Exact analysis and reanalysis methods for structures with nonlinear boundary conditions

Fast analysis and reanalysis methods are proposed in this work for both static and dynamic analysis of structures with nonlinear boundary conditions. To ensure the precision and accuracy, the technique is based on exact reanalysis methods, i.e. the Sherman-Morrison-Woodbury (SMW) formula and Indirect Factorization Updating (IFU). By applying the nonlinear boundary conditions locally and keeping the change of effective stiffness matrix to be local, a high efficiency of the proposed methods can be guaranteed. As a result, the key difficulties of error accumulation in the nonlinear reanalysis is solved consequently. Two benchmark tests, including a two-dimensional beam and a flexible multi-body system based robotic manipulator are adopted to demonstrate the proposed methodology. Numerical results show that the method can acquire same exact solutions as full analysis of the considered structures, but lead to about twice to five times higher efficiency than the latter. The proposed methods then provide an efficient measure for structures with nonlinear boundary conditions and local modifications.