveal that for massive spacecraft the arm’s flexible dynamics is mainly excited through deployment, while for small spacecraft the energy transfers to the arm base and the spacecraft rigid body motion is considerably stimulated. Moreover, this work has further highlighted the effects of ADT in the overall system response. The findings of this work show that the energy distribution between arm’s elastic dynamics and spacecraft rigid body motions is an important factor in the design of any control system to limit unwanted arm-tip motions.     

Optimal Trajectory Planning for Flexible Link Manipulators with Large Deflection Using a New Displacements Approach

The main objective of the present paper is to determine the optimal trajectory of very flexible link manipulators in point-to-point motion using a new displacement approach. A new nonlinear finite element model for the dynamic analysis is employed to describe nonlinear modeling for three-dimensional flexible link manipulators, in which both the geometric elastic nonlinearity and the foreshortening effects are considered. In comparison to other large deformation formulations, the motion equations contain constant stiffness matrix because the terms arising from geometric elastic nonlinearity are moved from elastic forces to inertial, reactive and external forces, which are originally nonlinear. This makes the formulation particularly efficient in computational terms and numerically more stable than alternative geometrically nonlinear formulations based on lower-order terms. In this investigation, the computational method to solve the trajectory planning problem is based on the indirect solution of open-loop optimal control problem. The Pontryagin’s minimum principle is used to obtain the optimality conditions, which is lead to a standard form of a two-point boundary value problem. The proposed approach has been implemented and tested on a single-link very flexible arm and optimal paths with minimum effort and minimum vibration are obtained. The results illustrate the power and efficiency of the method to overcome the high nonlinearity nature of the problem.     

基于动力学仿真的系留气球鼻锥有限元分析

针对系留气球进行了动力学仿真分析,在此基础上对一种用于固定球体的新型鼻锥结构进行了结构有限元分析,以确定其强度与刚度.首先采用计算流体力学CFD求得特定风速下系留气球所受的气动力,随后通过多体动力学软件Adams进行动力学仿真分析,确定作用在鼻锥上载荷的大小,并以此作为有限元分析的载荷边界条件;然后采用有限元分析的方法对鼻锥结构进行静力学和动力学分析;最后确定极限风速下艇首与鼻锥连接处的变形、载荷及应力情况.通过分析,为新型鼻锥结构进一步的设计改进与优化提供了参考依据.     

应用前馈神经网络的大柔性机翼阵风响应分析

大柔性飞行器因结构重量低、柔性大使得机翼等部件在受载时产生较大的弹性变形,呈现显著的几何非线性效应,因此准确的结构大变形建模方法对于几何非线性气动弹性分析至关重要,而神经网络对非线性系统具有强大的拟合能力,可通过将神经网络应用于非线性结构建模,构造适用于结构大变形的前馈神经网络预测模型,在样本特征和数据结构相对较优的条件下结合曲面涡格法,搭建非线性气动弹性分析框架,对某机翼模型进行阵风响应计算;结果表明神经网络模型能准确预测大柔性机翼结构大变形,应用到气动弹性分析后能进行准确的阵风响应计算,验证了将神经网络应用到结构大变形预测的可行性,为以后机器学习技术与气动弹性分析结合的研究提供思路和方法。     

On the tunability of a MEMS based variable capacitor with a novel structure

In this work a novel MEMS based variable capacitor has been presented. To increase the tunability and decrease the applied voltage, the conventional fixed-fixed beam used in CPW lines has been changed to a fixed-simple supported beam. The proposed structure is a simple cantilever micro-beam in the first step of deflection and is changed to a fixed-simple supported micro-beam in the second step of motion. In the capacitive micro-structures increasing the applied voltage decreases the equivalent stiffness of the structure and leads the system to an unstable condition by undergoing to a saddle node bifurcation. In the proposed structure to avoid pull-in instability and increase the capacitance tuning range, mechanical stiffness of the structure is increased by changing boundary conditions by locating a pedestal in the end of the cantilever beam. The governing nonlinear equation for static deflection of the micro-beam, based on Euler–Bernoulli micro-beam theory has been presented. The results show that the proposed structure increases the capacitance tuning range and decreases the applied voltage. The results also show that the position of the pedestal affects the tunability and the threshold voltage of the structure.     

