Higher-Order Theories for Structural Analysis Using Legendre Polynomial Expansions
Higher-Order Theories for Structural Analysis Using Legendre Polynomial Expansions
复制标题
使用勒让德多项式展开进行结构分析的高阶理论
DOI：
10.1115/1.3564767
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发表时间：
1969
期刊：
影响因子：
--
通讯作者：
A. Soler
中科院分区：
文献类型：
--
作者：
A. Soler
研究了平面弹性力学的控制方程，以确定合适的近似理论。问题中的每个因变量都被视为勒让德多项式中的级数展开，重点在于建立级数截断的逻辑方法。任何阶次近似理论的重要变量都是从能量考虑建立的，而所需的近似理论是通过直接约化场方程组和从能量的观点建立的。发展了一种新的“经典”梁理论，能够处理侧向表面上的位移边界条件。对高阶近似理论进行了研究，并与精确解作了一定的比较，结果表明，新方法得到的近似理论可能比以前类似近似水平的理论更精确。
Governing equations of plane elasticity are examined to define suitable approximate theories. Each dependent variable in the problem is considered as a series expansion in Legendre polynomials; attention is focused on establishment of a logical approach to truncation of the series. Important variables for approximate theories of any order are established from energy considerations, and the desired approximate theories are established by direct reduction of the field equations and also from an energy viewpoint. A new “classical” beam theory is developed capable of treating displacement boundary conditions on lateral surfaces. Higher-order approximate theories are studied to make certain comparisons with exact solutions; the results of these comparisons indicate that the new method yields approximate theories which may be more accurate than previous theories with similar levels of approximation.