Dynamic analysis of cracked plates based on a first-order shear deformation theory formulation by using an extended meshfree method

Abstract

An extended meshfree method is employed in this paper for investigating the dynamic behaviour of cracked plates based on the first-order shear deformation theory (FSDT). The FSDT is a straightforward formulation with the assumption of first-order shear deformation as its name implies, which is appropriate for relatively thick plates. In this study, the meshfree method is chosen as an alternative to the conventional mesh-based methods to model plate structures. Among various meshfree formulations, Moving Kriging (MK) is a method that satisfies the Kronecker delta property, allowing for the easy imposition of essential boundary conditions. An extended MK formulation is proposed in this paper to model cracked plates without explicitly pre-defining the crack in the geometry domain. In the extended concept, the extrinsic enriched functions are employed to model the discontinuity due to the crack. Particularly, the Heaviside step function is employed to describe the discontinuity of the displacement fields on two sides of the crack surface. And the asymptotic enriched functions are used for stress singularity around the crack tip. In the dynamic analysis of cracked plates, one of the important factors that must be evaluated is the dynamic stress resultant intensity factor (DSRIF). In this paper, the DSRIFs are shown through many numerical examples and compared with analytical solutions and other numerical methods, showing the accuracy and efficiency of the present extended MK approach.