Evaluation of stress concentration in multi-wedge systems with functionally graded wedges

A common apex of structural elements with different physical properties is a point of stress concentration leading to dangerous effects like fracture, corrosion and fatigue. As the concentration may be reduced by proper functional grading of the elements, there is need in evaluating the influence of various grading on the singularity of a field at the apex. In the paper, we present and compare two efficient methods (exact and approximate) to reach this goal. The exact method employs eigenfunctions of the ordinary differential equation, to which the partial differential equation of a considered problem is reduced after the Mellin’s transform. The approximate method consists in piece-wise constant approximation of the physical modules of a graded wedge. Numerical examples for antiplane strain illustrate high efficiency of the methods and beneficial influence of functional grading when the latter provides continuity of shear modulus.