层合板问题几种求解方法的比较

为比较Lagrange 体系和Hamilton 体系的有限元法在求解层合板问题时的优劣,以寻求此类问题较合适的数值方法,本文在已有研究的基础上,将几种有限元法应用到层合板问题的计算中,编程并对相关算例进行计算和分析. 数值结果表明：Hamilton 体系常规有限元和改进有限元,Lagrange 体系理性有限元在计算此类问题时各有其优势,而Lagrange 体系常规有限元在求解此类问题时的精度较差.

THE COMPARISON OF SEVERAL METHODS FOR THE LAYERED PLATE PROBLEM

In order to compare the merits and demerits of the finite element methods in the Lagrange system and the Hamilton system for the problem of layered plates and to choose appropriate numerical methods, several finite element methods are applied for the layered plates. With the use of MATLAB, an example is calculated and analyzed. Numerical results show that the conventional FEM (finite element method) and the improved FEM in the Hamilton System and the rational FEM in the Lagrange system all have their advantages, while the accuracy of the conventional FEM in the Lagrange system is poor.