ABSTRACT
The triangle is a simple, but very useful shape for developing a basic understanding of the fundamentals of finite element analysis of stress and seepage in two dimensions. The unknowns in stress analyses are almost always the displacements. In seepage analysis, the unknowns are usually fluid pressures. Once an adequate theory is developed for interpolating the unknowns in the interior of a triangle from the known values at the triangle corners, explicit expressions for linear interpolation functions can be obtained that are suitable for programming into a finite element package. However, the numerical quality of a linear triangle is low and is used to illustrate the concept of interpolation in a simple intuitive manner. Linear interpolation of displacements over a triangle leads to constant strains within the triangle and jumps in strains between adjacent triangles. A smoother strain approximation can be obtained by a higher-order displacement approximation.
