基于网格退化和重组技术的类桁架拓扑优化方法

发展了一种基于有限元网格退化和重组技术的类桁架拓扑优化方法,可在不改变设计域包络的情况下(如维持流型、艺术外观和附加功能等)对结构进行减重。首先,分别对二维问题和三维问题发展相应的有限元网格退化算法,并在刚度等效的意义上对网格进行重组,建立了具有杆元拓扑特征的有限元模型。其次,以全局种子网格的长度尺寸和杆元横截面积为优化变量,构造了域内双层驱动拓扑优化问题,得到具有最优体分比的杆元拓扑结构。数值算例表明,所提方法可获得新型式的结构拓扑优化方案,并可将结构拓扑优化理论推向工程化应用。     

结构非平稳随机响应分析的快速虚拟激励法

虚拟激励法能够方便地应用于结构非平稳随机响应分析,但在每个离散频点处都涉及到虚拟激励作用下动力方程的时程积分,对于大型复杂结构,其计算量是难以接受的。将结构动力方程写成状态方程形式,采用精细积分法对状态方程进行数值求解,导出了结构动力响应关于离散时刻处激励的显式线性表达式。利用这一显式表达式,只需要变换离散时刻处的激励数值,就可以方便快捷地求出新的激励作用下的结构动力响应。效率分析和数值算例表明,相对于传统虚拟激励法,本文提出的改进算法在求解非平稳激励下结构随机振动方面具有更高的计算效率。     

一种模拟动边界绕流的锐利界面浸入边界法

When the structural wall moves over a fixed grid, the structure coverage will change, resulting in many dead and emerging elements. To avoid the influence of malformation and reconstruction of body-fitted grids on the calculation efficiency and accuracy of the fluid-structure interaction problems with coupled boundary movement on the fixed grid, an improved numerical method for describing the interaction between an immersed rigid body and fluid based on a sharp-interface is proposed. In this method, both the fluid and solid are regarded as pure fluid domains in the whole computational domain, and the solid boundary is divided into several Lagrangian grid points. The flow parameter or velocity is reconstructed by interpolation at the interface element, which is then directly used as the boundary condition of the flow field, thus reflecting the influence of the wall boundary conditions. The method constructs the calculation structure of “virtual point, force point and vertical foot point”, and the velocity of the virtual point is obtained by bilinear interpolation. Then, the velocity of the force point is calculated by forcing the solid boundary to meet the no-slip condition, and the equations of the coupling system based on the immersion boundary method are finally solved to realize the numerical simulation of the flow with a complex moving boundary. The numerical program for this immersed boundary method is established using C++, then the accuracy and reliability of the proposed method are validated by comparison with the literature and experimental results of the basic numerical example of flow around a cylinder. Furthermore, the effects of the structural shape and the angle of attack on the trailing vortex structure, the vortex shedding frequency, and the lift/ coefficient characteristics of the flow around the elliptical cylinder have been analyzed. The anti-symmetric S-type, “P+S” Ⅰ-type and “P+S” Ⅱ-type trailing vortex shedding modes, as well as the variation laws of the vortex structure size, vortex shedding frequency and lift-drag coefficients ratio with axis ratio and angle of attack, are captured. The critical angle of attack (25°) corresponding to the maximum lift-drag ratio is determined as 25°.     

Identification of the tensile force in high-tension bars using modal sensitivities

In certain field applications involving the repair or replacement of structural members, the knowledge of the tensile forces in tension members may be critical in the selection of the retrofit or rehabilitation process. To date, several methods have been presented to estimate in situ tensile forces using static and/or dynamic responses of the tension members. However, each and every one of these methods has its disadvantages as well as advantages in its procedures, level of accuracy, and equipment requirements. This paper presents a practical method to identify the tensile force in a high-tension bar using the changes in the modal sensitivities. The methodology can identify not only the tensile force but also other related parameters such as the magnitude of end constraint. The methodology utilizes the sensitivity relationship between the natural frequencies, the structural parameters, and the tensile force in the member. In this paper, the basic elements of the approach are summarized and the proposed method is validated using both numerical and experimental data. Also, the impact of model uncertainty to the performance of the parameter identification is investigated.     

