A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements t...

Anisotropic strain gradient elasticity theory is applied to the solution of a mode III crack in a functionally graded material. The theory possesses two material characteristic lengths, , and ,8, which describe the size scale effect resulting from the underlining microstructure, and are associated to volumetric and surface strain energy, respectively. The governing differential equation of the ...

An analysis is presented of the diffraction of a pressure wave by a periodic grating including the influence of the air viscosity. The direction of the incoming pressure wave is arbitrary. As opposed to the classical nonviscous case, the problem cannot be reduced to a plane problem having a definite 3-D character. The system of partial differential equations used for solving the problem consist...

Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for inte...

The boundary integral equation (BIE) method is applied for the thermal analysis of fiber-reinforced composites, particularly the carbon-nanotube (CNT) composites, based on a rigid-line inclusion model. The steady state heat conduction equation is solved using the BIE in a two-dimensional infinite domain containing line inclusions which are assumed to have a much higher thermal conductivity (lik...

A long matrix crack in a unidirectional bre{reinforced composite, perpendicular to the bre direction and subjected to Mode{I loading, is considered. The intact composite material is modelled as homogeneous linearly elastic and the bridging bres are replaced by restraining tractions acting on the crack surfaces. The problem is formulated in terms of a hypersingular integral equation with respect...

Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm converge...

This chapter is concerned with cracks . Real cracks in solids are complicated: they are thin cavities, their two faces may touch, and the faces may be rough. We consider ideal cracks. By definition, such a crack is modelled by a smooth open surface Ω (such as a disc or a spherical cap); the elastic displacement is discontinuous across Ω, and the traction vanishes on both sides of Ω (so that the...