Sharif Digital Repository

In this paper, the evolution of elastic–plastic damage in the composite laminates under fatigue conditions is modeled. Continuum damage mechanics (CDM) has been coupled with the bridge micromechanics model to estimate the fatigue damage and life for laminated composite structures. Based on the elastic–plastic bridging model, three damage variables are defined. These variables estimate the fiber, matrix, and fiber/matrix damage response at the ply scale. To model the beginning of plastic deformation, a yield function is utilized, and evolution equations of the damage variables are obtained. Then the developed deformation plastic model is calculated. The model parameters are calibrated by... 

A fully analytical solution of the classic coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads is presented. Axisymmetric thermal and mechanical boundary conditions are considered in general forms of arbitrary heat transfer and traction, respectively, at the inner and outer radii of the disk. To solve the governing system of equations, an analytical procedure based on the Fourier-Bessel transform is employed. Closed form formulations are presented for temperature and displacement fields. The results of the present formulations are in good agreement with the numerical results available in the literature. The radial distribution and time history... 

Elastic stability of shell structures under certain loading conditions is characterized by a dramatically unstable postbuckling behavior. The presence of simultaneous 'competing' buckling modes (corresponding to the same critical buckling load) is understood to be largely responsible for such behavior. In this paper, within the framework of linear bifurcation eigenvalue analysis and Donnell shallow shell theory, the presence of simultaneous buckling modes in axially compressed isotropic cones is determined using the semi-analytical method of Galerkin. The results are presented in the plane of the dimensionless reciprocal meridional and circumferential buckling half wavelengths, and are... 

This paper describes a systematic numerical investigation into the nonlinear elastic behavior of conical shells, with various types of initial imperfections, subject to a uniformly distributed axial compression. Three different patterns of imperfections, including first axisymmetric linear bifurcation mode, first non-axisymmetric linear bifurcation mode, and weld depression are studied using geometrically nonlinear finite element analysis. Effects of each imperfection shape and tapering angle on imperfection sensitivity curves are investigated and the lower bound curve is determined. Finally, an empirical lower bound relation is proposed for hand calculation in the buckling design of conical... 

This study presents the bending analysis of functionally graded conical panels under transverse compression with various boundary conditions. Equations was derived using first order shear deformation theory (FSDT) and solved using generalized differential quadrature (GDQ) method. Using this method results in the capability of studying any combinations of boundary conditions on four edges of the panel. Results are compared and validated with the results available in the literature. Effect of boundary conditions, volume fractions, panel length, semi-vertex angle and subtended angle on deflection of the panel was investigated  

In the present investigation, the buckling of generally laminated conical shells with various boundary conditions subjected to axial pressure is studied using an analytical approach. The governing equations are obtained using classical shell theory with Donnell assumptions in strain–deformation relations and the principle of minimum potential energy. The differential equations are solved using trigonometric functions in circumferential and power series in longitudinal directions. All types of boundary conditions can be applied in this method. The results are compared and validated with the results available in the literature, and good agreement is observed. Finally, the effects of the... 

The nonlinear aeroelastic behavior of a three-dimensional general laminated composite plate at high supersonic Mach numbers is investigated using von Karman's large deflection plate theory and quasisteady aerodynamic theory. Galerkin's method is used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method. Nonlinear flutter results are presented with the effects of in-plane force, static pressure differential, fiber orientation and aerodynamic damping  

A variable kinematic 1D finite element (FE) method is presented for 3D thermoelastic analysis of rotating disks with variable thickness. The principle of minimum potential energy is used to derive general governing equations of the disks subjected to body forces, surface forces, concentrated forces, and thermal loads. To solve the equations, the 1D Carrera unified formulation (CUF), which enables to go beyond the kinematic assumptions of classical beam theories, is employed. Based on the 1D CUF, the disk is considered as a beam, which can be discretized into a finite number of 1D elements along its axis. The displacement field over the beam’s cross section is approximated by Lagrange... 

The finite deformation displacement-based and hybrid-mixed four-node quadrilateral elements using the sampling surfaces (SaS) technique are developed. The SaS formulation is based on choosing inside the plate N not equally spaced SaS parallel to the middle surface to introduce the displacements of these surfaces as basic plate unknowns. Such choice of unknowns with the consequent use of Lagrange polynomials of degree N–1 in the thickness direction permits the presentation of the plate formulation in a very compact form. The SaS are located at only Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To circumvent shear locking and have... 

The fracture behavior of a hybrid-rubber-modified epoxy system was investigated. The modified epoxy included amine-terminated butadiene acrylonitrile (ATBN) rubber and recycled tire particles as fine and coarse modifiers, respectively. The results of the fracture toughness (K IC) measurement of the blends revealed synergistic toughening in the hybrid system when 7.5-phr small particles (ATBN) and 2.5-phr large particles (recycled tire) were incorporated. Transmission optical micrographs showed different toughening mechanisms for the blends; fine ATBN particles increased the toughness by increasing the size of the damage zone and respective plastic deformation in the vicinity of the crack... 