一种改进的残余力向量法在结构损伤识别中的应用

残余力向量法是结构损伤识别中常用的方法,复杂结构中单元数量较多而损伤位置较少,容易造成无关变量增多,进而导致计算量过大的问题。鉴于此,本文提出一种改进的残余力向量法用于结构的损伤识别。该方法利用刚度联系向量与残余力向量之间线性相关的特性,以向量投影值作为损伤定位的影响系数,初步筛选出结构可能出现损伤的单元范围。在此基础上,构建出残余力向量对应的线性方程组,根据顺序主子式不为零的条件,对线性方程组进行行初等变换,再根据单元的数量保留前n维线性方程,通过求解该方程组的代数解可得到该结构单元的刚度损伤参数。以简支梁为例的数值模拟表明,本文方法可减少无关单元变量的计算,降低残余力向量的维度并且具有较好的抗噪能力。     

A mixed modal-differential quadrature method for free and forced vibration of beams in contact with fluid

A simple and accurate mixed modal-differential quadrature formulation is proposed to study the dynamic behavior of beams in contact with fluid. Both free and forced vibration problems are considered. The proposed mixed methodology uses the modal technique for the structural domain while it applies the differential quadrature method (DQM) to the fluid domain. Thus, the governing partial differential equations of the beam and fluid are reduced to a set of ordinary differential equations in time. In the case of forced vibration, the Newmark time integration scheme is employed to solve the resulting system of ordinary differential equations. The proposed formulation, in general, combines the simplicity of the modal method and high accuracy and efficiency of the DQM. Its application is shown by solving some beam-fluid interaction problems. Comparisons with analytical solutions show that the present method is very accurate and reliable. To demonstrate its efficiency, the test problems are also solved using the finite element method (FEM). It is found that the proposed method can produce better accuracy than the FEM using less computational time. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.     

模拟结构倒塌破坏的有限质点法

有限质点法是以向量式力学为基础的新兴结构分析方法,本文将其应用于冲击荷载作用下的网壳结构的倒塌破坏模拟中。以空间杆单元为例建立了有限质点法的基本方程,推导了求解几何和材料非线性问题的基本公式。为计算断裂问题,建立了空间杆单元的断裂准则和断裂模型,发展了有限质点法进行断裂分析的基本算法。通过对某双层网壳冲击荷载下破坏过程的模拟和分析,验证了该方法在结构倒塌破坏过程模拟中的有效性和适用性。     

Structural–acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme

The complete interaction between the structural domain and the acoustic domain needs to be considered in many engineering problems, especially for the acoustic analysis concerning thin structures immersed in water. This study employs the finite element method to model the structural parts and the fast multipole boundary element method to model the exterior acoustic domain. Discontinuous higher‐order boundary elements are developed for the acoustic domain to achieve higher accuracy in the coupling analysis. Structural–acoustic design sensitivity analysis can provide insights into the effects of design variables on radiated acoustic performance and thus is important to the structural–acoustic design and optimization processes. This study is the first to formulate equations for sound power sensitivity on structural surfaces based on an adjoint operator approach and equations for sound power sensitivity on arbitrary closed surfaces around the radiator based on the direct differentiation approach. The design variables include fluid density, structural density, Poisson's ratio, Young's modulus, and structural shape/size. A numerical example is presented to demonstrate the accuracy and validity of the proposed algorithm. Different types of coupled continuous and discontinuous boundary elements with finite elements are used for the numerical solution, and the performances of the different types of finite element/continuous and discontinuous boundary element coupling are presented and compared in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

非平稳随机激励下结构体系动力可靠度时域解法

将结构动力方程写成状态方程形式,采用精细积分法对其进行数值求解,导出了非平稳激励下结构随机响应的时域显式表达式,该过程的计算量仅相当于两次确定性时程分析的计算量. 基于该显式表达式,结合首次超越失效准则,提出了非平稳随机激励下结构体系动力可靠度的数值模拟算法. 与功率谱方法相比,该方法无需同时在时频域内进行大量数值积分,也无需引入关于响应过程跨越界限次数概率分布, 以及各失效模式相关性等方面的假定. 通过数值算例, 对比了该方法与泊松过程法、马尔可夫过程法、传统蒙特卡罗法的计算精度和计算效率,结果显示该方法具有理想的精度和相当高的效率.      

