含裂纹功能梯度Euler-Bernoulli梁和Timoshenko梁的屈曲载荷计算与分析  

Buckling of functionally graded Euler-Bernoulli and Timoshenko beams with edge cracks

作　　者：魏东[1] 刘应华[1] 

机构地区：[1]清华大学航天航空学院工程力学系,北京100084

出　　处：《复合材料学报》2010年第4期124-130,共7页Acta Materiae Compositae Sinica

基　　金：国家重点基础研究专项基金(2001CB409603)

摘　　要：含裂纹构件的屈曲载荷是结构是否安全的判定准则之一,其计算与分析也是结构健康监测和安全评价中关注的重要问题。基于Euler-Bernoulli梁理论和Timoshenko梁理论,建立了一种求解含裂纹功能梯度材料梁的屈曲载荷计算方法。首先裂纹导致的构件截面转角不连续性由转动弹簧模型进行模拟,再根据功能梯度材料Euler-Bernoulli梁和Timoshenko梁的屈曲控制方程及其闭合解,由传递矩阵法建立了求解含裂纹功能梯度材料梁在多种边界条件下屈曲载荷的循环递推公式和特征行列式,使问题通过降阶的方法得到快速准确的解答。数值算例研究了剪切变形、裂纹的不同数目及位置、材料参数变化、长细比和不同边界约束条件等对含裂纹功能梯度材料梁屈曲载荷的影响。结果表明该方法可以简单、方便和准确地计算不同数目裂纹和任意边界条件下功能梯度材料梁的屈曲问题。In this paper, an analytical approach was proposed for solving the buckling of functionally gradient material （FGM） Euler - Bernoulli and Timoshenko beams with cracks. The discontinuity of rotation caused by the cracks was simulated by means of the rotational spring model. The governing differential equations for buckling of an FGM beam were established and their solutions were found firstly. The recurrence formula of solution using the transfer matrix method was developed in the current research. Then the eigenvalue equations for buckling of an FGM beam can be conveniently obtained from a third order determinant. A comprehensive parametric study is conducted to investigate the influences of the locations and number of cracks, shear deformation, material properties, slenderness ratio and various end supports on the critical buckling loads of cracked FGM beams. Numerical examples show that the developed method can simply, exactly and effectively solve the buckling of cracked FGM beams with various conditions.

关 键 词：功能梯度材料 含裂纹梁 屈曲 传递矩阵法 剪切效应 

分 类 号：O343[理学—固体力学] TB330.1[理学—力学]