Optimum design of geometrically nonlinear space trusses

A structural optimization algorithm is developed for geometrically nonlinear three-dimensional trusses subject to displacement, stress and cross-sectional area constraints. The method is obtained by coupling the nonlinear analysis technique with the optimality criteria approach. The nonlinear behaviour of the space truss which was required for the steps of optimality criteria method was obtained by using iterative linear analysis. In each iteration the geometric stiffness matrix is constructed for the deformed structure and compensating load vector is applied to the system in order to adjust the joint displacements. During nonlinear analysis, tension members are loaded up to yield stress and compression members are stressed until their critical limits. The overall loss of elastic stability is checked throughout the steps of algorithm. The member forces resulted at the end of nonlinear analysis are used to obtain the new values of design variables for the next cycle. Number of design examples are presented to demonstrate the application of the algorithm. It is shown that the consideration of nonlinear behaviour of the space trusses in their optimum design makes it possible to achieve further reduction in the overall weight. The other advantage of the algorithm is that it takes into account the realistic behaviour of the structure, without which an optimum design might lead to erroneous result. This is noticed in one of the design example where a tension member changed into a compression one at the end of nonlinear analysis.     

Optimization of airplane wing structures under landing loads

A methodology is presented for the optimum design of aircraft wing structures subjected to landing loads. The stresses developed in the wing during landing are computed by considering the interaction between the landing gear and the flexible airplane structure. The landing gear is assumed to have nonlinear characteristics typical of conventional gears, namely, velocity squared damping, polytropic air-compression springing and exponential tire force-deflection characteristics. The coupled nonlinear differential equations of motion that arise in the landing analysis are solved by using a step-by-step numerical integration technique. In order to find the behavior of the wing structure under landing loads and also to obtain a physical insight into the nature of the optimum solution, the design of the typical section (symmetric double-wedge airfoil) is studied by using a graphical procedure. Then a more realistic wing optimization problem is formulated as a constrained nonlinear programming problem based on finite element modeling. The optimum solutions are found by using the interior penalty function method. A sensitivity analysis is conducted to find the effect of changes in design variables about the optimum point on the various response parameters on the wing structure.     

Shape optimizations and static/dynamic characterizations of deformable microplate structures with multiple electrostatic actuators

Micromirrors used in many optoelectronic devices can be considered as microplates. The functions and accuracy of the micromirrors depend on the static and dynamic deflection shapes of microplates. The objective of this study is to develop an efficient method for predicting the shapes of the microplates subjected to unsymmetrical electrostatic forces produced by electrostatic actuators such that micromirrors can be effectively optimized and controlled in their real time operation. The non-classical boundary conditions which result from the microfabrication process were modeled with artificial springs at the edges. A classical energy method using boundary characteristic orthogonal polynomials was applied to formulate the equations of motion of the microsystem. Based on this method, influence functions were built and least squares method was used to optimize the desired deflection under electrostatic forces from the electrostatic actuators. Softening effect of the electrostatic stiffness was also evaluated and considered in the simulation. Static deflections and dynamic responses were compared with those from finite element analysis (FEA) using Reduced Order Modeling (ROM) method. This study found that the static and dynamic responses of microplates predicted from the proposed method were highly consistent with those calculated from FEA. However, the proposed method is simpler and more efficient than FEA and can be conveniently used for any non-classical boundary condition situations. These features make the proposed method useful to effectively control and optimize the shape of a microplate with multiple electrostatic actuators.     

