ON SOME NUMERICAL PROBLEMS IN THE ANALYSIS OF A STRAIN SOFTENING BAR

Abstract

Numerical problems associated with strain softening and localisation in static and dynamic one dimensional analysis are discussed. Mesh sensitivity and load step sensitivity issues are considered. The theory of plasticity has been used and its capability in solving the above problems explored. Static and dynamic analysis of one dimensional strain softening bar was carried out. In plasticity computations the importance of updating stresses only at equilibrium states after convergence has been achieved is reiterated. Total residual strategy and subincremental residual strategy are discussed. Computational issue of elasto-plasticity are discussed. Some methodologies for updating the stiffness matrix for static softening problems are explored. Dyanamic numerical analysis of a strain softening bar, for which closed form solution is available, is carried out using the Newmark's implicit integration scheme in conjunc-tion with the total residual strategy, to study if localised solutions can be obtained.