Application of penalty-equilibrium hybrid stress element method to crack problems

Abstract Based on a penalty Hellinger–Reissner principle, two special hybrid stress elements ensuring traction-free conditions along arbitrary boundaries are introduced to improve the penalty-equilibrium hybrid stress element method (PEHS). In the element formulation, the stresses are approximated by complete polynomials of global co-ordinates. The path independence of J 1 - and I ∗ 1 -integrals is examined. These integrals are then used for the determination of the stress intensity factor (SIF) at the tip of a crack in mode I or II in a linear isotropic or orthotropic material. Studies on the validity of the dual analysis concept for both materials are also carried out. Confirmative numerical results for typical cracked specimens are presented and discussed.

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