Authors:Kirk C. Valanis Pages: 1671 - 1679 Abstract: Hitherto, the Caratheodory Principle proved useful in the proof of existence of entropy. Here, we prove existence in reversible as well as irreversible material bodies, on the basis of a physical law. In the presence of a reversible and adiabatic process, this law, which we call the adiabat, is a constraint on the independence of the state variables and is in fact a functional relation between temperature and deformation. The adiabat leads to the integrability of the First Law and the existence of entropy density. We show that the integrating denominator is a function of temperature alone, a result that has far-reaching consequences. PubDate: 2017-05-01 DOI: 10.1007/s00707-016-1785-0 Issue No:Vol. 228, No. 5 (2017)

Authors:Chang Tao; Yiming Fu Pages: 1711 - 1724 Abstract: Based on a new modified couple stress theory for composite laminates, considering geometric nonlinear theory and Timoshenko beam hypothesis, the governing equations for size-dependent composite laminated microbeams in thermal environment are derived using Hamilton’s principle. Analytical and numerical solutions are employed in solving the present problem, respectively. An auxiliary function is introduced to reduce the governing equations to a single fourth-order integral-differential equation, and the exact solutions for the thermal buckling and postbuckling of microbeams with combination of in-plane immovable simply supported boundary conditions are obtained. By introducing the differential quadrature method, the governing equations are transferred into a system of nonlinear algebraic eigenvalue equations. In numerical examples, comparison between the present results and those obtained in the literature verifies the validity and efficiency of the present analytical and numerical methods. The effects of thermal expansion coefficients and material length scale parameter are discussed. Numerical results indicate that the above-mentioned effects play very important roles for the thermal buckling and postbuckling of the composite laminated microbeams. PubDate: 2017-05-01 DOI: 10.1007/s00707-016-1770-7 Issue No:Vol. 228, No. 5 (2017)

Authors:Harshad Mishra; J. Arout Chelvane; A. Arockiarajan Pages: 1909 - 1921 Abstract: The primary application areas of magnetostrictive thin films are in the field of micro-electro-mechanical systems. Devices which use the actuation capability of thin films put to advantage the induced mechanical deformations in them upon being subjected to a magnetic field. In this study, experiments are conducted, in a thermal environment, on Tb–Dy–Fe thin film samples to determine their characteristic magnetization curves. The thin films are subjected to a periodically varying magnetic field of \(\sim \) \(\pm \) 0.7 T, in a thermally controlled environment, and the deflections at the tip are measured at elevated temperatures 50, 75 and 100 \(^{\circ }\) C. An analytical model constructed from the theories of elasticity, considering transversely isotropic material properties of both the film and the substrate layers, has been proposed to predict the deflections. The study has been extended to predict the tip deflections numerically (Finite Element Method) using COMSOL Multiphysics. PubDate: 2017-05-01 DOI: 10.1007/s00707-016-1794-z Issue No:Vol. 228, No. 5 (2017)

Authors:İ. Özdemir Abstract: Resistive force theory is concise and reliable approach to resolve flow-induced viscous forces on submerged bodies at low Reynolds number flows. In this paper, the theory is adapted for very thin shell-type structures, and a solution procedure within a nonlinear finite element framework is presented. Flow velocity proportional drag forces are treated as configuration-dependent external forces and embedded in a commercial finite element solver (ABAQUS) through user element subroutine. Furthermore, incorporation of magnetic forces induced by external fields on magnetic subdomains of such thin-walled structures is addressed using a similar perspective without resolving the magnetic field explicitly. The treatment of viscous drag forces and the magnetic body couples is done within the same user element formalism. The formulation and the implementation are verified and demonstrated by representative examples including the bidirectional swimming of thin strips with magnetic ends. PubDate: 2017-05-20 DOI: 10.1007/s00707-017-1873-9

