Finite element analysis of subregions using a specified boundary stiffness/force method

The accurate finite element analysis of subregions of large structures is difficult to carry out because of uncertainties about how the rest of the structure influences the boundary conditions and loadings of the subregion model. This dissertation describes the theoretical development and computer implementation of a new approach to this problem of modeling subregions. This method, the specified boundary stiffness/force (SBSF) method, results in accurate displacement and stress solutions as the boundary loading and the interaction between the stiffness of the subregion and the rest of the structure are taken into account. This method is computationally efficient because each time that the subregion model is analyzed, only the equations involving the degrees of freedom within the subregion model are solved.

Numerical examples are presented which compare this method to some of the existing methods for subregion analysis on the basis of both accuracy of results and computational efficiency. The SBSF method is shown to be more accurate than another approximate method, the specified boundary displacement (SBD) method and to require approximately the same number of computations for the solution. For one case, the average error in the results of the SBD method was +2.75% while for the SBSF method the average error was -0.3%. The comparisons between the SBSF method and the efficient and exact zooming methods demonstrate that the SBSF method is less accurate than these methods but is computationally more efficient. In one example, the error for the exact zooming method was -0.9% while for the SBSF method it was -3.7%. Computationally, the exact zooming method requires almost 185% more operations than the SBSF method. Similar results were obtained for the comparison of the efficient zooming method and the SBSF method.

Another use of the SBSF method is in the analysis of design changes which are incorporated into the subregion model but not into the parent model. In one subregion model a circular hole was changed to an elliptical hole. The boundary forces and stiffnesses from the parent model with the circular hole were used in the analysis of the modified subregion model. The results of the analysis of the most refined mesh in this example had an error of only -0.52% when compared to the theoretical result for the modified geometry.

The results of the research presented in this dissertation indicate that the SBSF method is better suited to the analysis of subregions than the other methods documented in the literature. The method is both accurate and computationally efficient as well as easy to use and implement. The SBSF method can also be extended to the accurate analysis of subregion models with design changes which are not incorporated into the parent model.