Sub-structure analysis for elastic fields with stress singularities

In the complex structures of Nuclear Engineering, interfaces between different materials give rise to steep stress gradients under load, thermal or other environments. In an elastic sense, the structural field contains stress singularities. Continuum-finite hybrid formulations have been suggested, in which a differential equation solution is used conjointly with a normal finite element breakdown of the structure. There are situations where this concept can be very effectively extended to develop a finite element formulation of the sub-structure type, in which each sub-structure consists of a 'single finite element', so that the total structure is represented by only a handful of finite elements. To illustrate the method, the 'end problem' of a rectangular strip in which one end is clamped, the opposite end is stressed or stretched, and the two transverse edges are stress free is considered. The special features of this analysis are that complex configurations can be considered, only a few elements are needed, matrix orders are small, stress singularities are properly estimated, solution convergence is through element refinement and, results are highly accurate. (Auth.)