浅曲梁大变形分析的杂交应力法

本文基于增量余能原理,导出了用于曲梁几何非线性分析的假定应力杂交模型。根据单元体边界和内部位移的协调内插以及满足单元体内应力平衡的应力分布假定,列出了有限元公式,而最后的矩阵公式中只包含节点未知位移。由此我们建立了二节点、十二个自由度的曲梁单元。由于曲梁几何形状的简单性,我们采用了完全满足应力平衡方程的一致模式。梁单元的有关公式都是在更新的拉格朗日坐标系统(Updated Lagfangjan system)中建立的。最终的数值计算结果表明,用杂交应力模式分析粱结构的大变形是很有效的。     

空间曲梁单元的扭转修正系数研究

三维空间曲梁有限单元模型是模拟曲梁结构的有效数值方法,可以考虑曲梁的弯扭耦合特性,最为符合曲梁的几何和受力特征.由于有限元法采用梁理论的平截面假定,空间曲梁单元上的扭转剪应力分布与实际曲梁截面上的扭转剪应力不同,从而会导致扭转刚度和扭转变形的计算失真.本文基于剪切应变能等效原理,推导了不同长宽比的矩形截面空间曲梁单元的扭转刚度修正系数η和截面边中点处扭转剪应力的修正系数λ,并采用曲线悬臂梁进行了验证.验证结果表明,根据本文提出的η作为校正因子的空间曲梁单元模型,对任意矩形截面曲梁计算的扭转变形均与实体单元模型的结果吻合良好;且只有截面为正方形时,扭转剪应力修正系数η才恰好与弯曲剪应力修正系数(1.2)一致.     

带集中质量的旋转柔性曲梁动力学特性分析

本文对带集中质量的平面内旋转柔性曲梁动力学特性进行了研究.基于绝对节点坐标法推导出曲梁单元,其中该曲梁单元采用Green-Lagrangian应变,并根据曲梁变形前后的曲率变化和曲率的精确表达式计算了曲梁单元弹性力所作的虚功.通过虚功原理,利用δ函数和中心刚体与悬臂曲梁之间的固支边界条件,建立了带集中质量的旋转柔性曲梁非线性动力学模型.基于该模型,本文仿真计算了悬臂曲梁的纯弯曲问题和带有刚柔耦合效应的旋转柔性曲梁动力学响应问题,以此分别讨论了所提出曲梁单元的收敛性和动力学模型的正确性.进一步应用D’Alembert原理,将旋转曲梁等效为带离心力的无旋转曲梁,通过线性摄动处理得到系统的特征方程,以此分别研究了旋转角速度、初始曲率和集中质量对曲梁动力学特性的影响.最后重点分析了旋转曲梁的频率转向和振型切换问题,并阐述了两者之间的相互关系.研究结果表明:随着旋转角速度的增大,曲梁的频率特性与直梁的频率特性相近,以及曲梁拉伸变形占主导的模态振型会提前.     

带集中质量的旋转柔性曲梁动力学特性分析

本文对带集中质量的平面内旋转柔性曲梁动力学特性进行了研究.基于绝对节点坐标法推导出曲梁单元,其中该曲梁单元采用Green-Lagrangian应变,并根据曲梁变形前后的曲率变化和曲率的精确表达式计算了曲梁单元弹性力所作的虚功.通过虚功原理,利用$\delta$函数和中心刚体与悬臂曲梁之间的固支边界条件,建立了带集中质量的旋转柔性曲梁非线性动力学模型.基于该模型,本文仿真计算了悬臂曲梁的纯弯曲问题和带有刚柔耦合效应的旋转柔性曲梁动力学响应问题,以此分别讨论了所提出曲梁单元的收敛性和动力学模型的正确性.进一步应用D'Alembert原理,将旋转曲梁等效为带离心力的无旋转曲梁,通过线性摄动处理得到系统的特征方程,以此分别研究了旋转角速度、初始曲率和集中质量对曲梁动力学特性的影响.最后重点分析了旋转曲梁的频率转向和振型切换问题,并阐述了两者之间的相互关系.研究结果表明:随着旋转角速度的增大,曲梁的频率特性与直梁的频率特性相近,以及曲梁拉伸变形占主导的模态振型会提前.      

基于拟应变法的壳单元大变形分析及在冲击动力问题中的应用

为了简便有效地解决板壳结构的大变形问题，本文针对八节点相对自由度壳单元进行研究。该单元的位移场由壳的中面节点位移和上表面节点的相对位移组成，不带有转动变量。所有的研究都是基于完全的三维位移、应力、应变场。采用拟应变法，对应变场另行假设，能够改善该单元在大变形情况下的计算精度。通过引入Wilson非协调模式，构造了大变形情况下的拟应变场表达式，给出了该单元用于解决非线性动力分析问题的有限元求解方程。通过算例表明，本文针对相对自由度壳单元提出的方法及推导的公式，能够解决冲击动力问题中的大变形问题。     

A NEW SPATIAL THIN-WALLED BEAM ELEMENT INCLUDING TRANSVERSE AND TORSIONAL SHEAR DEFORMATION

基于Timoshenko梁及Benscoter薄壁杆件理论,建立了考虑剪切变形、弯扭耦合以及翘曲剪应力影响的空间任意开闭口薄壁截面梁单元. 通过引入单元内部结点,对弯曲转角和翘曲角采用三节点Lagrange独立插值的方法,考虑了剪切变形和翘曲剪应力的影响并避免了横向剪切锁死问题;借助载荷作用下薄壁梁的截面运动分析,在位移和应变方程中考虑了弯扭耦合的影响. 通过数值算例将该单元的计算结果与理论解以及商用有限元软件和其他文献中的数值解进行对比和验证,结果对比表明该薄壁梁单元具有良好的精度和收敛性.     

