【摘要】 本文在文献[1]所得结果的基础上,建立了零曲率闭口壳当载荷沿壳表面及沿边界变化不过于急剧时,在各种边界条件下的二次近似渐近解法.将壳中的应力状态分为三种基本类型:薄膜应力状态(包括薄膜静力平衡方程的特解与齐次解)、纯弯应力状态及简单边界效应应力状态.按面向约束是否“完全”,即能否保证中心面为“不可变”的两种不同情况讨论了求解步骤.当中心面为“不可变”时,可以先解出薄膜及纯弯应力状态,然后求解简单边界效应应力状态.文中给出了在各种边界条件下各基本应力状态的相对量级关系.当中心面“可变”时,只在当载荷满足一定条件的特殊情况下才能按上述步骤求解,而在一般载荷情况下上述步骤不再适用,必须将各应力状态联立求解.更多还原

【Abstract】 On the basis of the results obtained in a previous paper,a second-order asymptotic solution is here presented for the shell of zero Gaussian curvature with closed boundary curves when the load variation along the surface and boundary curves of theshell is not too abrupt(e.g.the case of concentrated load is excluded).The state ofstress in the shell is divided into three basic ingredients:the membranous state(inclu-ding the particular and homogeneous solutions of the membrane equations of equilibrium),the pure bending state and the simple boundary effect.Two cases of surfacewise con-straints are distinguished:“complete”,if the surfacewise constraints exclude any pure bendingdisplacements without strains in the middle surface of the shell and“incomplete”,if theopposite is true.In the case of“complete”surfacewise constraints,the membrane and purebending states can be determined prior to the simple boundary effect while in the case of“incomplete”surface constraints,all basic ingredient states of tress are coupled and must be determined simultaneously except for very special loads.For the case of“complete”surfacewise constraints,the relative orders of magnitude for basic ingredient states ofstress under various boundary conditions are obtained.An example is given to illustratethe method of finding a solution for the case of“incomplete”surfacewise constraints.更多还原