再论弹性理论变分泛函的代入构成法与一组新的变分泛函

The Further Discussion on “The Method of Substitution for Constituting Variational Functional in the Theory of Elastisity” and a Sequence of New Variational Functionals

以小位移弹性理论为例,再次论述了由场方程出发推导相应的变分泛函的数学方法——代入构成法。给出了该法的数学证明。指出了以同一方程作为约束条件及欧拉方程的两个泛函之间的转换关系。通过实例说明了如何选定代入构成法的起始表达式。给出了以应力应变关系为约束条件的一组新的变分泛函,从而说明以前的变分泛函是以应力应变关系为其欧拉方程的。

The theory of elastisity with small dispacement is taked as example , 'The Method of Substitution for Constituting Variational Functional' is further discussed. Mathematical proof of the method is given. Conversion relations between two variational functionals that take respectively same equation as their constrain condition and Euler's e-quation are obtained. By giving examples, it is explained how to specify initial representative in the method of substitution. A series of new variational fuctionals that take really stress- strain relation as constrain condition is given, this illustrates that former variational functionals take stress -strain relation as their Euler's equations.