International Journal of Applied Mechanics

The purpose of present study is to investigate the effects of field dependent viscosity on swirling flow of an incompressible electrically non-conducting ferrofluid over a porous rotating disk with suction and heat transfer at the wall. Karman's similarity transformations are used to convert the governing boundary layer equations involved in the problem to a system of nonlinear coupled differential equations. The solution of this system is obtained by using a second-order numerical scheme which combines the features of Finite Difference method and Newton's zero finding algorithms. The flow characteristics including velocity and temperature profiles and boundary layer displacement thickness are studied for various values of MFD (magnetic field dependent) viscosity and suction parameter. Beside these, skin friction coefficients and the rate of heat transfer are also calculated on the surface of the disk. Magnetic field dependent viscosity and suction at the surface of porous rotating disk affect significantly the velocity and temperatures fields, rate of heat transfer and other flow characteristics in the generated ferrofluid boundary layer.

A steel pipeline of about 60 m long containing several pipes and structural singularities (bends, welds, clamps, etc.) is inspected in this work using a guided-waves technique. The inspection system is a pair of transducer-rings operating with the torsional mode T(0,1) and allows the long-range fast screening of the structure from defined measurement points. Recorded signals have submitted some numerical treatments in order to make them interpretable. The wavelet analysis is one of them and serves for denoising the raw signals. Besides, the Hilbert transform (HT) is applied in order to obtain the wave signals' envelopes leading to simplified curves easy to interpret. The processed signals are analyzed to identify defects' reflections from structural-singularities' echoes in the pipeline. The inspection system prove its efficiency for a global screening of such a long-range pipeline by detecting and localizing the defects.

This paper represents the second part of the work that considers the identification and sizing of machined defects in a pipeline. This study deals with the torsional-mode reflection from defects and structural singularities in an industrial pipeline in order to perform the defect sizing. The wave finite element method (WFEM) is used to construct a numerical database of reflection coefficients from rectangular defects by varying thickness, axial and circumferential extents. Calculation is made depending on the frequency. The approximation of defects' sizes is carried out by sweeping the numerical database to find the suitable combination of dimensions for a given defect. The axial and circumferential extents are evaluated by fixed intervals for each possible thickness. Reflections from structural singularities (elbows, concrete blocks, clamps and welds) are also treated by comparing reflection coefficients obtained by the WFEM to those evaluated experimentally. Results show a good agreement for most of the structural singularities but not for the others.

In this paper, a theoretical model based on the finite deformation beam theory is established to study the self-assembled behavior of graphene around a nanotube due to the van der Waals interactions. The morphology of graphene, governed by the nanotube diameter, is quantitatively determined by using the energy minimization approach in the theoretical model. From present results, it is demonstrated that the morphology of graphene predicted by the theoretical model agrees well with those obtained in molecular dynamics simulations. Furthermore, the influence of nanotube diameter, the binding energy and bending rigidity on the morphology of graphene has been investigated. It is found that the nanotube diameter has remarkable effect on the morphology of graphene while the morphology has tiny change with the change of binding energy. We hope that the present results offer the guideline in design of nanoelectronics based on graphene.

We study the linear analysis of electrohydrodynamic capillary instability of the interface between a viscous fluid and viscoelastic fluid of Maxwell type, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when fluids are subjected to the radial electric field. Here, we use an irrotational theory known as viscous potential flow (VPF) theory in which viscosity enters through normal stress balance but shearing stresses are assumed to be zero. A quadratic dispersion relation that accounts for the growth of axisymmetric waves is obtained and stability criterion is given in terms of a critical value of wave number as well as electric field. It is observed that the radial electric field has dual effect on the stability of the system.

In this paper, a closed-form solution to determine location of yield in rotating thick-walled cylindrical shells made of functionally graded materials (FGMs) using both Tresca's and von Mises yield criteria is presented. The cylindrical shell is subjected to uniform internal and external pressure. The material properties are assumed to vary according to power law functions and the Poisson's ratio is assumed to be constant. Moreover, the plane strain condition is used to drive expressions for distributions of stresses and radial displacement. In the present work, rotation, internal and external pressure and variation of material properties are considered simultaneously. To the best of authors' knowledge, in previous researches in which onset of yield is investigated, variation of material density is ignored, while density is not constant in FGM rotating thick cylindrical shells. Our results show that the density variation has a significant effect on the stress distributions. Our research has also tried to explain the effect of different Poisson's ratio on the value of the critical material parameter.