Authors:Zhaopu Guo; Zhongmin Deng; Xuxu Li; Yongwei Han Abstract: In this paper, by using a combination of finite element analysis and a hybrid random convex model, a new numerical algorithm named hybrid perturbation Lagrange method (HPLM) is presented to address an uncertain static response problem of structures with a mixture of random and convex variables. The random variables are used to treat the uncertain parameters with sufficient statistical information, whereas the convex variables are used to describe the uncertain parameters with limited information. The expectation and variance of the random convex responses can be calculated effectively based on the matrix perturbation theory. Then, the interval bounds of these probabilistic characters of the structural responses can be obtained by means of the first-order Taylor series and the Lagrange multiplier method. Numerical results illustrate the feasibility and effectiveness of the proposed method to solve the static response problem of structures with hybrid or pure uncertain parameters. PubDate: 2017-05-19 DOI: 10.1007/s00707-017-1869-5

Authors:Gökhan Adıyaman; Erdal Öner; Ahmet Birinci Abstract: In this study, the continuous and discontinuous contact problem of a functionally graded (FG) layer resting on a rigid foundation is considered. The top of the FG layer is subjected to normal tractions over a finite segment. The graded layer is modeled as a non-homogenous medium with a constant Poissons’ ratio and exponentially varying shear modules and density. For continuous contact, the problem was solved analytically using plane elasticity and integral transform techniques. The critical load that causes first separation and contact pressures is investigated for various material properties and loadings. The problem reduced to a singular integral equation using plane elasticity and integral transform techniques in case of discontinuous contact. The obtained singular integral equation is solved numerically using Gauss–Jacobi integral formulation, and an iterative scheme is employed to obtain the correct separation distance. The separation distance and contact pressures between the FG layer and the foundation are analyzed for various material properties and loading. The results are shown in Tables and Figures. It is seen that decreasing stiffness and density at the top of the layer result in an increment in both critical load in case of continuous contact and separation distance in case of discontinuous contact. PubDate: 2017-05-19 DOI: 10.1007/s00707-017-1871-y

Authors:Viet-Thanh To; Vincent Monchiet; Quy Dong To Abstract: In this paper, we provide fast Fourier transform (FFT) iterative schemes to compute the thermal diffusivity of a periodic porous medium. We consider the fluid flow through a porous rigid solid due to a prescribed macroscopic gradient of pressure and a macroscopic gradient of temperature. As already proved in the literature, the asymptotic homogenization procedure is reduced to the resolution of two separated problems for the unit cell: (i) the fluid flow governed by the Stokes equations with an applied gradient of pressure, and (ii) the heat transfer by both convection and conduction due to an applied macroscopic gradient of temperature. We develop new numerical approaches based on FFT for the implementation of the cell problems. In a first approach, a simple iterative method based on the primal variable (gradient of temperature) is provided to solve the heat transfer problem. In order to improve the convergence in the range of high values of the prescribed gradient of pressure, we propose a more sophisticated iterative scheme based on the polarization. In order to evaluate their capacities, these FFT algorithms are applied to some specific microstructures of interest including flows past parallel pores (Poiseuille flows) and periodically or randomly distributed cylinders. PubDate: 2017-05-19 DOI: 10.1007/s00707-017-1885-5

Authors:M. A. N. Dewapriya; S. A. Meguid Abstract: Linear elastic fracture mechanics concepts have been widely used to characterize the fracture of nanoscale materials. In these concepts, pre-existing cracks in two-dimensional problems are assumed to be planar during the crack propagation. However, a perfect planar configuration of atomically thin nanostructures is not achievable in many applications due to complex interatomic interactions at the atomic scale. Formation of ripples and wrinkles has been experimentally observed in freestanding two-dimensional materials such as graphene. In this study, we employ molecular dynamics simulations to investigate the influence of out-of-plane deformation of a propagating Griffith crack. A numerical nanoscale uniaxial tensile test of a graphene sheet with a central crack is conducted. Two main aspects of the study are considered. The first is devoted to examining the influence of the crack orientation and the out-of-plane deformation of the crack surfaces on the crack-tip stress field. The second is concerned with the influence of the out-of-plane deformation on the fracture resistance of graphene. The analysis of the crack-tip stress field reveals a remarkably high transverse compressive stress at the crack surfaces, which induces the out-of-plane deformation. Moreover, our results reveal that in the absence of the crack out-of-plane deformation, the fracture resistance of graphene approaches the value given by Griffith’s criterion at a relatively smaller crack length as compared to the case involving out-of-plane deformation. PubDate: 2017-05-19 DOI: 10.1007/s00707-017-1883-7

