By Petia Dineva
Dynamic Fracture of Piezoelectric Materials makes a speciality of the Boundary fundamental Equation technique as an effective computational software. The presentation of the theoretical foundation of piezoelectricity is by way of sections on primary recommendations and the numerical consciousness of the boundary price difficulties. significant components of the booklet are dedicated to the answer of difficulties in homogeneous and inhomogeneous solids. The e-book contains contributions on coupled electro-mechanical types, computational tools, its validation and the simulation effects, which exhibit diverse results worthy for engineering layout and perform. The publication is self-contained and well-illustrated, and it serves as a graduate-level textbook or as additional examining fabric for college kids and researchers.
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Additional info for Dynamic Fracture of Piezoelectric Materials: Solution of Time-Harmonic Problems via BIEM
4. Different illustrative numerical examples are presented in Chaps. 5– 15, where we consider uncoupled problems, multiple cracks and dynamic crack interaction phenomena, unbounded and bounded domains, inhomogeneous domains, domains with hole or crack and hole. For every particular case the BVP will be stated together with the corresponding boundary integral equation formulation. References 1. Aliabadi AM, Rooke D (1991) Numerical fracture mechanics. Computational Mechanics, Southampton 2. Alshits VIA, Chadwick P (1997) Concavities on the zonal slowness section of a transversely isotropic elastic material.
Solution of Eq. 44) is a vector-valued function with components u J ∈ C 2 (R 2 \Scr ) that satisfies the equation and boundary condition. In Chap. 44) into an integro–differential equation on Scr , the unknown is the crack opening displacement Δu J = u J | Scr+ − u J | Scr− . 45) In addition the unknown u J must satisfies the Somerfield type condition at infinity. Solution of Eq. 45) is a vector-valued function with components u J ∈ C 2 (R 2 \Scr ) that satisfies the equation and boundary condition.
23– 25]. Dynamic fundamental solutions in the time and frequency domain were also derived by Wang et al.  and Wang and Zhang  by using Radon transforms technique. Denda et al.  applied the obtained fundamental solutions to study 2D eigenvalue problems. Fundamental solutions for homogeneous isotropic/anisotropic elastic solids were obtained in Rangelov et al.  and for piezoelectric solids in Gross et al. [23–25] and in the next sections we will follow these works. 2 Preliminaries Fundamental solutions are generalized functions and the method to derive them is based on integral transformation technique.
Dynamic Fracture of Piezoelectric Materials: Solution of Time-Harmonic Problems via BIEM by Petia Dineva