大范围运动刚体-柔性梁刚柔耦合动力学分析

对自由大范围运动情况下刚体-柔性梁系统的刚柔耦合动力学特性进行了研究.考虑系统作平面大范围运动及柔性梁的纵向和横向变形,在纵向变形位移中计及横向弯曲引起的轴向缩短,即耦合变形项.采用假设模态法对柔性梁进行离散,运用拉格朗日方程推导出系统刚柔耦合动力学方程.分大范围运动为转动、平动,平面运动进行了动力学仿真,重点探讨了大范围平动下的刚体-柔性梁系统的刚柔耦合动力学特性.首先研究了系统在外界激励作用下的耦合动力学,其次分析了已知大范围平动对柔性梁小变形运动的影响.结果表明:零次近似模型不能反映大范围平动和柔性梁小变形运动之间的耦合作用;在不同的大范围平动加速度下,柔性梁中既可存在动力刚化效应,也可存在动力柔化效应.     

作大范围运动的柔性梁的动力学分析

对附着在空间运动体上的柔性悬臂梁的动力学进行了研究，利用微元法建立了中心刚体作任意三维大位移运动时柔性悬臂梁作横向和纵向振动的动力学方程，此动力学方程计及了动力刚化效应。在对柔性梁离散求解时考虑了横向弯曲对纵向变形的影响，最后通过几个例子分析了运动基上柔性梁的动力学行为。     

改进EFG法用于旋转梁的刚柔耦合动力学研究

采用全域插值广义移动最小二乘(IGMLS)的改进无网格伽辽金(EFG)法,对旋转中心刚体-柔性梁系统的刚柔耦合动力学特性进行研究。利用考虑了柔性梁横向变形引起的非线性耦合项的一次近似耦合模型,根据Hamilton原理和EFG离散方法得到刚柔耦合系统的无网格动力学离散方程。在大范围运动未知的情况下,采用数值方法对刚柔耦合系统进行动力响应的仿真计算,并对EFG法的主要影响因素进行了讨论分析。通过与有限元法的数值计算结果对比,验证EFG法用于刚柔耦合系统动力学研究的有效性及可行性,并为无网格法用于更复杂的柔性多体动力学的研究提供了理论依据。     

柔性梁的刚-柔耦合动力学特性研究

该文研究在大范围运动是自由的情况下柔性梁的刚－柔耦合动力学特征，从连续介质力学理论出发，在纵向变形位移中计及了耦合变形量，用Jourdain速度变分原理导出了柔性梁的刚－柔耦合动力学方程，用频谱分析方法对带中心刚体的悬臂梁进行动力学分析表明，柔性梁的系统一阶固有频率低于把梁视作刚体的系统固有频率wr，频率的差异随着wr，增大而增加，在初始条件一定的情况下，系统的二阶固有频率随着wr增大而增高，揭示了大范围运动和变形运动的相互耦合的特征。     

计及变形耦合项的平面柔性梁动力学建模及频率分析

考虑了变形产生的几何非线性效应对作大范围运动的平面柔性梁的影响，在其纵向、横向的变形位移中均考虑了变形的二次耦合变量，从非线性应变-变形位移的原理出发，说明增加耦合变量后。使得剪应变近似为零，由此得出的变形模式更符合工程实际和简化需要。考虑两个方向的变形耦合后，采用有限元离散，通过Lagrange方程导出系统的动力学方程。最后对一作旋转运动的平面柔性梁进行仿真计算，并对其固有频率进行分析研究。将本文模型所得的结论。与一次耦合动力学模型、零次近似模型进行比较，说明了三种模型的差异。得到了作旋转运动的平面柔性梁的一些新特点。     

热载荷作用下大变形柔性梁刚柔耦合动力学分析

从非线性应变-位移关系式出发,用虚功原理建立了热载荷作用的柔性梁的热传导方程和旋转刚体-梁系统的刚-柔耦合动力学方程.由于考虑了刚度阵的高次变形项,适用于大变形问题.对温度、弹性变形和刚体运动变量联合求解.研究了热流引起的温度梯度对弹性变形和刚体转动的影响,以及在大变形情况下的几何非线性效应.     