Authors:Jiazhao Huang; Nhon Nguyen-Thanh; Kun Zhou Abstract: In this paper, the buckling analysis for the Mindlin–Reissner plates is performed by applying the isogeometric analysis (IGA) coupled with Bézier extraction operator. The Bézier extraction operator allows the incorporation of non-uniform rational B-spline-based IGA into the existing finite element method (FEM) work frame. For cracked plates, the extended IGA (XIGA) is employed. Unlike previous FEM approaches, the present method is expected to be more accurate and to achieve higher convergence as the polynomial order increases. A discrete shear gap is applied to address shear locking. The results obtained by the present method for the plates with and without crack are compared with the reference solutions. It is found that the present method possesses the following desirable properties: (i) the simulation results are found to be in good agreement with the reference solutions; (ii) the present method is able to preserve the exact geometry of complicated surfaces; and (iii) the method can be applicable to both moderately thick and thin plates straightforwardly. The effects of various plate shapes, side-to-thickness ratio, aspect ratio, crack length, and boundary conditions are also studied. PubDate: 2017-05-19 DOI: 10.1007/s00707-017-1861-0

Authors:Y. Appalanaidu; Anindya Roy; Sayan Gupta Abstract: A stochastic finite element-based methodology is developed for creep damage assessment in pipings carrying high-temperature fluids. The material properties are assumed to be spatially randomly inhomogeneous and are modelled as 3-D non-Gaussian fields. A spectral-based approach for random field discretization that preserves exactly the non-Gaussian characteristics is used in developing the stochastic finite element model. The meshing used in random field discretization is distinct from FE meshing, depends on the correlation characteristics of the random fields and is computationally efficient. The methodology enables estimating the failure probability and the most likely regions of failure in a section of a circular pipe. PubDate: 2017-05-19 DOI: 10.1007/s00707-017-1865-9

Authors:Chun-Ron Chiang Abstract: A micromechanics model for the prediction of elastic properties of reinforced polymers taking into account the agglomeration of fillers is developed. The influence of the shape of fillers on the results is discussed on the basis of a model developed earlier (Tandon and Weng in Compos. Sci. Technol. 27:111–132, 1986). The analysis is extended further for the consideration of possible agglomeration of fillers, and a micro-structure parameter \(\eta \) is accordingly introduced for its characterization. The values of the \(\eta \) -parameter are in the interval from zero to unity; higher value of \(\eta \) implies a greater degree of agglomeration of fillers. The applications of the model to some polymers reinforced with single-walled carbon nanotubes (SWNTs) are discussed; theoretical predictions are compared with experimental and numerical results available in the literature. It is concluded that the \(\eta \) -parameter increases with the volume fraction of fillers in current fabrication processes, and the agglomeration of fillers renders the reduction of the stiffness-enhancement capability of SWNTs. PubDate: 2017-05-13 DOI: 10.1007/s00707-017-1856-x

Authors:M. Apostol Abstract: Unphysical terms in the elastic Hertz potentials are identified, and a regularization procedure is devised for removing them. The solutions of the equation of elastic motion are given for tensorial forces (seismic moment forces) and vectorial forces (Stokes problem) concentrated in both space and time. PubDate: 2017-05-13 DOI: 10.1007/s00707-017-1854-z

