弹塑性体的可动边界变分原理

Variational Principles of the Variable Boundary for the Elastoplastic Body

利用可动边界的变分方法,在一阶变分为零的条件下,导出了待解函数应满足的数学物理方程,并建立了弹塑性体的可动边界变分原理,对弹塑性问题作了完整的描述。这类变分原理含有弹塑性区的交界方程、沿应变(应力)路径积分时,应变与应力应满足的本构方程、及在整体边界上力的附加边界条件。当略去边界可动性的影响时,这类变分原理就退化为通常的变分原理。

The variation problem of an elastoplastic body is considered as the variation problem of variable boundary.If the first variation vanishes, the mathematical physical equation satisfying the unknown function can be derived with calculus of variation for variable boundary and variational principles of variable boundary for an elastoplastic body can also be established which completely described the elastoplastic problem. These priciples comprise successive equation of elastic and plastic domains, the physical equation is satisfied by the stress and strain along the stress(strain) pass and the subsidiary boundary condition on the whole boundary of the given surface forces. If the influence of the variable boundary is neglected, this kind of variational principles is degenerated to the common variational principles.