多变量样条有限元法

本文提出了一种基于胡海昌－鹫津久一郎三类变量广义变分原理［１，２］的多变量样条有限元法，文中应用乘积型二元三次Ｂ样条插值函数来构造板壳的广义变量场函数，由三类变量广义变分原理来建立多变理样有限元模型。在计算种种场变量时，既不必求导，又无需用应力应变关系式，可直接算得其结果，因而对各种场变量均有足够的精度，文中，还解算了振动与稳定特征值问题，均得到了精度较好的数值结果。

THE MULTIVARIABLE SPLINE FINITE ELEMENT METHOD

This paper presents a multivariable spline finite element method which is based on Hu-Washizu generalized variational principle[1,2]. The cubic B spline of duality in product form is used to construct the generalized variable field functions, the computational model of the multivariable spline finite element method is established by the generalized varitional principle with three kind of variables. In calculating field variables not only the differential calculation but also the stress-strain relationships are not needed, we can directly obtain the numerical results. So all kind of field variables have enough precision. The eigen value problems of vibration and stability also have been solved for the plates and shells. all the numerical results have good accuracy.