An integrated approach for shape and topology optimization of shell structures

In this paper an automated approach for simultaneous shape and topology optimization of shell structures is presented. Most research in the last decades considered these optimization techniques separately, seeking an initial optimal material layout and refining the shape of the solution later. The method developed in this work combines both optimization techniques, where the shape of the shell structure and material distribution are optimized simultaneously, with the aim of finding the optimum design that maximizes the stiffness of the shell. This formulation involves a variable ground structure for topology optimization, since the shape of the shell is modified in the course of the process. The method has been implemented into a computational model and the feasibility of the approach is demonstrated using several examples.     

Design of a planar multibody dynamic system with ANCF beam elements based on an element-wise stiffness evaluation procedure

The absolute nodal coordinate formulation (ANCF) has been widely applied for large deformation analysis in flexible multibody dynamics. Although the formulation led to stable solutions for time integration under large rotations and deformations, excessive time consumption was recorded. The nonlinear relationship between the deformation and the internal force accounted for repeated adjustment to the force equilibrium state as the structure deformed. In this research, an equivalent model of the ANCF beam structure was constructed. The stiffness evaluation method was applied in an element-wise manner. In this model, the irrelevant parts were separated from those that relate to the displacements and design parameters enabling efficient updates of internal forces to achieve force equilibrium. Therefore, by using this model, optimization problems, in which displacements as well as design parameters keep changing can be efficiently approached. To verify the proposed method, two examples of optimization problems related to a free-falling pendulum and a slider-crank mechanism are demonstrated.     

仿人机器人轻型高刚性手臂设计及运动学分析

重点研究了7自由度轻型高刚性作业型仿人机器人手臂的机构设计和运动学分析方法.首先使用动力学仿真、有限元分析与实验测试相结合的方法,设计了仿人机器人手臂,该机械臂结构紧凑、质量轻、刚度高.同时,提出结合查询数据库和逆运动学计算去模仿人类手臂姿态,从而获得逆运动学最优解的方法.该方法不仅解决了冗余自由度带来的逆运动学多解问...     

Non-Rigid Stereo Factorization

In this paper we address the problem of recovering 3D non-rigid structure from a sequence of images taken with a stereo pair. We have extended existing non-rigid factorization algorithms to the stereo camera case and presented an algorithm to decompose the measurement matrix into the motion of the left and right cameras and the 3D shape, represented as a linear combination of basis-shapes. The added constraints in the stereo camera case are that both cameras are viewing the same structure and that the relative orientation between both cameras is fixed. Our focus in this paper is on the recovery of flexible 3D shape rather than on the correspondence problem. We propose a method to compute reliable 3D models of deformable structure from stereo images. Our experiments with real data show that improved reconstructions can be achieved using this method. The algorithm includes a non-linear optimization step that minimizes image reprojection error and imposes the correct structure to the motion matrix by choosing an appropriate parameterization. We show that 3D shape and motion estimates can be successfully disambiguated after bundle adjustment and demonstrate this on synthetic and real image sequences. While this optimization step is proposed for the stereo camera case, it can be readily applied to the case of non-rigid structure recovery using a monocular video sequence. Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

Vibration suppression control of a flexible arm using a nonlinear observer with simultaneous perturbation stochastic approximation

The main objective in this study is the vibrational control of a one-link flexible arm system. A variable structure system (VSS) nonlinear observer has been proposed in order to reduce the oscillation when controlling the angle-of the flexible arm. The parameters of the nonlinear observer are optimized using a modified version of the simultaneous perturbation stochastic approximation (SPSA) algorithm. The SPSA algorithm is especially useful when the number of parameters to be adjusted is large, and makes it possible to estimate them simultaneously. For the vibration and position control, a model reference sliding-mode control (MR-SMC) has been proposed. The MR-SMC parameters are also optimized using a modified version of the SPSA algorithm. The simulations show that vibrational control of a one-link flexible arm system can be achieved more efficiently using our method. Therefore, by applying the MR-SMC method to a nonlinear observer, we can improve the performance in this kind of model using our proposed SPSA algorithm, and we can determine the control parameters very easy and efficiently.     

