摘要
本文提出了一条比巳有文献更简单更直接的新途径,系统地建立了耦合热弹性力学中各种Gurtin型变分原理。文中首先给出一个重要的以卷积表示的积分关系式,然后从该式出发,系统地导出成互补关系的八类变量、七类变量、六类变量、五类变量、四类变量、三类变量及二类变量的变分原理。而Nickell和Sackman,Carlson所给出的变分原理,只是本文所建立的新的更一股广义变分原理的部分特殊形式。并且,通过这条新途径,不仅能清楚地阐明各种Gurtin型变分原理之间的内在联系,而且能说明仅以应力场和热流场为独立变量的变分原理的建立过程。
In this paper, a new approach is proposed for the systenatic derivation of various Gurtin-type variation principles in coupled thermoelasticity. Based on an important integral relation in terms of convolutions given by the author, the new approach can be used to derive more simply and directly the complementary functionals for the eight-field,seven-field, six-field, five-field, four-field, three-field and two-field Gurtin-type variation principles. The variation principles given by Nickell and Sackman, Carlson are only the particular forms of the new and more general variation principles proposed in this paper. And with this approach, not only the intrinsic relationship among various Gurtin-type variation principles but also the derivation of variation principle involvirtg only the independent stress and heat flux fields can be explained clearly.
出处
《上海力学》
CSCD
1990年第1期43-53,共11页
Chinese Quarterly Mechanics
基金
国家自然科学基金
