摘要:
旋转壳的边界条件,传统的表达方式是在中面位移μ,μ,ω,ψ或相应的四个力共八个量当中给定四个.而以节圆广义位移作为基本未知数,一个节圆上未知数的数目超过四个[1][2][3][4].在这种情况下关于边界条件的处理问题尚无令人满意的解决办法.本文利用虚功原理,导出一组壳边广义量与非广义量关系公式.研究了七种类型常见边界,给出用广义力与广义位移表示的边界条件公式.每一种边界条件公式的数目可以和一个节圆上所采用的未知数数目相一致.有了这些公式,即可直接将边界条件代入广义位移法运动方程以求解广义位移.这样做,避免了文献[2]关于未知数的变换与逆变换过程,不仅道理上简明而且也简化了计算.有了边界条件广义表达式,使得旋转壳广义位移法在理论上也更为完善.
Abstract:
As for the boundary conditions of shells of revolution, traditionally, four out of the eight quantities which are the four displacements on the middle surface u, v, w and ψ together with the four corresponding forces, are given. when the generalized displacements on the nodal circles are used as basic unknowns, the number of unknowns on a nodal circle is more than four[1][2][3][4]. In this case, how to deal with the boundary conditions is still a problem that has not been solved satisfactorily yet. In this paper,the relations between the generalized and nongeneralized quantities of a shell's edge are derived according to the principle of virtual work. Seven types of common edges are studied and their expressions of boundary conditions in the form of generalized displacements or forces are qiven. The number of expressions for each type of edge may correspond with the number of unknowns used on a nodal circle. Kith these expressions, boundary conditions can be put directly into equations of motion of generalized displacement method so as to solve the generalized displacements. By so doing, the process of transformation and inverse transformation about unknowns in [2] is avoided. Not only is the argument simple and clear, but the calculation work is reduced.Having the set of generalized expressions of boundary conditions, the generalized displacement method of the shell of revolution may be more perfect in theory.
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