柔性冗余度机器人振动抑制的一种方法

新一代机器人要求具有轻质、高速、重载、高精度以及高度灵活性的 ，上于结构柔引起的振动使实现高精度控制十分困难。研究柔性冗余度机器人就是为了克服现有机器人的不足。     

Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates

To consider large deformation problems in multibody system simulations afinite element approach, called absolute nodal coordinate.formulation,has been proposed. In this formulation absolute nodal coordinates andtheir material derivatives are applied to represent both deformation andrigid body motion. The choice of nodal variables allows a fullynonlinear representation of rigid body motion and can provide the exactrigid body inertia in the case of large rotations. The methodology isespecially suited for but not limited to modeling of beams, cables andshells in multibody dynamics.This paper summarizes the absolute nodal coordinate formulation for a 3D Euler–Bernoulli beam model, in particular the definition of nodal variables, corresponding generalized elastic and inertia forces and equations of motion. The element stiffness matrix is a nonlinear function of the nodal variables even in the case of linearized strain/displacement relations. Nonlinear strain/displacement relations can be calculated from the global displacements using quadrature formulae.Computational examples are given which demonstrate the capabilities of the applied methodology. Consequences of the choice of shape.functions on the representation of internal forces are discussed. Linearized strain/displacement modeling is compared to the nonlinear approach and significant advantages of the latter, when using the absolute nodal coordinate formulation, are outlined.     

谱元法在求解刚架结构动力学问题中的应用

把谱元法应用于刚架结构的动力学响应计算和分析中.建立了杆和梁的谱单元动力学刚度阵,针对刚架结构组装了整体动力学刚度阵,建立了整体结构的运动方程,计算了结构的固有频率和时域响应,并与采用有限元方法得到的结果进行了对比.从结果中可以看出谱元法在数值模拟中的独特优势.     

Seismic optimum design of triple friction pendulum bearing subjected to near-fault pulse-like ground motions

Triple Friction Pendulum Bearing (TFPB) as a novel seismic isolator, provides different combinations of stiffness and damping during its course of motion. The adaptive behavior of TFPBs is one of the practical solutions for unsuitable performance of seismic isolation systems under near-fault ground motions. Selecting the TFPB’s design variables (curvature radii, friction coefficients and displacement capacity of sliding surfaces) is complicated process while finding the optimized combination of these variables depends on input ground motion characteristics and seismic performance objectives of the superstructure. Here first, comprehensive nonlinear dynamic analyses are performed to identify influence of the design variables on superstructure response (roof acceleration and displacement of isolated level). Next, a specific numerical optimization method based on Genetic Algorithms (GA) is applied to determine the optimum values of the design variables that minimize superstructure demands. In this process, near-fault ground motions are employed with ranges of pulse periods and hazard levels as input excitations. According to GA results, the derived optimum design variables of TFPB have significantly distinct intervals for different target responses such as story drift and TFPB displacement. Therefore response targets (single objective functions) are combined to make a new fitness function. The proposed optimization method for determining design variables and design intervals can be used for investigating many other types of superstructures with similar behaviors.     

冲击载荷作用下金属防护外壳的防爆仿真分析

为了降低和防止爆炸冲击波对目标的破坏,提高防爆抗冲击能力,使用多孔材料或轻质材料设计多层复合结构,已经成为当前国内外防爆安全研究的热点.有限元分析是模拟爆炸实验的重要手段.鉴于目前飞机黑匣子不能满足在爆炸冲击的极限工作环境下正常工作的要求,采用通用有限元软件ABAQUS作为结构非线性动力学仿真分析的工具,调用显式分析模块ABAQUS/Explicit进行了数值汁算,提出并论证了采用中间柔性材料缓冲层的复合防护结构,能够延缓爆炸载荷对黑匣子核心单元的冲击作用,保护黑匣子内部模块不受严重破坏,为飞机黑匣子保护外壳的设计提供了重要指导.