Polymer-bonded explosives (PBXs) are particulate composite materials composed of crystalline explosive grains bound in a relatively soft polymeric binder. It is important to optimize the fracture properties, while still maintaining the low sensitiveness and high explosiveness of PBX. This paper describes a study on the fracture properties and failure modes of a PBX by adopting a newly proposed dynamic fracture experimentation method — notched semi-circular bend (NSCB) specimen loaded with split Hopkinson pressure bar (SHPB) which was used in this study. This method offers the advantage of simultaneously determining the fracture initiation toughness, fracture energy, fracture propagation toughness and fracture velocity. The crack propagation is monitored by using a synchronous high-speed camera, which allows the observation of strain field history via digital image correlation process. The experimental results indicate that both the initiation toughness and the propagation toughness linearly increase with loading rate. The propagation fracture toughness is found to increase with fracture velocity, and a limiting fracture velocity is obtained. The failure modes are interpreted by using various theoretical models. Results suggest that the debonding strength of the binder is much smaller than the crystal fracture strength. The tensile strength is similar to the debonding strength, while the compression strength is somewhere intermediate between them.

The innovative fuzzy weighting input estimation method is used to estimate the ground motion acceleration of a soil–structure interaction system in this study. The input estimation method is comprised of the Kalman filter without the input term and the fuzzy weighting recursive least square estimator. The recursive least squares estimator (RLSE) is weighted using the fuzzy weighting factor. The superior capabilities of this inverse method are demonstrated by solving the soil–structure interaction estimation problem. The precision of the proposed method is verified using the actual earthquake acceleration. The results show that this method has the advantages of stability and accuracy.

Adequate proliferating model including each cell's growth and division in 3D is key for the simulation of tissue growth in early stages as embryo, avascular tumor and so on. This paper proposed a novel model to perform the simulation based on a nonlinear finite element method. With the mechanism of cellular growth controlled by total energy of volume and surface of cells, the surface of each cell is divided by triangular elements and the nodal displacements determine the variation of the cellular surface and volume uniquely when cells grow. The nonlinear finite element equations of nodal displacements were deduced by the minimum energy increment in each growth's step. Further, by using the volume-based algorithm to determine cellular division and the modified penalty function method, the nonlinear procedure of the cellular proliferation (growth-division-regrowth) was solved. The numerical results show that the method can simulate both tissue and tissue's every cell well in each growth-division step, and will do great help to model the growth of varied tissues in their early stages.

The isolation of surface wave-induced vibration using periodically modulated piles in soil is investigated. We demonstrate through simulations the dependence of complete bandgaps on the lattice symmetries, geometric parameters of the piles and material properties of the soil. The simulated results suggest that the piles modulated with square and hexagonal lattices are much more favorable for the formation of complete bandgaps than those modulated with honeycomb lattice. The height of the piles also plays a significant role in governing the evolution of complete bandgaps. Besides, complete bandgaps can be tuned by tailoring the volume fraction of the piles and the geometries of the pile cross section. Our results indicate that the contrast in the Young's modulus and the density is vital for the evolution of complete bandgaps and the viscosity of the soil should be considered as well. The analysis of surface wave propagation in a finite number of piles confirms the simulated complete bandgaps and also reveals that the complete bandgaps stem from Bragg interferences. This paper not only demonstrates the promising application of periodically modulated piles as wave barriers but also provides design guidelines for civil engineers.

In this paper, free vibration of functionally graded (FG) rectangular plates subject to different sets of boundary conditions within the framework of classical plate theory is investigated. Rayleigh–Ritz method is used to obtain the generalized eigenvalue problem. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any sets of boundary conditions. Material properties of the FG plate are assumed to vary continuously in the thickness direction of the constituents according to power-law form. The objective is to study the effects of constituent volume fractions, aspect ratios and power-law indices on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. Comparison with the results from the existing literature are provided for validation in special cases. Three-dimensional mode shapes are presented for FG square plates having various boundary conditions at the edges for different power-law indices. The present investigation also involves the rectangular FG plate to lay on a uniform Winkler elastic foundation. New results for the eigenfrequencies associated with foundation parameters are also reported here with the validation in special cases after checking a convergence pattern.