旋转柔性梁的动力学建模及分析

基于一次近似理论，采用弧坐标分量和Cartesian坐标分量共同描述柔性梁的变形场，并采用Green应变张量描述应变能，用Hamilton原理建立系统动力学方程。揭示产生动力刚化现象的力学本质。采用有限元方法进行离散，基于数值实验系统地研究旋转柔性梁的动力刚化现象。计算表明，旋转柔性梁的横向固有频率随旋转角速度和中心刚体半径的增大而增大．从而只存在一阶临界转速，且当中心刚体半径超过临界半径时．不存在临界转速。     

考虑附加质量的旋转柔性梁的随机动力学分析

摘要：研究了带有附加质量的中心刚体-柔性悬臂梁系统在参数具有随机性时作大范围运动的动力响应问题。基于假设模态法和Lagrange方程建立了带有附加质量的中心刚体-柔性悬臂梁系统的一次近似耦合随机动力学方程,利用混沌多项式结合高效回归法将其转化为完全隐式纯微分方程,求解方程得到柔性悬臂梁变形位移响应的数字特征。最后,通过数值仿真对物理参数和几何参数具有随机性的系统进行动力特性研究。仿真结果表明：利用随机参数的动力学模型能客观地反映出系统的动力学行为;部分随机参数的分散性对柔性体动力响应的影响不可忽视。     

温度场中的柔性梁系统动力学建模

研究温度场下带集中质量的柔性梁系统的动力学问题。考虑几何非线性，在纵向变形与轴向伸长的关系式中计及了与横向变形有关的二次耦合项。考虑温度变化对系统动力学性态的影响，在本构关系式中计及了热应变。用假设模态法对各柔性梁进行离散，从虚功原理出发，根据各柔性梁之间的运动学约束关系，建立了带集中质量的柔性梁系统的动力学方程。仿真结果表明．即使在转速较低的情况下，随着集中质量的增大和温度的急剧变化，纵向变形的二次耦合项的影响不容忽视，此外，温度的变化还引起轴向变形和轴向约束力高频振荡。     

三维柔性多体梁系统非线性动力响应分析

研究了三维柔性多体梁系统的非线性动力响应问题。将空间柔性梁的变形分解为轴向变形以及在x-y平面的弯曲变形和在x-z平面的弯曲变形，引用各自的精确振动模态描述变形场，利用拉格朗日乘子法建立起柔性多体梁系统约束非线性动力学方程。结合Newmark直接积分法和Newton-Raphson迭代法，导出了求解该非线性代数一微分方程组的数值方法。仿真算例证明了该方法的正确性和有效性。     

A pseudo-elastic local meshless method for analysis of material nonlinear problems in solids

This paper aims to develop an effective meshless technique for the analysis of elasto-plastic problems. The material nonlinearity will be studied by a new pseudo-elastic local radial point interpolation formulation which is based on the local Petrov–Galerkin form and the radial basis function (RBF) interpolation. Hencky's total deformation theory is used to define the effective Young's modulus and Poisson's ratio, which are treated as spatial field variables, and considered as functions of the final stress state and material properties. These effective material parameters are obtained in an iterative manner using the strain controlled projection method. Several numerical examples are presented to illustrate the effectivity of the newly developed formulation, and the numerical results obtained by the present method closely agree with the results obtained by other methods. It has proven that the present pseudo-elastic local meshless method is effective and easy to apply to the analysis of elasto-plastic materials subjected to proportional loading.     

Numerical solution of two-dimensional inverse force function in the wave equation with nonlocal boundary conditions

In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the inverse time-dependent force function in the wave equation on regular and irregular domains. The SMRPI is developed for identifying the force function which satisfies in the wave equation subject to the integral overspecification over a portion of the spatial domain or to the overspecification at a point in the spatial domain. This method is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. Since the problem is known to be ill-posed, Thikhonov regularization strategy is employed to solve effectively the discrete ill-posed resultant linear system. Three numerical examples are tested to show that numerical results are accurate for exact data and stable with noisy data.     

A new method for meshless integration in 2D and 3D Galerkin meshfree methods

A method for the evaluation of regular domain integrals without domain discretization is presented. In this method, a domain integral is transformed into a boundary integral and a 1D integral. The method is then utilized for the evaluation of domain integrals in meshless methods based on the weak form, such as the element-free Galerkin method and the meshless radial point interpolation method. The proposed technique results in truly meshless methods with better accuracy and efficiency in comparison with their original forms. Some examples, including linear and large-deformation problems, are also provided to demonstrate the usefulness of the proposed method.     

