Search

A mode-I crack in a one-dimensional (1D) orthorhombic quasicrystal (QC) strip under in-plane phonon and phason stress loading is considered. Fourier transforms are applied to reduce the mixed boundary value problem of the mode-I crack to solving a system of simultaneous singular integral equations. Asymptotic expressions of the phonon and phason stresses and displacement fields near the crack tips have been obtained in an explicit form. The crack-tip singularities of the mode-I crack have been investigated and the intensity factors of the stresses in the phonon and phason fields are derived explicitly. The stress intensity factors (SIFs) and the hoop stress intensity factors (HSIFs) have been determined to investigate the effect of the geometric size and the crack kinking phenomenon. The effect of the thickness ratio of the cracked strip on the SIFs and energy release rates has been investigated. When the thickness of the cracked strip becomes infinite large, the results obtained for the crack problem can be reduced to the analytic solution for a mode-I crack in an infinite 1D orthorhombic QC media. [ABSTRACT FROM AUTHOR]

In this work, the bending response of Euler–Bernoulli beam is analyzed with three nonlocal strain gradient model with high-order boundary conditions and modified nonlocal strain and stress gradient models, in which the integral constitutive equation is transformed to an equivalent differential equation with two extra constraint equations. The corresponding differential equations are solved uniquely by the Laplace transformation and its inverse version. Under different boundary and loading conditions, the inconsistency of a nonlocal strain gradient model is examined extendedly, and consistent softening and toughening responses can be observed while using modified nonlocal strain and stress gradient model. [ABSTRACT FROM AUTHOR]