This paper presents a close-form solution for the anti-penetrating postbuckling problem of fiber reinforced, rectangular laminates. The laminate has a through-width debonded region buried at the center position and is simply supported at its four edges subjected to the in-plane compressive load. Based on the previous analysis of the contact kinematics from micro mechanics of composite material, the nonlinear contact effects at the interfaces of the debonded region are considered and characterized by a contact factor. Governing equations are established and are solved using the perturbation approach. Asymptotic solutions from perturbation analysis are presented. It is found that for fiber reinforced, debonded laminates the postbuckling deformation involves global deflection and local buckling with amplitude of the global one 10⁴ times larger than the local one. The global deflection is induced by the postbuckling load and the local buckling is caused by the anti-penetrating contact effects. Due to the contact effects, the load carry capacity of the delaminated laminate is tremendously enhanced. Further examination indicates that both the buckling load and the contact performances are intrinsic properties of the laminates. Parametric analyses show that (i) the buckling load decreases with the increasing of the delamination length and the delamination depth and is very sensitive to the changing of the aspect ratio, (ii) the contact performances, including the location and size of the contact areas, rely only on the geometries of the debonded region and the material properties but are hardly affected by the aspect ratio. The analysis is in effect by comparing with the well established results.

Elastic-plastic stress analysis on a matrix crack interacting with near-by circular inclusions (the fibers) in fiber-reinforced composites has been carried out. The crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. To more accurately study the fracture behavior of the crack, plastic zone correction is introduced first time for such a crack-inclusion interaction problem. To determine the plastic zone sizes (PZSs) at the crack tips, a generalized Irwin model is proposed for the current mixed-mode problem where the von Mises stress yielding criterion is employed. With the aid of distributed dislocation method, the physical problem is formulated into a set of singular integral equations and solved through a numerical schism. The effective stress intensity factor (SIF), the PZS, crack tip opening displacement (CTOD) are evaluated accordingly. In the numerical examples, the influence of the crack orientation angle, the fiber/matrix shear modulus ratio, and fiber volume fraction on the fracture behavior of the crack is discussed in detail. It is found that the crack orientation angle has great effect on the normalized values of PZS, CTOD, and effective SIF, while the effects of shear modulus ratio and fiber volume fraction depend highly on the conditions of the inclusion (the fiber) and matrix.

In this paper, the wavy contact between piezoelectric materials and an isotropic solid is considered. The Papkovich–Neuber potentials for the isotropic solid and three harmonic functions for piezoelectric materials are also presented. The stated problem is reduced to a pair of dual series equations and then recast as an integral equation of the Abel type. Employing the product relation for trigonometric functions and the Mehler integral yields an exact solution of the reduced Abel type integral equation. The relationship between contact length and the level of loading, and the distribution of the surface normal stress are given in terms of elementary functions. The derived results agree well with the previous ones for the purely elastic solid. It is found that a critical loading exists for the disturbance. For limiting cases, such as the low level of loading case and full contact case, corresponding contact behaviors are presented. Numerical analyses are done to reveal the influence of the level of loading on the contact behaviors.

Elastic stress wave theory is developed and the stress waves in the impacted plate are examined in the paper. Generalized linear elasticity is adopted where the couple stress and curvature tensor are both deviatoric tensors and they meet a linear constitutive relation. It is found that there exist volumetric, rotational, and deviatoric waves in the generalized elastic solids. However, for macro-scale elastic solids only two wave modes, namely a volumetric wave and a deviatoric wave should be taken into account. Wave motion in plate impact tests is studied that a volumetric wave and a deviatoric wave are proposed. A set of exact solutions is attained for elastic stress waves in an impact plate. Excitation of stress waves at impact surface and reflection at free surface are formulated. Propagation of stress waves in the plate is analyzed in the waveforms. The predicted stress history in a ceramic plate under impact is agreed very well with the experiment measurement.