Authors:A. R. Ashoori; S. A. Sadough Vanini Abstract: Free vibration of pre-/postbuckled circular functionally graded piezoelectric (FGP) plates is studied in this research. The buckled configurations are considered to be resulting from either thermoelectrical bifurcation buckling or limit load buckling due to lateral loading of thermally preloaded plates. The nonlinear governing equations of motion and associated boundary conditions are extracted by the generalized form of Hamilton’s principle. The Ritz finite element method is then implemented to construct the matrix representation of governing equations which are solved by two different strategies including Newton–Raphson scheme and cylindrical arc-length method. The thermoelectromechanical properties of FGPM plates are considered to be graded in the thickness direction on the basis of a power law function. Moreover, two cases of thermal loading, i.e., uniform temperature rise and heat conduction across the thickness as well as two types of boundary conditions, including clamped and simply supported, are considered. Comparison studies are presented to validate the numerical results. Furthermore, extensive parametric studies are conducted to assess the influence of involved parameters. PubDate: 2017-05-13 DOI: 10.1007/s00707-017-1857-9

Authors:Y. Heydarpour; M. M. Aghdam Abstract: Based on the three-dimensional theory of elasticity, the transient response of variable stiffness composite laminated (VSCL) plates with curvilinear fibers subjected to time-dependent concentrated load on elastic foundation is investigated. The fiber orientation angle varies linearly with respect to the in-plane coordinate in each layer. The layerwise theory in conjunction with a mixed integral–differential quadrature method is used to discretize the equations of motion and relevant boundary conditions in the spatial domain with arbitrary boundary conditions. Then, a novel multi-step method based on B-spline curves is presented to obtain a solution for the resulting system of ordinary differential equations in the temporal domain. Simplicity, accuracy and reliability of the novel combined I-DQ approach and in particular the multi-step techniques with respect to the Newmark time integration scheme are demonstrated. By performed comparison studies with available solutions in the open literature, the convergence and accuracy of the presented technique are demonstrated. Finally, the effects of fiber orientation, different geometric parameters, boundary conditions and elastic foundation coefficients on the transient behavior of the VSCL plates are parametrically studied. It is expected that the presented multi-step technique is to be used in a variety of science and engineering problems in future studies. PubDate: 2017-05-13 DOI: 10.1007/s00707-017-1850-3

Authors:Jing-Yan Li; Zhuo-Cheng Ou; Yi Tong; Zhuo-Ping Duan; Feng-Lei Huang Abstract: Considering the heterogeneity of real materials, a simple statistical model is proposed to describe a ubiquitiformal crack extension in quasi-brittle materials. The complexity of the ubiquitiformal crack is obtained by using the box-counting dimension. In the model, it is assumed that the crack propagates in the direction of the minimum energy dissipation and the heterogeneity of material properties is characterized by the Weibull distribution. The calculated numerical results of the complexity are found to be in good agreement with previous experimental data. Moreover, it is also verified that the complexity is uniquely determined by the Weibull distribution parameters, though the styles of crack extension in each computation are a little bit different from each other, due to the randomness of the spatial distribution of the material properties. PubDate: 2017-05-10 DOI: 10.1007/s00707-017-1859-7

Authors:Sergey V. Ershkov Abstract: A new approach is developed here for resolving the Poisson equations in case the components of angular velocity of rigid body rotation can be considered as functions of the time parameter t only. A fundamental solution is presented by the analytical formulae in dependence on two time-dependent, real-valued coefficients. Such coefficients are proved to be the solutions of a mutual system of 2 Riccati ordinary differential equations (which has no analytical solution in the general case). All in all, the cases of analytical resolving of Poisson equation are quite rare (according to the cases of exact resolving of the aforementioned system of Riccati ODEs). So, the system of Euler–Poisson equations is proved to have analytical solutions (in quadratures) only in classical simplifying cases: (1) Lagrange’s case or (2) Kovalevskaya’s case or (3) Euler’s case or other well-known but particular cases (where the existence of particular solutions depends on the choice of the appropriate initial conditions). PubDate: 2017-05-06 DOI: 10.1007/s00707-017-1852-1

