The present paper shows the applicability of the dual boundary element method to analyse plastic, viscoplastic and creep behaviours in fracture mechanics problems. Several models with a crack, including a square plate, a holed plate and a notched plate, are analysed. Special attention is taken when the discretization of the domain is performed. In fact, for the plasticity and viscoplasticity cases, only the region susceptible to yielding was discretized, whereas the creep case required the discretization of the whole domain. The proposed formulation is presented as an alternative technique to study these kinds of nonlinear problems. Results from the present formulation are compared to those of the well‐established finite element technique, and they are in good agreement. Important fracture mechanic parameters like KI, KII, J‐integrals and C‐integrals are also included. In general, the results, for the plastic, viscoplastic and creep cases, exhibit that the highest stress concentrations are in the vicinity of the crack tip and they decrease as the distance from the crack tip is increased.

The current paper shows the application of the boundary element method for the analysis of plates under shear stress causing plasticity. In this case, the shear deformation of a plate is considered by means of Reissner’s theory. The probability of failure of a Reissner’s plate due to a proposed index plastic behavior IPB is calculated taking into account the uncertainty in mechanical and geometrical properties. The problem is developed in three dimensions. The classic plasticity’s theory is applied and a formulation for initial stresses that lead to the boundary integral equations due to plasticity is also used. For the plasticity calculation, the von Misses criterion is used. To solve the nonlinear equations, an incremental method is employed. The results show a relatively small failure probability (PF) for the ranges of loads between 0.6<W^<1.0. However, for values between 1.0<W^<2.5, the probability of failure increases significantly. Consequently, for W^≥2.5, the plate failure is imminent. The results are compared to those that were found in the literature and the agreement is good.

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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. e von Mises yield criterion is used to evaluate the plastic zone and is supposed to have elasticperfectly plastic material behaviour. An initial stress formulation is used to formulate the boundary integral equations. e domain integrals are evaluated using a cell discretization technique. A total incremental method is applied to solve the nonlinear boundary integral equations. e approach is illustrated in a plate subjected to incremental load. e 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.

Large number of earthquakes have epicenters in offshore areas and their effects are a matter of great concern. This paper applies, for two dimensional problems, the Indirect Boundary Element Method to calculate the seismic pressure profile with the water depth due to the incidence of P- and SV-waves on the seabed, which can be characterized using the soil properties. Moreover, seismic amplifications of the seabed are highlighted. Our formulation can be considered as a numerical implementation of the Huygens’ Principle in which the diffracted waves are constructed at the boundary from which they are radiated. Thus mathematically, it is fully equivalent to the classical Somigliana’s representation theorem. Numerical results show the importance of knowing the properties of the marine soil because the pressure profile has an enormous dependence with respect to them. In some cases, pressure amplifications of six times between extreme values of soil materials can be expected. In addition, results from a layered numerical model evince that large seismic amplifications may be found, they can reach values up to 15.57 and 18.36 times the incident P- and SV-waves, respectively.