Applications of Trilinear Coordinates to Some Problems in Plane Elasticity

摘要

The report 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: using 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 to trilinear variables. A few functional relations between the trilinear variables are also developed. (Author)