具有任意阶奇异性的有限单元的研究

Study on the Finite Elements with Arbitrary Singularities

本文构造了一类具有任意阶奇异性的平面和空间等参数和亚参数单元,并证明了在单元内部和边界上具有相同的奇异性且在缺口或裂缝尖端总应变能处处有界。此外,文中还讨论了它们在线弹性V型口和幂硬化材料裂缝等问题中的应用。

In the paper, the plane and three--dimensional isoparametric and subparametrc elements with arbitrary singularities are presented, and the facts as follows are proved: 1. the singularities in the element and its boundary are similar, 2. the total strain energy in notch or crack tip is limited, in addition, their applications to V-notch of linear elast. c. ty and line c ack of powet-law hardening material are also discussed,