采用有限单元法计算梁任意形状截面特性

采用将梁截面离散化的方式,用数值积分计算截面的几何特性,并根据梁剪切变形和扭转理论,利用变分原理建立截面的有限元法方程,求解任意形状截面的扭转常数、剪切中心以及剪切面积修正系数等特性.本方法适用于各种形式的截面,具有计算精度高及适应性强的特点.根据上述理论编制了相应程序,按照不同的单元划分方式,分别计算出矩形截面截面特性,与理论解进行比较;又对舟山市定海长峙至岙山预应力混凝土连续箱梁截面进行了计算,并与Ansys结果进行比较,均证明采用本文的计算方法能得到满意的结果,且该方法适用于各种形状的截面形式.

Evaluation of arbitrary cross sectional properties with finite element method

The determination of the sectional properties of cross-section depends upon the solution of a two-dimensional boundary value problem.By making use of warping function,the torsion and flexure problems are formulated,a finite element procedure of two-dimensional torsion and flexure problem is developed for arbitrary cross-section by using the theorem of minimum potential energy.The cross-section is discretized with six-node and eight-node isotropic plane element to evaluate the torsional coefficient,shear center and the shear area correction coefficients of any beam with irregular cross-section.The sectional area and inertial moment are also calculated with the numerical integration,a finite element program is developed with this method,Two numerical examples are given,the result of a rectangular cross-section and the result of cross-section of box beam of SongAo bridge are compared with theoretical solution and the result with Ansys respectively to demonstrate the efficiency and accuracy of the method.