关于Hadamard定理的一个数值方法

对超弹性材料静力稳定性问题的Hadamard定理，利用Hadamard不等式中一些主子式是齐次函数的特点，引入球坐标系，将这些主子式正定性的判别转化为判别一个初等的二元函数在一个矩形区域上不小于零的问题．对于一个具体问题，只要平衡解的位移给出，则可判别超弹性体中任一点是否满足Hadamard不等式．因此，这种数值方法可以用于分析各种具体问题．该文还给出超弹性材料稳定性分析的一个算例．

NUMERICAL METHOD FOR HADAMARD THEOREM

Hadamard theorem is used to slove the static stability of hyperelastic materials. Based on the characteristic that some main subdeterminants in Hadamard inequalities are homogeneous functions, and by introducing the spherical coordinates, the positive definition judgment of these main subdeterminants is transformed to the problem that an elementary binary function is not less than zero in a rectangular area. For a specific problem, we can justify if any point in a superelastic body satisfies the Hadamard inequalities as long as the displacement of the equilibrium solutions are given. An numerical example is presented for the stability analysis of superelstic materials.