A special crack tip element for bending of plates with through cracks from a sixth-order plate theory

A special crack tip element for bending of plates with through cracks is developed. The element formulation is based on a general crack tip solution obtained from a continuum analysis based on Mindlin's theory satisfying all the three natural conditions on crack surface. A special feature of the element formulation is that in setting up of the element stiffness matrix, only line integrations are involved rather than usual area integration, thus enabling choice of any shape for the element. It is demonstrated through numerical examples that this crack tip element can be used in combination with conventional elements for accurate evaluation of stress intensity factors in practical problems. Numerical studies reveal that there exists an optimum crack tip element size with reference to thickness of plate which gives the best possible value of stress intensity factor.