摘要
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阶,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,算例表明本法计算量少,级数收敛快,所用方法可靠。
In this paper, Navier's double triangular series method for all edges simply supported plates is generalized to geometrically nonlinear analysis of trapezoidal shallow shells.Under Margueree's assumption of shells, orders of differential equations are successfully reduced by introducing two new functions. The singularity of the tangential stiffness matrix at stationary points in equilibrium path of the shell also is avoided by finding restrained equation in load-displacement space of Rn+1-dimension.The examples show that the method has the advantages of less CPU time and rapid convergence, and is also reliable for geometrically nonlinear analysis of the plates and shallow shells.
