Limit load solutions of plates with extended surface cracks under combined biaxial forces and cross-thickness bending

Abstract

Lower bound limit load solutions for extended surface cracks in plates with free ends (pin-loaded) under combined biaxial positive/negative force/stress and positive/negative through-thickness bending are developed based on the lower bound limit load theorem and both Tresca and Mises criteria. An existing Mises limit load solution for extended surface cracks in plates with fixed ends under combined biaxial tension and positive moment is extended to general solutions for combined biaxial positive/negative force/stress and positive/negative through-thickness bending moment. Corresponding reference stress expressions are also derived and presented.