Sharif Digital Repository

Using Hamilton's principle, exact equations of motion for non-linear planar and spatial Euler-Bernoulli beams are derived. In the existing non-linear Euler-Bernoulli beam formulations, some elastic terms are dropped by differentiation from the incomplete Green-Lagrange strain tensor followed by negligible elastic deformations of cross-sectional frame. On the other hand, in this article, the exact strain field concerning considerable elastic deformations of cross-sectional frame is used as a source in differentiations. As a result, the achieved closed-form equations are exact and more accurate than formerly reported equations in the literature. Moreover, the applicable dynamic model of... 

This Letter is devoted to the investigation of the tip, substrate and particle flexibility effects on the elastic deformation, the maximum repulsive force and the topography images in tapping mode (amplitude modulation) atomic force microscopy (TM-AFM). Several quantitative comparisons among the different models are presented and the effects of the elastic deformations on TM-AFM measurement are investigated  

A large amount of research in computational mechanics has biased toward atomistic simulations. This trend, on one hand, is due to the increased demand to perform computations in nanoscale and, on the other hand, is due to the rather simple applications of pairwise potentials in modeling the interactions between atoms of a given crystal. The Cauchy–Born (CB) hypothesis has been used effectively to model the behavior of crystals under different loading conditions, in which the comparison with molecular dynamics simulations presents desirable coincidence between the results. A number of research works have been devoted to the validity of CB hypothesis and its application in post-elastic limit.... 

The magnetic response of a polyamide nanocomposite membrane under applying a magnetic field has been modeled to evaluate elastic deformation order of magnitude. A PA-Fe3O4 nanocomposite membrane is considered to be modeled under influence of volume plane stress caused by a magnetic field. The modeling of the mechanical behavior of Fe3O4-PA nanocomposite membrane suggests that nanoparticle displacements within the nanocomposite, in the order of 200 nm under applying an external magnetic field, are greater than free volumes or porosities of the polyamide membrane. The membrane can be excited to mechanically vibrate by applying an alternating magnetic field lower than 0.1 T. As the results... 

The behavior of foams is typically rate-dependent and viscoelastic. In this paper, multiplicative decomposition of the deformation gradient and the second law of thermodynamics are employed to develop the differential constitutive equations for isotropic viscoelastic foams experiencing finite deformations, from a phenomenological point of view, i.e. without referring to micro-structural viewpoint. A model containing an equilibrium hyperelastic spring which is parallel to a Maxwell model has been utilized for introducing constitutive formulation. The deformation gradient tensor is decomposed into two parts: elastic deformation gradient tensor and viscoelastic deformation gradient tensor. A... 

In this paper, the method of additive plasticity at finite deformations is generalized to the micropolar continuous media. It is shown that the non-symmetric rate of deformation tensor and gradient of gyration vector could be decomposed into elastic and plastic parts. For the finite elastic deformation, themicropolar hypo-elastic constitutive equations for isotropicmicropolar materials are considered.Concerning the additive decomposition and the micropolar hypo-elasticity as the basic tools, an elastic-plastic formulation consisting of an arbitrary number of internal variables and arbitrary form of plastic flow rule is derived. The localization conditions for the micropolar material obeying... 

The effect of the interface stresses is studied upon the size-dependent elastic deformation of an elastic half-plane having a cylindrical inclusion with distinct elastic properties. The elastic half-plane is subjected to either a uniaxial loading at infinity or a uniform non-shear eigenstrain in the inclusion. The straight edge of the half-plane is either traction-free, or rigid-slip, or motionless, which represents three practical situations of mechanical structures. Using two-dimensional Papkovich-Neuber potentials and the theory of surface/interface elasticity, the elastic field in the elastic half-plane is obtained. Comparable with classical result, the new formulation renders the... 

In this paper, finite elastic-plastic deformations of hardening materials are analyzed based on the modified multiplicative decomposition of the left stretch tensor. This decomposition is the modified form of the Metzger and Dubey's decomposition used in the frame work of the principal axes of the left stretch tensor. For this purpose, basis-free corotational constitutive equations are derived for elastic-plastic hardening materials with the Armstrong-Frederick kinematic hardening and isotropic hardening models. The proposed governing equations are solved with different corotational rates for the simple shear problem with the material properties of the stainless steel SUS 304. The results... 

Tolerance analysis is essential for estimation of final error of key product characteristic (KPC) in a mechanical assembly caused by errors in production and assembly of individual parts. Many mechanical assemblies, especially in automotive and aerospace industries, include sheet metal parts with a small ratio of thickness to width or length. Such parts are substantially flexible and thus, are prone to large errors due to elastic deformations during assembly production. Phenomena such as deformation due to fixture force, spring back, welding distortion and so on are common to such parts. Unlike tolerance analysis of rigid parts, here, the elastic deformation of the parts plays a significant...