FGMs稳态热传导分析的重心Lagrange插值配点法

Steady Heat Conduction Analysis of Functionally Graded Materials with Barycentric Lagrange Interpolation Collocation Method

提出一种求解二维功能梯度材料(FGMs)稳态热传导问题的重心Lagrange插值配点法.基于Chebyshev节点构造二维重心Lagrange插值函数及其偏导数,然后基于配点法将其直接代入FGMs热传导问题的控制方程和边界条件,得到系统离散方程.重心Lagrange插值配点法是一种真正的无网格方法,很好地融合了重心Lagrange插值和配点格式的优势,具有高效、稳定、高精度和易于数值实现的优点.采用重心Lagrange插值配点法分别对指数型、二次型和三角型FGMs热传导问题进行数值模拟.结果表明:该方法具有较高的计算效率和计算精度,对材料梯度参数的变化不敏感.可以进一步拓展到FGMs瞬态问题和FGMs的热力耦合分析.

A new meshless method, named collocation method with barycentric Lagrange interpolation(BLIC), is presented for analyzing steady-state heat conduction in two-dimensional functionally graded materials(FGMs). Two-variable barycentric Lagrange interpolation function and its partial derivatives at Chebyshev nodes are derived. Then, based on a collocation method, it is directly introduced into controlling equations and boundary conditions of GEMs to obtain a linear discretijed equation. The method is a truly meshless method and takes advantages of both barycentric Lagrange interpolation and collocation method such as low computational cost, stable, accurate and easy to numerical implementation. Temperature fields of exponential, quadratic and trigonometrical FGMs models are simulated. It shows that the method is accurate and efficient, and is not sensitive to the change of material gradient parameters. It can be extended to solve transient heat conduction and thermal stress analysis of FGMs.