Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov–Galerkin approach with moving Kriging interpolation
Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov–Galerkin approach with moving Kriging interpolation
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DOI：
10.1016/j.compstruct.2013.08.001
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发表时间：
2014
影响因子：
6.3
通讯作者：
P. Zhu;Lu-Wen Zhang;K. Liew
中科院分区：
文献类型：
--
作者：
P. Zhu;Lu-Wen Zhang;K. Liew
提出了一种基于移动Kriging插值法的无网格局部Petrov-Galerkin方法，用于分析热环境(给定温度梯度或热流密度)下功能梯度板的几何非线性热弹性问题。Kriging插值法使构造的形函数具有Kronecker Delta函数性质，从而避免了实施本质边界条件的特殊技术。在热分析中，考虑了功能梯度材料的导热系数对温度的依赖关系，得到了一个非线性偏微分热传导方程。功能梯度板大挠度的非线性表述是基于von Kármán意义下的一阶剪切变形板理论，考虑了小应变和中等转动。通过泰勒级数展开得到了非线性方程的增量形式，并在局部无网格法的框架下以两种不同的方式显式展开了切线刚度矩阵。非线性解的计算采用牛顿-拉夫森迭代法。通过参数分析和收敛分析验证了该方法的稳定性，并通过几个算例验证了该方法在热环境下求解功能梯度板非线性弯曲问题的准确性和有效性。
A meshless local Petrov–Galerkin approach based on the moving Kriging interpolation technique is developed for geometrically nonlinear thermoelastic analysis of functionally graded plates in thermal environments (prescribed a temperature gradient or heat flux). The Kriging interpolation method makes the constructed shape functions possess Kronecker delta function property and thus special techniques for enforcing essential boundary conditions are avoided. In the thermal analysis, the dependency of thermal conductivity of functionally graded materials on temperature is involved, which gives rise to a nonlinear partial differential heat conduction equation. The nonlinear formulation of large deflection of the functionally graded plates is based on the first-order shear deformation plate theory in the von Kármán sense by taking small strains and moderate rotations into account. The incremental form of nonlinear equations is obtained by Taylor series expansion and the tangent stiffness matrix is explicitly developed in two different ways within the framework of the local meshless method. The nonlinear solutions are computed using the Newton–Raphson iteration method. Parametric and convergence studies are conducted to examine the stability of the proposed method and then several selected numerical examples are presented to demonstrate the accuracy and effectiveness of the method for nonlinear bending problems of functionally graded plates in thermal environments.