基于无网格法的Timoshenko曲梁动力分析

曲梁具有外形美观、受力性能良好的优点,故在工程中得到广泛应用。本文基于移动最小二乘近似和一阶剪切变形理论,提出一种对Timoshenko曲梁自由振动和受迫振动进行分析的无网格方法。通过一系列离散点离散曲梁,建立曲梁无网格模型,然后推导曲梁势能和动能方程,通过哈密顿原理给出曲梁自由振动和受迫振动的控制方程,因为本文方法不能直接施加边界条件,所以使用完全转换法处理本质边界条件,最后求解方程得到频率和振动模态。文末通过算例验证了本文方法的有效性,且通过收敛性分析表明本文方法具有较好的收敛性,并进一步分析了不同边界条件、跨高比和变截面变曲率对曲梁自由振动和受迫振动的影响,将计算结果与文献解或ABAQUS解进行对比分析,表明本文方法具有较高的精度,且适用于实际工程情况。     

十六结点四十自由度相对位移板壳单元

本文从三维弹性理论出发,构造了一个新的能很好反映横向剪切变形影响的十六结点四十自由度等参板壳元。为克服直接引用三维公式系统所造成的数值方面的困难,引入了相对位移。对于曲壳单元,采用正交曲线坐标系,大大加快了计算速度。算例表明,新单元与八结点四十自由度厚壳单元有相同的精度。由于新单元由三维单元退化而成,它便于与三维单元连接,便于计算变厚度壳。     

柔性曲梁多体系统的研究现状和展望

本文对近几年来柔性多体系统建模理论的研究进展进行了评述, 详细阐述了曲梁结构多体系统动力学研究的理论背景和工程意义. 结合连续介质力学和多体系统动力学理论, 介绍了平面曲梁、空间曲梁应变位移场的描述以及几何非线性问题研究现状. 通过国内外文献及已有的研究, 综述了现有曲梁的离散化方法, 以及这些方法对于定曲率、变曲率曲梁的适用性. 然后, 总结了曲梁刚柔耦合动力学建模和数值计算中的难点问题, 介绍了平面曲梁、空间曲梁实验研究的现状. 最后, 综合全文, 提出了目前研究存在的难点问题, 以及计划解决这些难点问题的方法.      

考虑自平衡条件T形曲梁的静力学特性分析

为了准确分析T 形曲梁的静力学特性,该文考虑了剪滞翘曲应力自平衡条件、剪力滞后和剪切变形等因素的影响. 同时为了更好地反映T 形曲梁翼板的位移变化,4 个广义位移函数被引入,分析中以能量变分原理为基础建立了T 形曲梁静力学特性的控制微分方程和自然边界条件. 算例中,分析了剪滞翘曲应力自平衡条件、不同载荷形式和曲梁半径R 等因素对T 形曲梁静力学特性的影响,该文解析解与有限元数值解吻合更好,说明了该文方法的有效性.     

A finite element beam model including cross-section distortion in the absolute nodal coordinate formulation

A new class of beam finite elements is proposed in a three-dimensional fully parameterized absolute nodal coordinate formulation, in which the distortion of the beam cross section can be characterized. The linear, second-order, third-order, and fourth-order models of beam cross section are proposed based on the Pascal triangle polynomials. It is shown that Poisson locking can be eliminated with the proposed higher-order beam models, and the warping displacement of a square beam is well described in the fourth-order beam model. The accuracy of the proposed beam elements and the influence of cross-section distortion on structure deformation and dynamics are examined through several numerical examples. We find that the proposed higher-order models can capture more accurately the structure deformation such as cross-section distortion including warping, compared to the existing beam models in the absolute nodal coordinate formulation.     

