侧向荷载作用下等腰梯形底扁壳的非线性弯曲

本文将 Navier 提出的四边简支矩形板线性弯曲的双三角级数解法推广到梯形底扁壳,采用 Margueree 的理论对其进行了线性和非线性弹性平衡问题的研究。文中通过引进新的未知函数成功地将原方程降低,并找到了荷载位移空间 R~(n+1) 中跟踪解曲线的简洁有效的约束方程,从而避免了求解由 Navier 法导出的非线性代数方程组在壳体平衡路径中极值点附近切线刚度矩阵的奇异性,算例表明计算量少,级数收敛快,所用方法可靠。

Nonlinear Bending of Trapezoidal Shallow Shells Under Lateral Loading

In this paper,Navier's double triangular series method for rectangular plates with all edges simply supported is generalized to the geometrically nonlinear analysis of trapezoidal shallow shells.Under Margueree's assumption of shells,the order of differential equations is reduced by introducing two new functions.The singularity of the tangential stiffness matrix at stationary points in equilibrium path of the shells is avoided by using the restrained equation in load-displacement space of R~(n+1) -dimension.The examples included show that this method has the advantages of less CPU time and rapider convergence,and is reliable for the geometrically nonlinear analysis of the plates and shallow shells.