Probability of Exceeding Damage States in Plates Using BEM

An approach to obtain fragility curves taking into account the formulation for shear deformable plate theory with combined geometric and material nonlinearities and the boundary element method is proposed. It is assumed that the material undergoes large deflection with small strains. The von Mises yield criterion is used to evaluate the plastic zone and is supposed to have elastic-perfectly plastic material behaviour. An initial stress formulation is used to formulate the boundary integral equations. The domain integrals are evaluated using a cell discretization technique. A total incremental method is applied to solve the nonlinear boundary integral equations. The approach is illustrated in a plate subjected to incremental load. The uncertainties in both geometric and mechanical properties are considered in order to obtain the structural response. Results show that there are high probabilities of exceeding the damage state, d, equal to 0.05 while for the rest of the values of d, these probabilities are low.