Development of a New Method to Investigate the Dynamic Friction Behavior of Interfaces Using a Kolsky Tension Bar

To understand interfacial interaction of a bi-material during an impact loading event, the dynamic friction coefficient is one of the key parameters that must be characterized and quantified. In this study, a new experimental method to determine the dynamic friction coefficient between two metals was developed by using a Kolsky tension bar and a custom-designed friction fixture. Polyvinylidene fluoride (PVDF) force sensors were used to measure the normal force applied to the friction tribo pairs and the friction force was measured with conventional Kolsky tension bar method. To evaluate the technique, the dynamic friction coefficient between 4340 steel and 7075-T6 aluminum was investigated at an impact speed of approximately 8 m/s. In addition, the dynamic friction coefficient of the tribo pairs with varied surface roughness was also investigated. The data suggest that higher surface roughness leads to higher friction coefficients at the same speed of 8 m/s.     

梯度密度黏弹性材料的波传播研究

梯度密度黏弹性材料中波的传播比较复杂。为了研究其在冲击载荷作用下黏弹性响应特征,基于控制方程的Euler形式,利用Laplace变换,得到了这种材料中的波传播规律的一个理论公式;并据此分析了双层周期性黏弹性介质中的应力情况。选择具有梯度密度特性的钛-硼化钛（Ti-TiB₂）材料和碳纤维树脂材料,采用不同的叠合方向和方式,利用分离式霍普金森压杆（split Hopkinson pressure bar,SHPB）加载装置进行了动态冲击实验,并用三波法对得到的实验结果进行处理。同时,采用数值Laplace逆变换方法,结合SHPB测得的入射波与透射波数据,使用推导的理论公式计算出理论解,并与实验结果进行了比较。结果表明:（1）梯度钛-硼化钛材料由于内界面和叠层界面的存在,表现出一定的黏性特性;单层Ti-TiB₂材料的计算结果和三波法分析得到的结果基本一致,双层Ti-TiB₂材料叠合后的计算结果与三波法分析结果存在一定的差异。（2）双层碳纤维树脂材料表现出较强的黏弹性特征,应力波的衰减幅度较大,三波法分析结果与该材料的冲击性能有较大的差异。由此可知,无论是细微观结构特征产生的黏性,还是材料本身的黏性,对材料动力学行为的影响都不可忽略。。     

Stochastic response of an axially loaded composite Timoshenko beam exhibiting bending–torsion coupling

A spectral finite element method is proposed to investigate the stochastic response of an axially loaded composite Timoshenko beam with solid or thin-walled closed section exhibiting bending–torsion materially coupling under the stochastic excitations with stationary and ergodic properties. The effects of axial force, shear deformation (SD) and rotary inertia (RI) as well as bending–torsion coupling are considered in the present study. First, the damped general governing differential equations of motion of an axially loaded composite Timoshenko beam are derived. Then, the spectral finite element formulation is developed in the frequency domain using the dynamic shape functions based on the exact solutions of the governing equations in undamped free vibration, which is used to compute the mean square displacement response of axially loaded composite Timoshenko beams. Finally, the proposed method is illustrated by its application to a specific example to investigate the effects of bending–torsion coupling, axial force, SD and RI on the stochastic response of the composite beam.     

阶梯式Timoshenko梁自由振动的DCE解

本文基于微分容积法和区域叠加技术提出了微分容积单元法（Differential Cubature Element method，以下简称DCE方法），并用之求解阶梯式变截面Timoshenko梁的自由振动问题。根据梁的变截面情况将其划分为几个单元，在每个单元内应用微分容积法将梁的控制微分方程和边界约束方程离散成为一组关于该单元内配点位移的线性代数方程组，将这些方程组写在一起并在各单元之间应用连续性条件和平衡条件得到一组关于整个域内各点位移的齐次线性代数方程组，这是一广义特征值问题，由子空间迭代法求解该特征问题便可求得系统的自振动频率。数值算例表明，本方法能稳定收敛、并有较高的数值精度和计算效率。     

Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment

In this study, a unified nonlinear dynamic buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear dynamic buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for dynamic buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the dynamic buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural dynamic buckling behavior in the presence of damping effects under thermal environment are conducted.     

