摘要
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.
This paper presents a multivariable spline element method for analysis of shallow shells based on Hu-washizu principle. The interpolate function of cubic B splines of duality in a product form is used to establish the field functions with three kinds of variables for shallow shells,including displacement, generalized force and strain. The multivariable spline finite element model of the shallow shells has been formulated by using Hu-Washizu principle. Differentiation and stress-strain relationship are not necessary while computing the field variables. In addition, the field functions are established independently, the spline functions have good properties, both analytical and numerical feature, enough continuity, high precision in approximation and less unknowns to be determined.Several numerical examples for bending, vibration and stability of plates and shells are given in the paper.Also the calculated values from the numerical examples are used to investigate the physical relationship. It can be found that the stress-strain relationship is satisfied approximately. The present method can be extended to the areas of physical and engineering problems on multivariable fields.
出处
《土木工程学报》
EI
CSCD
北大核心
1996年第4期11-20,共10页
China Civil Engineering Journal
基金
国家自然科学基金资助项目
