浅梁弯曲经典计算公式的精度讨论

提出一种新的简支梁变形模式，横截面内除了有挠度、转角外，还考虑了面内变形，并对受集中荷载作用简支浅梁弯曲挠度计算公式的适用范围进行研究。运用U变换法和四结点矩形单元，分析了简支梁的平面弯曲问题，求解出二维有限元格式下受集中荷载作用梁的上下自由表面位移的解析解，并将所得的解析解，与材料力学关于浅梁弯曲的挠度计算公式相比较，讨论经典计算公式的适用范围，并对其误差进行了定量讨论。

Study on the Precision of the Bending Formulae for Simply Supported Beams

An new bending mode of simply supported beam are presented. Besides the deflection and slope, the plain transmutation at the cross section is considered. And then an exact investigation on the working condition of the deflection and slope formula of beams with two ends simply supported are presented in the paper. By using the U-transformation method and the rectangular element with four nodes, the paper analyze the plane bending problem of beams, and the precise analytical displacements on the upper and bottom surface under a uniform load are obtained. Comparing the analytical element solutions with the deflection given out in material mechanics, the precision of the later is discussed exactly.