The equations of motion and bending of Euler-Bernoulli beam are formulated using the nonlocal elasticity theory for cantilever microtubules (MTs). The method of differential quadrature (DQ) has been used for numerical modeling. The size effect is taken into consideration using the Eringen’s non-local elasticity theory. Frequencies and deflections of MTs are obtained. Numerical results are prese...

The classical linear elasticity theory is based on the assumption that the size of the displacement gradient tensor is small. In many engineering applications, although the basic assumption is violated due to, e.g., corner singularities, the linear elasticity system is still used to approximate the reality. In this paper, we give a-posteriori error analysis for the eeect of the linearization on...

The weakness of existing relationships correlating off-axis modulus of elasticity E� to shear mod­ ulus G12 for wood composite panels is demonstrated through presentation of extensive experimental data. A new relationship is proposed that performs better than existing equations found in the literature. This relationship can be manipulated to calculate the shear modulus G12 of orthotropic specim...

This paper deals with local buckling analysis of rectangular functionally graded material plates using finite strip method and based on classical plate theory. The modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The principle of minimum total potential energy is employed to obtain stiffness and sta...

We are interested in the phase transformation from austenite to martensite. This transformation is typically accompanied by the generation and growth of small inclusions of martensite. We consider a model from geometrically linear elasticity with sharp energy penalization for phase boundaries. Focusing on a cubic-to-tetragonal phase transformation, we show that the minimal energy for an inclusi...

Constitutive relations for two-dimensional deformations of cohesionless granular materials are considered. The granular materials are assumed to be isotropic and rate-independent. One of the current trends in modelling the behaviour of granular materials is to study constitutive relations of the hypo-elastic The general hypo-elastic constitutive relation, originally proposed by Tr~esdell ,~ is ...

In this paper, buckling and free vibration analysis of a circular tapered nanoplate subjected to in-plane forces were studied. The linear variation of the plate thickness was considered in radial direction. Nonlocal elasticity theory was employed to capture size-dependent effects. The Raleigh-Ritz method and differential transform method were utilized to obtain the frequency equations for simpl...

The present study investigates buckling characteristics of both nonlinear symmetric power and sigmoid functionally graded (FG) beams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by the sigmoid-law distribution (S-FGM), and the symmetric power function (SP-FGM). These functions have smooth variation of properties across the boundary rather tha...

Abstract— A classical plane problem of the theory elasticity about a crack in stretched orthotropic elastic unbounded is considered, which leads to singular solution for stresses vicinity edge. The relations generalized elasticity, including small scale parameter, are given. equations higher order than and allow eliminating singularity solution. parameter determined experimentally. results obta...