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Numerical method for stability analysis of functionally graded beams on elastic foundation

机译：弹性地基上功能梯度梁稳定分析的数值方法

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摘要

This paper considers the problems of stability of non-uniform and axially functionally graded (FG) Euler-Bernoulli beams on elastic foundation. The boundary conditions of the beam are given in general form covering different classical supporting conditions. Furthermore, the boundary conditions are transformed into convenient form in order to avoid handling infinity values of the stiffness coefficients. The method of initial parameters in differential form is used for the numerical solution of the problem. The solution of the posed boundary value problem is reduced to the iterative solution of two initial value problems and homogeneous linear algebraic system of order two. The Richardson extrapolation method is employed to improve the accuracy of results. The performance of the method proposed has been validated by several numerical examples.
机译：本文考虑了弹性地基上非均匀轴向功能梯度（FG）Euler-Bernoulli梁的稳定性问题。梁的边界条件以一般形式给出，涵盖了不同的经典支撑条件。此外，将边界条件转换为方便的形式，以避免处理刚度系数的无穷大值。微分形式的初始参数方法用于数值求解。提出的边值问题的解被简化为两个初值问题和二阶齐次线性代数系统的迭代解。理查森外推法用于提高结果的准确性。所提出的方法的性能已通过几个数值示例得到了验证。

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