Numerical Approximation and Error Analysis for the Timoshenko Beam Equations with Boundary Feedback

In this paper,the numerical approximation of a Timoshenko beam with bound- ary feedback is considered.We derived a linearized three-level difference scheme on uniform meshes by the method of reduction of order for a Timoshenko beam with boundary feedback.It is proved that the scheme is uniquely solvable,unconditionally stable and second order convergent in L_∞norm by using the discrete energy method. A numerical example is presented to verify the theoretical results.     

A difference scheme for solving the Timoshenko beam equations with tip body

In this article, a Timoshenko beam with tip body and boundary damping is considered. A linearized three-level difference scheme of the Timoshenko beam equations on uniform meshes is derived by the method of reduction of order. The unique solvability, unconditional stability and convergence of the difference scheme are proved. The convergence order in maximum norm is of order two in both space and time. A numerical example is presented to demonstrate the theoretical results.     

说梁-----力学史札记之十九

本文简略介绍了梁的理论从提出到发展成熟的过程。简要叙述了伽利略、马略特、胡克、伯努利、帕朗、纳维以及铁摩辛科等学者的工作。并且提出一些近代关于梁的研究问题。     

铁摩辛柯梁单元刚度矩阵推导

为明确ANSYS中基于铁摩辛柯梁理论的Beam188单元的单刚矩阵,以形函数为基础,根据最小势能原理系统给出了铁摩辛柯梁单元的刚度矩阵推导过程,尤其将常规2节点单元的刚度矩阵扩展至3节点单元,包括等截面梁和变截面梁,并给出了各自的单刚矩阵理论表达式。以矩形、圆形、箱形和圆环四种截面为例,分别给出单刚矩阵理论值与ANSYS中Beam188单元刚度矩阵进行对比。结果表明,3节点等/变截面梁的单刚矩阵与理论推导所得结果一致,但2节点梁的单刚矩阵与理论推导所得结果存在偏差,且此偏差仅表现在与弯曲相关的元素中,并且随着单元长度的减小,两者的偏差也越来越小。另外,对比时应注意,ANSYS所得截面参数如剪切系数和极惯性矩与理论值存在较大偏差。     

材料力学方法分析接触问题的精度与梁理论的改进

讨论了材料力学经典梁理论与考虑横向剪切变形的铁摩辛柯梁理论分析接触问题的精度. 通过计入横向拉压变形效应改进铁摩辛柯梁理论, 获得了与完全三维分析吻合很好的结果. 对于细长梁, 如果仅计算提起段高度, 经典梁理论已经有足够的精度; 如果计算悬空段长度,需要采用铁摩辛柯梁理论; 如果计算接触应力, 则需要考虑横向剪切和拉压变形效应, 采用修正的铁摩辛柯梁理论.     

铁摩辛柯基础梁的解析解和广义克雷洛夫函数

河南省自然科学基金项目（９８４０７０７００）资助摘要 定义并讨论了一类广义克雷洛夫函数，给出了用该函数表示的弹性地基上铁摩辛柯梁的解析解     

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全面系统地介绍了力学家和工程结构大师铁摩辛柯教授在前苏联和美国等地从事的学术活动和关于经典材料力学、工程振动、结构理论、弹性理论、板壳理论等著作内容, 为学习和研究铁摩辛柯教授的教育与工程思想和他的二十余种著作提供重要依据和较详细的资料.