【摘要】 根据对偶互补的基本思想,系统地建立了非线性弹性薄壳静力学的各类变分原理.文中首先给出非线性薄壳静力学的广义虚功原理的表式,然后从该式出发,不仅能得到非线性薄壳静力学的虚功原理,而且通过所给出的广义Legendre变换,还能系统地成对导出非线性弹性薄壳静力学的3类变量(U,ε,,χN,M)、2类变量(U,N,M)变分原理、以及总势能驻值原理和总余能驻值原理的互补泛函.同时,通过这条新途径还能清楚地阐明这些原理的内在联系.更多还原

【Abstract】 According to the dual-complementarity,a few variational principles for nonlinear statics of elastic thin shells have been established systematically.An important integral relation is given,which can be considered as the generalized principle of virtual work for nonlinear statics of thin shells.Based on this relation,it is possible not only to obtain the principle of virtual work for nonlinear statics of thin shells,but also to derive systematically the complementary functionals for three-field(U,ε,χ,N,M),two-field(U,N,M)variational principles and principles of stationary total potential energy and stationary total complementary energy for nonlinear statics of elastic thin shells by the generalized Legendre transformation given in this paper.Furthermore,the intrinsic relationship among various principles can be illustrated clearly with this approach.更多还原