According to the basic idea of classical yin-yang complementarity and modem dual-com plementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type vari ational principles for geometri...According to the basic idea of classical yin-yang complementarity and modem dual-com plementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type vari ational principles for geometrically nonlinear coupled thermoelastodynamics can be established system atically. The new unconventional Hamilton-type variational principle can fully characterize the initia boundary-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlin ear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of vir tual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton type variational principles by the generalized Legendre transformations given in this paper. Further more, with this approach, the intrinsic relationship among various principles can be explained clearly.展开更多
The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of pertu...The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of perturbed first-order ordinary dif- ferential equations systems and approximate solutions are obtained by using these symmetries.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 10172097, 19672074 & 19902022) Research Grand Council of Hong Kong. No. RGC 97/98, HKUST6055/97E.
文摘According to the basic idea of classical yin-yang complementarity and modem dual-com plementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type vari ational principles for geometrically nonlinear coupled thermoelastodynamics can be established system atically. The new unconventional Hamilton-type variational principle can fully characterize the initia boundary-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlin ear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of vir tual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton type variational principles by the generalized Legendre transformations given in this paper. Further more, with this approach, the intrinsic relationship among various principles can be explained clearly.
基金Supported by the National Natural Science Foundation of China(11326167,11226195)the Natural Science Foundation of Henan Province(142300410354)Foundation of Henan Educational Committee(13A110119,15B110012)
文摘The approximate generalized conditional symmetries of nonlinear filtration equation with a small parameter are studied. The initial-value problem of the equation can be transformed to perturbed Cauchy problem of perturbed first-order ordinary dif- ferential equations systems and approximate solutions are obtained by using these symmetries.
