Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 29, No 1, (2018), 81p-92p
Aim of the study is to propose, develop, verify and apply in intensive simulations an efficient non-hypersingular traction boundary integral equation method (BIEM) for solution of anti-plane dynamic problem of a finite exponentially inhomogeneous piezoelectric solid with a nano-crack. The modelling approach is in the frame of continuum mechanics, wave propagation theory, the Gurtin and Murdoch surface elasticity theory and linear fracture mechanics. The simulations reveal the dependence of the stress concentration field on the electromechanical coupling, on the type and characteristics of the dynamic load, on the position-dependent material parameters, on the surface elasticity, on the size effect and on the wave-nanocrack-material gradient interaction. 2010 Mathematics Subject Classification: 35Q74, 74S15, 74H35.