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本文提出一种基于胡-鹫津原理的多变量样条有限元法分析扁壳问题.文中应用乘积型双三次B样条插值函数来构造扁壳的多变量场函数,其中包括位移、广义力和广义应变三类场函数,根据胡-鹫津广义变分原理建立扁壳的多变量样条有限元模型,在计算各类场变量时,不用求导,也不用应力应变关系.其次,独立设置各类场函数,由于样条函数具有解析与数值的双重特性,连续性强,以及逼近精度高等优点,因而,对各类场变量均有足够的精度.文中给出若干板壳结构的弯曲、振动与稳定问题的数值算例,应用文中所得的计算数据,验算了应力应变关系式,得到了近似满足.本文方法可推广应用于工程与物理领域中的多变量场问题.
In this paper, a multivariable spline finite element method based on Hu-Jitsu principle is proposed to analyze the shallow shell problem. The multi-variable field function of the shallow shell is constructed by using the product bicubic B-spline interpolation function, including displacement and generalized force. And three generalized strain field functions, the multi-variable spline finite element model based on Hu-Jitsu generalized variational principle is established. When calculating various field variables, no derivative or stress-strain relationship is needed. Second, independent Set various types of field functions, because the spline function has the dual characteristics of analytical and numerical values, strong continuity, and the advantages of high approximation accuracy. Therefore, it has sufficient accuracy for all kinds of field variables. The bending of several plate and shell structures are given in this paper. The numerical examples of the vibration and stability problems were applied to the calculation data obtained in the paper. The stress-strain relationship was calculated and approximated. This method can be applied to multivariable field problems in engineering and physics.