微分求积法在弹性压应力波下直梁的动力压曲稳定分析中的应用  

The Differential Quadrature Method for Dynamic Buckling of Straight Beam under Elastic Compression Wave

作　　者：汪亚运[1] 陈得良[1] 彭旭龙[1] 周露[1] 

机构地区：[1]长沙理工大学土木与建筑学院,湖南长沙410004

出　　处：《湘潭大学自然科学学报》2016年第3期30-34,共5页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金项目(11172051;11202038);湖南省自然科学基金项目(2015JJ4006;2016JJ3002);长沙理工大学研究生科研创新项目(CX2016SS02)

摘　　要：基于欧拉-伯努利梁理论及能量守恒原理,建立了直梁压曲稳定微分控制方程及其应力波波前附加边界条件,对应力波反射前等截面梁屈曲与压应力波耦合动力屈曲问题进行了研究.利用微分求积法(DQM)并结合边界条件,将直梁压曲稳定控制微分方程离散成线性代数方程组,进而得到了系统的动力屈曲特征方程,并研究了加载端简支远端固支梁在压应力波反射前的动力屈曲问题.数值研究表明该方法具有可靠的精度和收敛性.Based on the Euler-Bernoulli beam theory and the principle of conservation of energy,the buckling governing equation and the boundary conditions at the compression stress wave front for a uniform beam are established.Then,the dynamic buckling of uniform straight beam under coupled stress wave propagating and dynamic buckling before reflection of compression wave is investigated.And the eigen-equation is obtained with the differential quadrature method（DQM）and the boundary conditions by transferring governing equation into the linear algebraic equation sets.Moreover,a numerical investigation for dynamic buckling of the beam simply supported at loaded end and clamped at other end is carried out.The results shows that the present method has good accuracy and convergence.

关 键 词：等截面直梁 压应力波 微分求积法 动力屈曲 

分 类 号：O347[理学—固体力学]