Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

A mathematical model for nonlocal vibration and buckling of embedded two-dimensional(2 D) decagonal quasicrystal(QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2 D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional(3 D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories.Numerical examples are provided to display the effects of the quasiperiodic direction,length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence,and medium elasticity on the vibration frequency and critical buckling load of the 2 D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate.This feature is useful since the frequency and critical buckling load of the 2 D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

Line-integral representations for extended displacements, stresses,and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials （e.g., BaTiO3）, piezomagnetic materials （e.g., CoFe2O4）, and multiferroic com-posite materials （e.g., BaTiO3-CoFe2O4 composites） also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displace-ments, extended stresses, self-energy, and interaction energy of arbitrarily shaped, three-dimensional （3D） dislocation loops with a constant extended Burgers vector in trans-versely isotropic magneto-electro-elastic （MEE） bimaterials （i.e., joined half-spaces）. The derived solutions can also be simply reduced to those expressions for piezoelectric, piezo-magnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials.

Effects of generally anisotropic crustal rocks on fault-induced displacement and strain fields

We present a new solution for the elastic displacement and strain fields on or near Earth’s surface due to rectangular faults in an anisotropic half-space,expressed as a summation of(A)the solution in an infinite space which is singular,and(B)the complementary part which is regular and well-behaved.These two solutions are expressed in terms of the mathematically elegant and computationally powerful Stroh formalism and can be applied to the generally anisotropic rock half-space or a transversely isotropic rock mass with any oriented plane of isotropy.For any flat fault of polygonal shape,one needs only to carry out a simple line integral from 0 to 7 r in order to express the fault-induced response.Numerical examples are presented to demonstrate the significant effect of the rock anisotropy and layer orientation on the fault-induced displacement and strain fields in anisotropic rocks.Potential applications are wide ranging,from faults in sedimentary strata to strongly deformed metamorphic rocks with steeply dipping foliation.