Authors:Soumen Shaw; Basudeb Mukhopadhyay Abstract: In this article, the discontinuities of the theory of heat conduction model with memory-dependent derivatives are emphasized. To analyse the discontinuities, the memory-dependent model is applied to a transient thermo-mechanical process. The fundamental equations of the problem are expressed in the form of a vector matrix differential equation. Applying modal decomposition technique the vector matrix differential equation is solved by an eigenvalue approach in the Laplace transform domain. In order to obtain the solution in the physical domain an approximate method by using asymptotic expansion is applied for short time domain and to analyse the nature of the waves and discontinuity of the solutions. Finally, a suitable Lyapunov function, which will be an important tool to study several qualitative properties, is proposed. PubDate: 2017-05-06 DOI: 10.1007/s00707-017-1853-0

Authors:M. Shojaee; A. R. Setoodeh; P. Malekzadeh Abstract: As a first endeavor, the free vibration behavior of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) skewed cylindrical panels, as a most general geometry of panels in practical applications, is investigated. The first-order shear deformation shell theory is used to model the kinematics of deformations, and Hamilton’s principle is applied to drive the differential governing equations and the related boundary conditions. An analytical transformation together with the differential quadrature method, namely transformed differential quadrature method, is employed to discretize the governing equations subjected to general boundary conditions. This method offers superior practicality and applicability in directly discretizing the governing differential equations for an arbitrary physical domain. The correctness of the computational method is investigated through several numerical examples that include FG-CNTRC skew plates, homogeneous skewed cylindrical panels and FG-CNTRC cylindrical panels. Eventually, the effects of geometrical shape parameters like thickness/radius-to-length and aspect ratios, different distributions and volume fractions of CNTs and boundary conditions on the non-dimensional frequency parameters of the FG-CNTRC skewed cylindrical panels are studied. PubDate: 2017-05-06 DOI: 10.1007/s00707-017-1846-z

Authors:Famida Fallah; Ali Khakbaz Abstract: Based on the first-order shear deformation plate theory, two approaches within the extended Kantorovich method (EKM) are presented for a bending analysis of functionally graded annular sector plates with arbitrary boundary conditions subjected to both uniform and non-uniform loadings. In the first approach, EKM is applied to the functional of the problem, while in the second one EKM is applied to the weighted integral form of the governing differential equations of the problem as presented by Kerr. In both approaches, the system of ordinary differential equations with variable coefficients in r direction and the set of ordinary differential equations with constant coefficients in \(\theta \) direction are solved by the generalized differential quadrature method and the state space method, respectively. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified with the available published works in the literature. It is observed that the first approach is applicable to all supports with an excellent accuracy while the second approach does not give acceptable results for a plate with a free edge. Furthermore, various response quantities in FG annular sector plates with different boundary conditions, material constants, and sector angles are presented which can be used as a benchmark. PubDate: 2017-05-06 DOI: 10.1007/s00707-017-1851-2

Authors:C. Jiang; N. Y. Liu; B. Y. Ni Abstract: In recent years, the authors developed a non-random vibration analysis method for structural dynamic analysis under uncertain excitations. In non-random vibration analysis, the interval process model is employed to describe the uncertain dynamic load rather than the traditional stochastic process model, and the structural dynamic response is obtained in the form of upper and lower bounds, rather than its precise probability distribution. Since the probability distribution information is not required, the non-random vibration analysis generally could decrease the dependence on large experimental sample number; meanwhile, the bounds of dynamic response are easy to understand conceptually and convenient to use in practical structural reliability or safety design. On the basis of our previous work, this paper further proposes a Monte Carlo simulation method, aiming to provide a general way for non-random vibration analysis and also offer a reference solution for other non-random vibration analysis methods proposed in the future. Firstly, a sampling approach is presented to realize the precise sampling of the single interval process and the multi-dimensional interval process vector. Then, based on the sampling approach, a calculation procedure of non-random vibration analysis is constructed to obtain the structural dynamic response bounds under uncertain dynamic load. Finally, the proposed method is not only applied to single-degree-of-freedom and multi-degree-of-freedom linear vibration systems, but also to more complex vibration systems such as nonlinear systems and continuum structures. PubDate: 2017-05-03 DOI: 10.1007/s00707-017-1842-3