基于哈密顿体系的平面无限解析元

在有限元法中,无限域的问题不便于处理求解。但无限域往往可以由规则的无限外域再加上有限的局部域组成。将无限域问题中的有限局部域用有限元法处理,在规则的无限外域中建立极坐标系,将规则无限域问题导向哈密顿体系,利用本征向量展开的方法,推导出一种新的半解析无限解析元,其刚度阵是精确的。该单元可用常规方法作为一个超级有限单元与有限的局部域连接。数值计算结果表明,该单元具有精度高,应用方便,数据处理非常简单的特点。对无限域问题的数值求解有重要意义。该方法可推广到三维无限域问题中。

Plane Infinite Analytical Element and Hamiltonian System

It is not convenient to solve those engineering problems defined in an infinite field by using FEM.An infinite area can be divided into a regular infinite external area and a finite internal area.The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate.All governing equations were transformed into the Hamiltonian system.The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element,like a super finite element,can be combined with commonly used finite elements.The proposed method was verified by numerical case studies.The results show that the preparation work is very simple,the infinite analytical element has a high precision,and it can be used conveniently.The method can also be easily extended to a three-dimensional problem.