正交异性钢桥面板局部振动计算的组合板梁单元法

Combined Plate-Beam Element Method for Local Vibration Computation of Orthotropic Steel Bridge Deck

针对大跨度钢桥中采用梯形加劲肋的正交异性钢桥面板,提出一种计算钢桥面板局部振动的组合板梁单元法.其中顶板用平板壳单元分析,梯形加劲肋视为板梁单元,两者的位移模式根据板与肋的变形协调关系建立.组合板梁单元的刚度矩阵通过能量变分原理得到,利用各子单元的形函数可以求得组合板梁单元的一致质量矩阵与一致荷载列阵,进而得到相应的有限元动力平衡方程组.最后编制了组合板梁单元的有限元动力计算程序,将其前10阶自振频率与板壳有限元计算结果进行比较,验证了该方法的可行性与高效性.

Proposed in this paper is a combined plate-beam element method to calculate the local vibration of the orthotropie steel bridge deck with trapezoid stiffened fibs, which is used in the long-span steel bridge. In this method, the top plate and the trapezoid stiffened rib are respectively taken as the flat shell element and the plate-beam element, and the corresponding displacement model is established according to the deformation coordination relationship between the plate and the rib. Moreover, the stiffness matrix of the combined plate-beam element is obtained based on the energy-variation principle, and the consistent mass matrix and the consistent load matrix are obtained based on the shape function of each sub-element. Then, the finite dynamic equilibrium equations are obtained. Finally, a calculation program of dynamic finite element is presented for the combined plate-beam element, and the first 10 consequent natural frequencies are compared with those of the shell finite element, finding that the latters accord well with the formers. Thus, the proposed method proves to be feasible and efficient.