Abstract

The stability and deformation of a solid depends on the variability in its primary field variables, referred to as displacement field. Displacement, being the change in the position of particles at the atomic and sub-atomic levels within a solid; when, known, enables easier determination of the rate of deformation, and the force intensity within a solid. And the mathematical analysis of this cumbersome computational process has always being presented as a literature with little or no analytic details. Yes finite element analysis is a numeral method of solving a differential equation, a process where a solid of any shape is discretized into small coordinate locations in space called mesh, which contains nodes that represent the shape of the whole geometry. A structure may contain thirty thousand mesh, but its displacement field can only be determined by the computational analysis of a single mesh. The rest will be the assembling of the whole into a system. All these descriptions had always being in words. Here, we give a detailed mathematical analysis to this process by considering a unit tetra-shaped finite element mesh.