Parallel point interpolation method for three-dimensional metal forming simulations

Parallel point interpolation method (PIM) is developed for metal forming with large deformation analysis of three-dimensional (3-D) solids, based on the Galerkin weak form formulation using 3-D meshless shape functions constructed using radial basis functions (RBFs). As the radial PIM (RPIM) shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite element method (FEM). The kinematics and the explicit integration scheme for PIM meshless method are given. The OpenMP parallelization toolkit is used to parallelize our meshless code, and the parallelization of the PIM meshless code has been conducted for a shared memory system using OpenMP. Some examples are then presented to demonstrate the efficiency and accuracy of the proposed implementations concerning the accuracy and efficiency of the code. It is demonstrated that the present parallel 3-D PIM meshless program is robust, stable, reliable and efficiency for metal forming analysis of 3-D problems.     

A three-dimensional semi-analytical model for the composite laminated plates with a stepped lap repair

A three-dimensional semi-analytical model of the static response and sensitivity analysis was established based on the state space methods and meshless method for the composite laminated plates with a stepped lap repair. Firstly, the meshfree formulations of Hamilton canonical equation and the linear spring-layer were deduced by the radial point interpolation method (RPIM) shape functions and the modified Hellinger–Reissner (H–R) variational principle of elastic solids. And then a three-dimensional hybrid governing equation of the static response analysis and sensitivity analysis were developed for the composite laminated plates with a stepped lap repair. The present three-dimensional semi-analytical model with no initial assumptions regarding displacement and stress accounts for the transverse shear deformation and rotary in the governing equation of structure. By using the hybrid governing equation in the response analysis and sensitivity analysis, the convoluted algorithm can be avoided in sensitivity analysis, and the response quantities and the sensitivity coefficients can be obtained simultaneously.     

Comparisons of two meshfree local point interpolation methods for structural analyses

 As truly meshless methods, the local point interpolation method (LPIM) and the local radial point interpolation method (LR-PIM), are based on the point interpolations and local weak forms integrated in a local domain of very simple shape. LPIM and LR-PIM are examined and compared with each other. They are also compared with the established FEM and the meshless local Petrov-Galerkin (MLPG) method. The numerical implementations of these two methods are discussed in detail. Parameters that influence the performance of them are detailedly studied. The convergence and efficiency of them are thoroughly investigated. LPIM and LR-PIM formulations are developed for structural analyses of 2-D elasto-dynamic problems and 1-D Timoshenko beam problems in the first time. It is found that LPIM and LR-PIM are very easy to implement, and very efficient obtaining numerical solutions to problems of computational mechanics. Received 31 August 2001 / Accepted 04 March 2002     

A point interpolation meshless method based on radial basis functions

A point interpolation meshless method is proposed based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis. This non‐singularity is useful in constructing well‐performed shape functions. Furthermore, the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least‐squares approximation. In addition, the partial derivatives of shape functions are easily obtained, thus improving computational efficiency. Examples on curve/surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high. Copyright © 2002 John Wiley & Sons, Ltd.     

随机激励下导引头伺服机构动力学特性的研究

导引头伺服机构的动力学分析大多采用理想模型,较少考虑设计公差、制造误差、摩擦磨损等随机因素对系统动力学特性的影响,难以准确描述实际的动力学特性。因此建立了随机激励下伺服机构的非线性动力学模型,综合运用随机平均法和点插值无网格法推导和求解系统的随机动力学FPK(Fokker-Planck-Kolmogorov)方程,计算得到了伺服机构的随机动力学响应,并且研究了摩擦参数对系统随机响应统计特征的影响,以为评价伺服机构的动力学特性提供理论依据。     

A review of meshless methods for laminated and functionally graded plates and shells

This review focuses mainly on the developments of element-free or meshless methods and their applications in the analysis of composite structures. This review is organized as follows: a brief introduction to shear deformation plate and shell theories for composite structures, covering the first-order and higher-order theories, is given in Section 2. A review of meshless methods is provided in Section 3, with main emphasis on the element-free Galerkin method and reproducing kernel particle method. The applications of meshless methods in the analysis of composite structures are discussed in Section 4, including static and dynamic analysis, free vibration, buckling, and non-linear analysis. Finally, the problems and difficulties in meshless methods and possible future research directions are addressed in Section 5.     

Numerical analysis of dental implants using a new advanced discretization technique

In this work an advanced discretization meshless technique is applied to analyze the elastostatic behavior of implants inserted in the mandible bone. The natural neighbor radial point interpolation method (NNRPIM) is a flexible and efficient meshless method capable of predicting smooth and accurate stress fields. One of the advantages of meshless methods over the finite element method (FEM) is the complete freedom of the domain computational discretization, allowing to discretize biological structures with higher accuracy. In order to show the NNRPIM efficiency, two implant systems' numerical models are analyzed with the NNRPIM and the obtained results are compared with the FEM.