ABSTRACT
In Chapters 2 and 3, we used well-known methods of structural analysis to develop the stiffness matrices of the bar and beam elements. The reason being that these elements are one-dimensional, and the exact solutions of the differential equations governing their behaviors are well known. For other structural problems in two and three dimensions, such direct approaches are inexistent for the obvious reason that it is not possible to find analytical solutions to the differential equations governing their behavior, except in the case of very simple geometries. The alternative is to replace the differential equations by approximate algebraic equations. This is achieved by using weighted residual methods.
