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首页> 外文期刊>Engineering analysis with boundary elements >Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov-Galerkin (MLPG) method
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Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov-Galerkin (MLPG) method

机译：无网格局部Petrov-Galerkin（MLPG）方法对厚功能梯度板的三维静态分析

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摘要

In this paper, a version of meshless local Petrov-Galerkin (MLPG) method is developed to obtain three-dimensional (3D) static solutions for thick functionally graded (FG) plates. The Young's modulus is considered to be graded through the thickness of plates by an exponential function while the Poisson's ratio is assumed to be constant. The local symmetric weak formulation is derived using the 3D equilibrium equations of elasticity. Moreover, the field variables are approximated using the 3D moving least squares (MLS) approximation. Brick-shaped domains are considered as the local sub-domains and support domains. In this way, the integrations in the weak form and approximation of the solution variables are done more easily and accurately. The proposed approach to construct the shape and the test functions make it possible to introduce more nodes in the direction of material variation. Consequently, more precise solutions can be obtained easily and efficiently. Several numerical examples containing the stress and deformation analysis of thick FG plates with various boundary conditions under different loading conditions are presented. The obtained results have been compared with the available analytical and numerical solutions in the literature and an excellent consensus is seen.
机译：在本文中，开发了一种无网格局部Petrov-Galerkin（MLPG）方法的版本，以获得厚功能梯度（FG）板的三维（3D）静态解。杨氏模量被认为是通过指数函数通过板的厚度分级的，而泊松比被假定为常数。局部对称弱公式是使用3D弹性平衡方程得出的。此外，使用3D移动最小二乘（MLS）逼近来近似字段变量。砖形域被视为本地子域和支持域。这样，可以更轻松，更准确地完成弱形式的积分和求解变量的近似值。所提出的构造形状和测试功能的方法使得有可能在材料变化的方向上引入更多的节点。因此，可以容易且有效地获得更精确的解决方案。给出了几个数值示例，其中包括在不同载荷条件下具有不同边界条件的厚FG板的应力和变形分析。将获得的结果与文献中可用的分析和数值解决方案进行了比较，并得出了很好的共识。

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