Internal Force Calculation of Four Edges Supported RectangularPlates under Local Uniformly Distributed Load

DOI：

 作者 单位 杨成永，马文辉?覮，韩薛果，程霖 （北京交通大学 土木建筑工程学院，北京 100044）

以矩形板的Navier解为基础，采用带补充项的傅里叶级数作为挠度函数，研究了局部均布荷载作用下四边支承矩形薄板的弯曲问题. 推导了确定待定系数的线性代数方程组，给出了简支边和固支边不同组合条件下的统一计算公式. 讨论了带补充项法级数解的收敛速度，并与叠加法级数解及有限元数值解分别进行了精度和计算量的对比. 结果表明，带补充项法的级数解达到收敛的级数项数约为40项. 带补充项法的级数解与叠加法级数解具有同样的求解精度. 有限元解随网格的细分，计算结果逐渐接近级数法解. 级数解法的计算量与有限元解法相比是微不足道的. 研究成果适于进行构筑物顶板受局部均布荷载作用的结构计算.

On the basis of Navier’s solution to rectangular plates, the bending problem was studied for the four edges supported thin plates under local uniformly distributed load, where the double Fourier series with additional terms was adopted as the deflection function of the plates. Linear algebraic equations for solving the undetermined coefficients were derived. A unified solution was obtained to the rectangular plates with clamped and simply supported edges. The rate of convergence was discussed on the solution of the series method with additional terms. The proposed method was compared both with superposition series method on accuracy, and with finite element numerical method on computational cost. The results show that 40 terms should be employed for a convergence of the series. The method with additional terms shows the same accuracy of solution as superposition series method does. The solution by finite element method gradually approaches that by the series method as the mesh gets finer and finer. In comparison with finite element method, the computational time by the series method is negligible. This work is applicable for structural analysis of the top plates of underground buildings under truck wheel pressure.