AUTOMATED SOLUTION PROCEDURES FOR NEGOTIATING ABRUPT NONLINEARITIES AND BRANCH-POINTS

In the inelastic stability analysis of plated structures, incremental- iterative finite element methods sometimes encounter prohibitive solut ion difficulties in the vicinity of sharp limit points, branch points and other regions of abrupt non-linearity. Presents an analysis system that attempts to trace the non-linear response associated with these types of problems at minor computational cost. Proposes a semi-heurist ic method for automatic load incrementation, termed the adaptive are-l ength procedure. This procedure is capable of detecting abrupt non-lin earities and reducing the increment size prior to encountering iterati ve convergence difficulties. The adaptive are-length method is also ca pable of increasing the increment size rapidly in regions of near line ar response. This strategy, combined with consistent linearization to obtain the updated tangent stiffness matrix in all iterative steps, an d with the use of a ''minimum residual displacement'' constraint on th e iterations, is found to be effective in avoiding solution difficulti es in many types of severe non-linear problems. However, additional pr ocedures are necessary to negotiate branch paints within the solution path, as well as to ameliorate convergence difficulties in certain sit uations. Presents a special algorithm, termed the bifurcation processo r, which is effective for solving many of these types of problems. Dis cusses several example solutions to illustrate the performance of the resulting analysis system.