Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported
Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported
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DOI：
10.1016/j.apm.2011.07.020
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发表时间：
2012
影响因子：
5
通讯作者：
B. Yang;H. Ding;Wei-qiu Chen
中科院分区：
文献类型：
--
作者：
B. Yang;H. Ding;Wei-qiu Chen
英格兰（2006）[13]提出了一种研究各向同性功能梯度板在横向双谐载荷作用下弯曲的新方法。他的方法在这里扩展到具有横向各向同性的材料的功能梯度板。基于满足双调和方程的横向载荷的三维弹性理论，采用复变方法，建立了位移场展开中出现的三个板块位移的控制方程。解可以用复变量的四个解析函数来表示，其中的未知常数可以从类似于经典板理论的边界条件中确定。推导了12种双调和多项式荷载作用下对边简支FGM矩形板的弹性解为控制方程通解和特解的适当和。本文对均布荷载的计算结果与已有的解进行了比较，两者吻合得很好。数值研究了边界条件、材料不均匀性和厚长比对载荷x2yq下板挠度和应力的影响。
England (2006) [13] proposed a novel method to study the bending of isotropic functionally graded plates subject to transverse biharmonic loads. His method is extended here to functionally graded plates with materials characterizing transverse isotropy. Using the complex variable method, the governing equations of three plate displacements appearing in the expansions of displacement field are formulated based on the three-dimensional theory of elasticity for a transverse load satisfying the biharmonic equation. The solution may be expressed in terms of four analytic functions of the complex variable, in which the unknown constants can be determined from the boundary conditions similar to that in the classical plate theory. The elasticity solutions of an FGM rectangular plate with opposite edges simply supported under 12 types of biharmonic polynomial loads are derived as appropriate sums of the general and particular solutions of the governing equations. A comparison of the present results for a uniform load with existing solutions is made and good agreement is observed. The influence of boundary conditions, material inhomogeneity, and thickness to length ratio on the plate deflection and stresses for the load x2yq are studied numerically.