General analytic solution of dynamic response of beams with nonhomogeneity and variable cross-section

In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only     

基于静力残余力向量的结构损伤评估方法

残余力向量法是一类常用的损伤识别方法,现有的残余力向量法都是基于动力测试的模态参数,和动力测试数据相比,静力测试数据往往精度更高,且无需模态分析等复杂操作.鉴于此,本文提出一种静力残余力向量法用于结构损伤评估.所提方法利用静力测试位移数据,并结合结构有限元模型的刚度矩阵,定义了静力残余力向量,根据该向量中不为零的元素来判断损伤自由度,再根据自由度和单元之间的对应关系来确定发生损伤的位置,并进一步提出一种求解损伤参数的代数解法.另外,针对实践中角位移难以测量的情况,进一步提出了一种静力缩聚残余力向量法,拓宽了所提方法的应用范围.以桁架结构和梁结构模型为例对所提方法进行了验证,数值算例结果说明所提方法合理有效.     

结构优化半解析灵敏度分析的改进算法

提出了结构半解析灵敏度分析的改进算法,该算法实现简便,对于设计变量摄动步长具有极佳的数值稳定特性。首先,从总体角度推导静力问题半解析法灵敏度分析新算法,提出了位移与应力灵敏度列式,并给出了算法实施途径;然后,将此思路推广于自振频率、屈曲临界荷载和瞬态响应等多种问题,提出了相应的计算步骤。以梁单元与壳单元等典型结构为例,开展了多个算例测试。测试表明,改进算法计算精度和效率均有提升,特别是设计变量步长有更大的数值稳定区域,为复杂工程结构形状优化的灵敏度分析提供了新途径。     

A MESH-FREE ALGORITHM FOR DYNAMIC IMPACT ANALYSIS OF HYPERELASTICITY

A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function(RBF)coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.     

基于有限时间收敛的双臂空间机器人捕获卫星主动对接力/位姿阻抗控制

针对双臂空间机器人捕获卫星主动对接力/位姿阻抗控制进行了研究. 为防止捕获过程中机械臂末端执行器与卫星接触、碰撞时产生的冲击载荷对机器人关节造成冲击破坏, 在各关节电机与机械臂之间加入了一种弹簧阻尼缓冲机构. 该机构可通过弹簧实现冲击力矩的卸载, 阻尼器则用于因弹簧引起的柔性振动的抑制. 为解决捕获过程中的非完整动力学约束及捕获后混合体系统的协调控制问题, 结合牛顿第三定律、捕获点的速度约束及闭链几何约束, 获得捕获后混合体系统的动力学方程, 且通过动量守恒关系计算碰撞冲击效应与碰撞冲击力. 通过分析对接装置在载体坐标系下的运动学关系, 建立对接装置相对载体的运动雅可比矩阵, 并基于此建立基于力的二阶线性阻抗模型, 实现对接装置输出力的精确控制. 考虑到主动对接操作过程要求控制器具有收敛速度快, 控制精度高的特点, 通过结合终端滑模与超扭滑模的特点, 提出一种非奇异快速终端滑模阻抗控制策略. 该策略即能实现主动对接操作中位姿与输出力的快速响应, 又能有效地抑制滑模的抖振以保证控制精度. 通过Lyapunov定理证明系统的稳定性; 利用数值模拟验证缓冲装置的抗冲击性能及所提阻抗控制策略的有效性.      

张拉整体结构的动力学等效建模与实验验证

为了实现张拉整体结构高效动力学计算, 并考虑其大范围运动中柔性杆局部动态屈曲, 提出了一种受压细长杆动力学降阶模型, 采用五节点弹/扭簧集中质量离散模型等效连续杆的静力学和动力学特性. 首先, 通过静力学等效分析推导了弹簧拉压刚度和扭簧弯曲刚度表达式, 可准确预测杆件受压屈曲和近似预测其后屈曲行为. 第二, 通过动能等效分析推导了集中质量表达式, 可准确预测杆在线速度场下的运动. 第三, 通过弯曲振动固有模态等效分析确定弯曲刚度和节点质量的分布参数, 合适的分布参数取值组合可将降阶模型前两阶固有频率相对误差均降低至1%以内. 第四, 在全局坐标系下建立张拉整体结构瞬态动力学方程, 并利用静力凝聚法实现方程高效迭代求解. 最后, 分别对球形张拉整体结构准静态压缩、模态分析和碰撞动力学进行仿真和实验对比分析, 证明了提出的动力学降阶模型可有效预测张拉整体结构的静力学行为、固有振动特性及瞬态动力学响应, 并分析了结构参数变化对其力学特性的影响规律. 本文提出的动力学等效建模与计算方法, 可望用于软着陆行星探测器、大型可展开空间结构及点阵材料等复杂张拉整体系统的动力学分析与控制.