Out-of-plane responses of a circular curved Timoshenko beam due to a moving load

For the cases of using the finite curved beam elements and taking the effects of both the shear deformation and rotary inertias into consideration, the literature regarding either free or forced vibration analysis of the curved beams is rare. Thus, this paper tries to determine the dynamic responses of a circular curved Timoshenko beam due to a moving load using the curved beam elements. By taking account of the effect of shear deformation and that of rotary inertias due to bending and torsional vibrations, the stiffness matrix and the mass matrix of the curved beam element were obtained from the force–displacement relations and the kinetic energy equations, respectively. Since all the element property matrices for the curved beam element are derived based on the local polar coordinate system (rather than the local Cartesian one), their coefficients are invariant for any curved beam element with constant radius of curvature and subtended angle and one does not need to transform the property matrices of each curved beam element from the local coordinate system to the global one to achieve the overall property matrices for the entire curved beam structure before they are assembled. The availability of the presented approach has been verified by both the existing analytical solutions for the entire continuum curved beam and the numerical solutions for the entire discretized curved beam composed of the conventional straight beam elements based on either the consistent-mass model or the lumped-mass model. In addition to the typical circular curved beams, a hybrid curved beam composed of one curved-beam segment and two identical straight-beam segments subjected to a moving load was also studied. Influence on the dynamic responses of the curved beams of the slenderness ratio, moving-load speed, shear deformation and rotary inertias was investigated.     

The role of plastic deformation on the impact behaviour of high aspect ratio aluminium foam-filled sections

The main objective of this work is to investigate the role of the plastic deformation of metal foams on the dynamic behaviour of aluminium foam-filled columns with respect to their energy absorbing capabilities. The influence of the cross-section shape as well as other parameters is thoroughly studied. A comparison with correspondent hollow-sections is performed concerning the dissipation of kinetic energy and the obtained deformed profiles. For this particular purpose, three-dimensional finite element modelling dynamic analyses are carried out using ABAQUS/Explicit in order to achieve an in-depth study of the structural crash behaviour, during which energy needs to be absorbed in a controlled manner. A comprehensive numerical study of the crush behaviour of aluminium foam-filled sections undergoing axial compressive loading is performed. The results obtained are also analysed with respect to the reduction in the length of the structural element and impact time, the effect of friction between the foam and the outer skin, the energy decomposition, the role of plastic deformation, the influence of the skin material and impact velocity, and the influence of the shape of the cross-section on the impact behaviour. A comparison with existing analytical expressions is made in order to corroborate the numerical results.     

基于三维模型的蜂窝材料有效弹性性能研究

采用三维模型预测了传统六角形蜂窝材料和带圆环结点六角形蜂窝材料的有效弹性性能.利用有限元法并结合周期边界条件计算了材料代表性体积单元的平均应力,进而由平均场理论获得了两种蜂窝材料全部的有效弹性常数.将传统蜂窝材料的计算结果与已有梁模型的计算结果和试验数据进行了对比,结果表明三维模型比梁模型具有更高的精度,分析了梁模型误...     

对称变截面平面曲杆的单元刚度矩阵

本以一种新的思路和做法对变截面曲杆进行单元分析,直接把变截面曲杆作为单元,采用弹性中心法导出了单元刚度矩阵通用公式,确定了截面按余弦规律变化时,轴线分别为圆弧形、抛物线形、半椭圆形平面曲杆的单元刚度矩阵精确式,供结构设计参考使用。     

Inelastic axial-flexure–shear coupling in a mixed formulation beam finite element

In this paper a beam element that accounts for inelastic axial-flexure–shear coupling is presented. The mathematical model is derived from a three-field variational form. The finite element approximation for the beam uses shape functions for section forces that satisfy equilibrium and discontinuous section deformations along the beam. No approximation for the beam displacement field is necessary in the formulation. The coupling of the section forces is achieved through the numerical integration of an inelastic multi-axial material model over the cross-section. The proposed element is free from shear-locking. Examples confirm the accuracy and numerical robustness of the proposed element and showcase the interaction between axial force, shear, and bending moment.     

变截面多稳态梁结构减振吸能分析与优化设计

基于多稳态梁结构具有吸能且可重复使用的特点，本文研究包含变截面多稳态梁的单胞结构及其周期性排布的减振吸能效应及其优化设计方法。对多稳态结构进行考虑几何非线性的位移加载/卸载有限元仿真，根据其载荷-位移曲线分析多稳态结构的减振吸能原理，并研究串联与并联周期性排布形式对结构整体吸能特性的影响规律。研究基于多参数调控的变截面梁结构形状表征方法，根据多稳态结构储能特点建立变截面多稳态单胞结构的结构优化模型，通过求解优化问题获得总质量不变条件下最优变截面梁结构形状。进一步地通过对优化结果的有限元分析验证优化的有效性，并对结构进行瞬态冲击荷载下动响应分析，证明多稳态结构的冲击保护作用。     

Nonlinear shell-type to beam-type fea simplifications for composite frp poles

This paper presents a semi-analytical finite element analysis of pole-type structures with circular hollow cross-section. Based on the principle of stationary potential energy and Novozhilov’s derivation of nonlinear strains, the formulations for the geometric nonlinear analysis of general shells are derived. The nonlinear shell-type analysis is then manipulated and simplified gradually into a beam-type analysis with special emphasis given on the relationships of shell-type to beam-type and nonlinear to linear analyses. Based on the theory of general shells and the finite element method, the approach presented herein is employed to analyze the ovalization of the cross-section, large displacements, the P-Δ effect as well as the overall buckling of pole-type structures. Illustrative examples are presented to demonstrate the applicability and the efficiency of the present technique to the large deformation of fiber-reinforced polymer composite poles accompanied with comparisons employing commercial finite element codes.