当前位置: X-MOL 学术Proc. Inst. Mech. Eng. C J. Mec. Eng. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Bending of orthotropic rectangular thin plates with two opposite edges clamped
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ( IF 2 ) Pub Date : 2019-11-20 , DOI: 10.1177/0954406219889082
Yangye He 1 , Chen An 2 , Jian Su 3
Affiliation  

This work presents integral transform solutions of the bending problem of orthotropic rectangular thin plates with constant thickness, subject to five sets of boundary conditions: (a) fully clamped; (b) three edges clamped and one edge simply supported; (c) three edges clamped and one edge free; (d) two opposite edges clamped, one edge simply supported, and one edge free; and (e) two opposite edges clamped and two edges free. By adopting eigenfunctions of Euler–Bernoulli beams with corresponding boundary conditions for each direction of the plate, the governing fourth-order partial differential equation is integral transformed into a system of linear algebraic equations. Boundary conditions at the free edges are treated exactly by carrying out integral transform in the boundary formulations, which are incorporated in the transformed governing equations by integration by parts. The numerical difficulties with the high-order beam functions are overcome by using modified exponential forms, thus limiting the eigenfunctions to the range between −2 and 2. Analytical integration forms are used for the integrals of the coefficients of the transformed equations, further avoiding numerical difficulties with large high-order eigenvalues. The accuracy and convergence of the solutions are shown through numerical examples in comparison with available solutions in the literature and with finite element solutions obtained by using Abaqus program.

中文翻译:

夹住两个对边的正交各向异性矩形薄板的弯曲

这项工作提出了具有恒定厚度的正交各向异性矩形薄板弯曲问题的积分变换解,受五组边界条件的约束:(a)完全夹紧;(b) 三边夹住,一边简支;(c) 三边夹住,一边松开;(d) 两个相对的边缘夹紧,一个边缘简单支撑,一个边缘自由;(e) 两个相对的边缘被夹住,两个边缘被释放。通过采用欧拉-伯努利梁的特征函数和板的每个方向对应的边界条件,控制四阶偏微分方程被积分转化为线性代数方程组。通过在边界公式中进行积分变换,可以精确处理自由边的边界条件,它们通过分部积分合并到转换后的控制方程中。使用修正指数形式克服了高阶梁函数的数值困难,从而将特征函数限制在 -2 和 2 之间的范围内。 解析积分形式用于对变换方程的系数进行积分,进一步避免了数值大的高阶特征值的困难。解的准确性和收敛性通过数值例子与文献中的可用解和使用 Abaqus 程序获得的有限元解进行比较。解析积分形式用于对变换方程的系数进行积分,进一步避免了高阶特征值大的数值困难。解的准确性和收敛性通过数值例子与文献中的可用解和使用 Abaqus 程序获得的有限元解进行比较。解析积分形式用于对变换方程的系数进行积分,进一步避免了高阶特征值大的数值困难。解的准确性和收敛性通过数值例子与文献中的可用解和使用 Abaqus 程序获得的有限元解进行比较。
更新日期:2019-11-20
down
wechat
bug