Buckling of generally laminated conical shells under uniform torsion with simply-supported boundary conditions is investigated. The Donnel type strain displacement relations are used to obtain potential strain energy of the shell and membrane stability equation is applied to acquire the external work done by torsion. The Ritz method is used to solve the governing equations and critical buckling loads are obtained. The accuracy of the results is validated in comparison of with other investigations and finite element method. The effects of lamination sequence, semi-vertex angle and length to radius ratio of the cone are evaluated and mode shapes are presented for two types of lamination... 

As a first endeavor, the aeroelastic responses of functionally graded carbon nanotube reinforced composite (FG-CNTRC) truncated conical curved panels subjected to aerodynamic load and axial compression are investigated. The nonlinear dynamic equations of FG-CNTRC conical curved panels are derived according to Green's strains and the Novozhilov nonlinear shell theory. The aerodynamic load is estimated in accordance with the quasi-steady Krumhaar's modified supersonic piston theory by taking into account the effect of the panel curvature. Matrix transform method along with the harmonic differential quadrature method (HDQM) are employed to solve the nonlinear equations of motion of the FG-CNTRC... 

This paper investigates the static and dynamic characteristics of composite thin-walled beams that are constructed from a single-cell box. The structural model considered herein incorporates a number of nonclassical effects, such as material anisotropy, transverse shear, warping inhibition, nonuniform torsional model and rotary inertia. The governing equations were derived using extended Hamilton's principle and solved using extended Galerkin's method. The effects of fiber orientation on static deflection and natural frequencies are considered and a number of important conclusions are outlined. © 2007 Elsevier Ltd. All rights reserved  

Prediction of shear plane angle is a way for prediction of the mechanism of chip formation, machining forces and so on. In this study, Merchant and Lee-Shaffer theories are used for prediction of shear plane angles and cutting forces in machining of Al/SiC p MMC with 20% of SiC as reinforcement particles. The experimental cutting forces are compared with the calculated cutting force based on shear plane angles extracted from Merchant and Lee-Shaffer theories. The variation of these cutting forces with cutting speed, feed rate and depth of cut has been discussed. The results showed that Merchant theory may be used as a good method for prediction of chip formation in machining of Al/SiC p MMC  

Toughening of epoxy with different types of modifiers produces a bimodal blend that might show better fracture resistance in comparison with single-modified ones. In this research, bimodal epoxy formulations including mixtures of glass microsphere and silica nanoparticles are explored for possible synergistic toughening. The influence of composition on the glass transition temperature (Tg), tensile characteristics, and fracture toughness (KIC) is investigated. Interestingly, a synergism in fracture toughness is observed when mixtures of modifiers were incorporated. For the fixed overall modifier content, KIC is higher when the volume fraction of glass microsphere is lesser than the volume... 

Herein, the fracture toughness of ternary epoxy systems containing nanosilica and hollow glass microspheres (HGMS) is investigated. The experimental measurements reveal synergistic fracture toughness in some hybrid compositions: The incorporation of 10 phr of HGMS and nanosilica alone modify the fracture toughness of epoxy by 39% and 91%, respectively. However, use of 10 phr hybrid modifier can enhance the fracture toughness of the resin up to 120%. Observations reveal different toughening mechanisms for the blends i.e., plastic deformation for silica nanoparticles and crack bifurcation for HGMS. Both of these toughening mechanisms additively contribute to the synergism in ternary epoxies  

This paper explores the capabilities of refined finite elements for 3D analysing of thermoelastic waves propagation in disks made of functionally graded materials. Based on the Lord-Shulman generalized theory of thermoelasticity, the field equations are written according to the three-dimensional formalism of the Carrera Unified Formulation (CUF). The system of the coupled equations is solved in the Laplace domain and, then, converted in the time domain by using numerical inverse Laplace transform. For a functionally graded disk exposed to thermal shock load, the time histories of displacement, temperature and stress fields are reported for different gradation laws. Propagation and reflection... 

This paper deals with the generalized coupled thermoelastic solution for disks with constant thickness. It is a sequel to the authors's previous work in which refined 1D Galerkin finite element models with 3D-like accuracies are developed for theories of coupled thermoelasticity. Use of the reduced models with low computational costs may be of interest in a laborious time history analysis of the dynamic problems. In this paper, the developed models are applied and evaluated for a 3D solution of the dynamic generalized coupled thermoelasticity problem in the disk subjected to thermal shock loads. Comparison of the obtained result with the results available in the literature verified the... 

The present study deals with vibrational behavior of two joined cross-ply laminated conical shells. The natural frequencies and mode shapes are investigated. The joined conical shells can be considered as the general case for joined cylindrical-conical shells, joined cylinder-plates or cone-plates, cylindrical and conical shells with stepped thicknesses and also annular plates. Governing equations are obtained using thin-walled shallow shell theory of Donnell type and Hamilton's principle. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section of the cones. The equations are solved assuming trigonometric response in... 

In this study, the authors present an analytical approach to find the axisymmetric buckling load of two joined isotropic conical shells under axial compression. The problem of two joined conical shells may be considered as the generalized form of joined cylindrical and conical shells with constant or stepped thicknesses. Thickness of each cone is constant; however it may be different from the thickness of the other cone. The boundary conditions are assumed to be simply supported with rigid rings. The governing equations for the conical shells are obtained and solved with an analytical approach. A simple closed-form expression is obtained for the buckling load of two joined truncated conical...