The research includes a new approach to develop more accurate and efficient techniques for solution of three dimensional problems with discontinuities and local nonlinearities. The finite element method owes its significance to its potentiality for the treatment of rather arbitrary geometry, and different material properties. One may build a special finite element that contains the discontinuity in the element formulation, and couple the special element to the mesh that models the rest of the system. The special element formulation, unlike others, will incorporate already existing classical solutions into the element formulations. The displacement function, for structural problems for example, used in approximations will exactly satisfy the analytical results wherever available. This will be achieved by invoking the classical solutions as constraints in the derivation of element stiffness coefficients. This research will bring about a new technique to handle discontinuities, local geometric-material nonlinearities at local level without requiring mesh refinements. For numerical comparison purposes a computer program will be developed.
