The Characteristic Singularity Analysis For V-notches In Engineering Structures

According to the linear elasticity theory, there is strong stress concentration near theV-notch tip, which is the stress singularity, and can be expressed as the asymptoticseries expansion. The singularity state is reflected by the singularity order and thecorresponding characteristic angular functions. In this paper, a new way is proposed todetermine the stress singularities for V-notches. Based on the asymptotic expansion ofthe displacement fields at the notch tip, the equilibrium equations are transformed into aset of characteristic ordinary differential equations with respect to the singularity orders.By adopting the variable substitution technique, the established non-linear characteristicequations are transformed into a set of linear ones. The interpolate matrix method isintroduced to solve the established equations for getting the stress singularity orders andcharacteristic angular functions.The singularity of notch in the Reissner plate, the notch in the shallow shell, the notchof the generalized plane strain in the composite material and the notch in thepiezoelectric plate are respectively analyzed. For the V-notch in Reissner plate andshallow shell， four kinds of radial boundary conditions are proposed to calculate thesingularity orders and characteristic angular functions. The iterative solution for thetranscendental equations is avoided in the present method. The orders of momentsingularity and shear forces singularity can be obtained at the same time and they can bedistinguished from the corresponding characteristic angular functions. Analysis of thesingularity for the composite material notch in the generalized plane strain indicate thatthe proposed method can be used to solve the generalized plane deformation problem inwhich the in-plane and anti-plane stress fields are coupled or decupled, respectively.The present method is versatile which can be degenerated to calculate the stresssingularity orders for a crack or an isotropic notch. The accuracy of the proposedalgorithm are investigated with comparison to the reference ones, it is demonstrated thatthe presented method is an effective and accurate way to analyze the stress singularityorders for the V-notch in engineering structure.