摘要
本文具体研究了定义在可变区域上或可变边界表面上的泛函的一阶、二阶变分问题，得到了与经典变分法相对应的关于可变区域问题的变分法。并用该变分法讨论了具有可变区域的弹性系统的势能原理。另一方面，与传统的数学规划相对应，研究了可变区域上泛函的约束极值问题——广义数学规划问题，给出了相应的广义Ｋｕｈｎ－Ｔｕｃｋｅｒ条件。
Based on the definition of the variation, the variational method of a functional definde on a variable domain or a variable domain or a variable boundary of domain is obtained. By use of the variational method,the potential energy principle of a elastic system on a variable domain is discussed.On the other hand,corresponding to the classical mathematical programming,the general-ized mathematical programming problem a constrained optimum problem on a variabledomain is researched and the generalized Kuhn-Tucker condition is given.
关键词
可变区域
变分法
泛函
弹性力学
variable domain,variational method, generalized mathematical programming,functional
