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A dual mesh finite domain method for the analysis of functionally graded beams

机译：一种用于功能梯度梁分析的双网状有限域方法

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摘要

A method that employs a dual mesh, one for primary variables and another for dual variables, for the numerical analysis of functionally graded beams is presented. The formulation makes use of the traditional finite element interpolation of the primary variables (primal mesh) and the concept of the finite volume method to satisfy the integral form of the governing differential equations on a dual mesh. The method is used to analyze bending of straight, through-thickness functionally graded beams using the Euler-Bernoulli and the Timoshenko beam theories, in which the axial and bending deformations are coupled. Both the displacement and mixed models using the new method are developed accounting for the coupling. Numerical results are presented to illustrate the methodology and a comparison of the generalized displacements and forces/stresses computed with those of the corresponding finite element models. The influence of the coupling stiffness on the deflections is also brought out.
机译：提出了一种采用双网格的方法，一个用于初级变量，另一个用于双变量，用于对功能梯度波束的数值分析。该配方利用主要变量（原始网格）的传统有限元插值和有限体积方法的概念，以满足双网格上的控制微分方程的整体形式。该方法用于使用Euler-Bernoulli和Timoshenko光束理论分析直线，贯通功能梯度梁的弯曲，其中轴向和弯曲变形耦合。使用新方法的位移和混合模型都是为耦合开发的。提出了数值结果以说明与相应的有限元模型计算的广义位移和力/应力的比较。还提出了耦合刚度对偏转的影响。

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