Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates
Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates
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DOI：
10.2514/2.1805
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发表时间：
2002
期刊：
影响因子：
2.5
通讯作者：
S. Vel;R. Batra
中科院分区：
文献类型：
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作者：
S. Vel;R. Batra
对于在其顶面和/或底面承受机械和热载荷的简支功能梯度矩形板的三维变形，得到了精确解。采用能完全满足边界条件的合适的温度和位移函数，将控制热 - 机械变形的偏微分方程简化为在厚度坐标下的一组耦合常微分方程，然后用幂级数法求解。该精确解适用于厚板和薄板。给出了两种成分的金属 - 陶瓷功能梯度矩形板的结果，其成分的体积分数沿厚度方向呈幂律变化。某点的有效材料性能通过Mori - Tanaka方法或自洽方法估算。利用机械和热载荷作用下几个位置的精确位移和应力来评估经典板理论、一阶剪切变形理论以及功能梯度板的三阶剪切变形理论的准确性。还计算了材料性能由Mori - Tanaka方法、自洽方法以及这两种方法组合得到的功能梯度板的结果。
An exact solution is obtained for three-dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and/or bottom surfaces. Suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate, which are then solved by employing the power series method. The exact solution is applicable to both thick and thin plates. Results are presented for two-constituent metal‐ceramic functionally graded rectangular plates that have a power law through-the-thickness variation of the volume fractions of the constituents. The effective material properties at a point are estimated by either the Mori‐Tanaka or the self-consistentschemes. Exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory, thee rst-ordershear deformation theory, and athird-order shear deformation theory for functionally graded plates. Results are alsocomputed for a functionally graded plate with material properties derived by the Mori‐Tanaka method, the self-consistent scheme, and a combination of these two methods.