Applications of trilinear coordinates to some problems in plane elasticity

This discourse considers some analytical aspects involved in the application of trilinear coordinates to boundary value problems in plane elasticity. Trilinear coordinates, also known as homogeneous point coordinates, are defined. The concepts of triaxial stress, strain, bending moments and curvature are introduced: utilizing these concepts, the stress-strain relationship, moment-curvature relationship and a few other basic equations of two dimensional elasticity are developed for an isotropic material. All these relationships are presented in matrix form - as an aid to finite element stress analysis. Governing equations corresponding to some two dimensional problems in elasticity are deduced for the trilinear system. An investigation was carried out on the method of integration of a function composed of trilinear variables. A few functional relations between the trilinear variables are also developed.

To illustrate the application of the theory, two examples on simply supported equilateral triangular plate are considered.