求解梁的切应力的高阶勒让德模型

梁作为最简单的构件在工程中广泛应用. 由于经典梁理论在求解梁的切应力时需要引入平衡方程和剪切修正系数, 使得求解问题变得复杂. 该文采用高阶勒让德级数形式的位移函数, 并考虑上下边界处切应力为零的特点, 建立了梁的切应力的求解方法. 并将所得的理论结果与有限元方法的数值结果进行比较, 结果符合很好. 结果表明, 该文的理论模型能够准确地确定梁内部的正应力和切应力. 该文的研究可为梁的力学分析提供新的理论方法.

A MODEL BASED ON THE HIGHER-ORDER LEGENDRE POLYNOMIALS TO SOLVE THE BEAM SHEAR STRESS

As a simple component, the beam is widely used in engineering. in the classical beam theory, a modification factor and an equilibrium of the internal forces are introduced to obtain the shear stress, which makes the process complicated. In this paper, a displacement function of Legendre polynomials is proposed to analyze the shear stress with consideration of the conditions of zero transverse shear stress at the top and the bottom. The excellent agreement between the theoretical results and those obtained by the finite element method shows that the theoretical model of Legendre polynomials is capable of determining the shear stress of the beam accurately. Therefore, the method may provide a new theoretical reference for the mechanics analysis of the beam.