UBC Theses and Dissertations
Infinite finite element Ungless, Ronald Frederick
This thesis is concerned with developing a finite element model of infinite size to facilitate the stress analysis of three dimensional, semi-infinite bodies governed by time independent linear equations. An element of triangular plan form extending to infinity in one direction is devised. There are three nodes per element, each node having three displacement degrees of freedom. The infinite element is used in conjunction with regular finite elements to represent the stiffness of the semi-infinite solid which has previously been assumed to be zero or infinite in regular finite element models. The infinite element relieves the computational problem caused by large numbers of elements which has limited the use of the finite element method in three dimensional halfspace problems. A large reduction in the number of degrees of freedom is possible with the use of the infinite element because the artificial boundary of previous models is eliminated. The accuracy of the element is tested on two examples whose exact solutions are known. Both involve a semi-infinite solid, one loaded with a surface perpendicular point load, and the other with a surface parallel point load. The results compare favourably with the theory of elasticity solutions.
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