Pointwise error estimate for a consistent beam theory
Pointwise error estimate for a consistent beam theory
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DOI：
10.1142/s0219530516500135
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发表时间：
2018
影响因子：
2.2
通讯作者：
Xiaoyi Chen;Zilong Song;H. Dai
中科院分区：
文献类型：
--
作者：
Xiaoyi Chen;Zilong Song;H. Dai
本文研究了由线弹性材料构成的梁的平面变形。从平面应力问题的场方程出发，采用底表面位移矢量的级数展开，一致地推导出含两个未知数的梁方程。成功的依靠是利用场方程和底部牵引条件建立精确的递推关系，使得所有的量都可以用位移的两个主要展开系数来表示。另一个特点是，该级数的余数可以转到梁方程中。然后，根据梁方程的通解和误差项，严格建立了位移场和应力场的逐点误差估计。考虑了三个具有二维精确解的基准问题。结果表明，这种新的束流理论可以恢复这些问题的精确解。在附录中还讨论了两种具有边界层效应的情况。
This paper studies the planar deformations of a beam composed of a linearly elastic material. Starting from the field equations for the plane-stress problem and adopting a series expansion for the displacement vector about the bottom surface, we deduce the beam equations with two unknowns in a consistent manner. The success relies on using the field equations together with the bottom traction conditions to establish the exact recursion relations, such that all quantities can be represented in terms of the two leading expansion coefficients of the displacements. Another feature is that the remainders of the series can be carried over to the beam equations. Then, based on the general solutions and the error terms of the beam equations, pointwise error estimates for displacement and stress fields are rigorously established. Three benchmark problems are considered, for which the two-dimensional exact solutions are available. It is shown that this new beam theory recovers the exact solutions for these problems. Two cases with boundary layer effects are also discussed in the appendix.