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This is a review on models for dynamic analyses of various drilling systems suitable for application in oil and gas industry. The rotary and also rotary–percussive drilling systems, vertical, horizontal and inclined, are physically and mathematically modeled. The basic physical model for analysis of the drilling system is the Timoshenko beam. Torsional, axial, transversal and combined vibrations of the drill string are considered. Special attention is given to bit–rock interaction models. Various mathematical expressions for bit–rock torque and force are suggested. Inclusion of these mathematical models in the drilling system consideration is expected in the future. In the paper advantages and disadvantages of drilling systems are also discussed. Finally, the aim of this review is to give direction for future research and improvement in drilling systems. [ABSTRACT FROM AUTHOR]

The present paper deals with the analytical study of Love-type wave propagation in a fiber-reinforced viscoelastic layer sandwiched between an orthotropic viscoelastic layer of finite thickness and an inhomogeneous viscoelastic half-space. A dispersion equation for Love-type wave propagation has been obtained using suitable boundary conditions. Some particular cases have also been calculated, and it is seen that the dispersion equation is reduced to the classical Love wave equation, which validates the present mathematical model. Numerical computations were carried out for involved parameters and illustrated with the help of graphs. The effects of viscoelastic parameters, thickness ratio, reinforced parameters, inhomogeneity parameters, and order of the depth variation in the dispersion curves are highlighted. The present study may be beneficial in geophysical applications and earthquake engineering to understand the nature of seismic wave propagation. [ABSTRACT FROM AUTHOR]

The article describes the simulation results of an unbalanced rotary machine with an automatic ball balancer with a deep chamber (ABB-DC) based on a mathematical model of such a system. The ABB chamber has a cylindrical shape and is filled with balls that can move freely in general motion. The model takes into account mutual collisions between the balls, as well as between the balls and the chamber. The model also includes friction forces and rolling resistance. The comparison of simulation results performed with two different construction types of the chamber, classic single-layer drum (ABB-SC) and ABB-DC, confirmed the better efficiency of the ABB-DC in the optimal range of the number of balls. The machine body movement was limited to planar motion. The correctness of such a limitation has been verified by analyzing waveforms of reaction forces of constraints and their moments. Waveforms were divided into transient and steady states. The results of the analysis indicate the additional constraints do not significantly affect machine body movements. However, this might affect the ball arranging process in the ABB chamber. The paper also presents details of performing numerical simulations based on the developed mathematical model and numerical tests to determine the optimal integration time-step. [ABSTRACT FROM AUTHOR]

In this paper, the structural vibration control of short-period systems by a sliding model of a tuned liquid column damper (herein referred to as STLCD) is investigated from both theoretical and experimental points of view. The proposed STLCD is essentially composed of a U-tube container with liquid inside, which can slide on a linear guide rail and is connected to the structure by a spring-dashpot system. Unlike traditional fixed TLCDs, this type of arrangement allows the proposed STLCD to be tuned to short-period structural systems since the spring can be used for tuning while the dashpot provides additional damping. Details on the selection of the optimal design parameters of the STLCD are provided, and the validity of the introduced mathematical model is verified both in time and frequency domains through experimental tests conducted at the Laboratory of Experimental Dynamics at the University of Palermo, Italy. For the experimental tests, a scale model of an STLCD-controlled structure is considered, focusing on the reduction of the roof accelerations. Finally, for comparison purposes, the control performance of the proposed control strategy for the vibration suppression of stiff structures is evaluated by analyzing its structural responses in contrast with the corresponding uncontrolled structure under harmonic excitations. [ABSTRACT FROM AUTHOR]

We learned at high school and university that Newton’s second law is F=ma. However, Newton never wrote this equation. Furthermore, there is no agreement among historians of science as to the equation that expresses Newton’s second law. On the other hand, Euler claimed to have discovered a principle of mechanics, which is F=ma. The respective paper of Euler provides us with the means of clarifying the issue. We can compare Newton’s second law and Euler’s principle with each other and verify whether there are significant differences between both laws. This is the task of the present paper. The result is that Newton’s axiomatic system and technique of decomposing force differ from Euler’s. [ABSTRACT FROM AUTHOR]

Tumor growth which undergoes complex bio-mechanical processes has been a significant focus for mathematical modeling, with particular interest in its dynamic behavior. In this paper, we consider a two-phase flow model for describing the dynamics of tumor growth. The model accounts for aggregate cell movement and mechanical interactions between tumor cells as well as cell proliferation. In suitable limits, by using the dynamical systems theory approach, tumor growth in this mechanical model is shown to occur in the form of traveling waves that can propagate either forward or backward, depending on the values of the parameters. Our results, in particular, the wave profiles of tumor cell density are more realistic and explain those obtained in a recently developed simple, experiment-based, model for studying non-spatial dynamics of tumor cells. [ABSTRACT FROM AUTHOR]

In this paper, the electromagnetic damper (EMD), which is composed of a permanent-magnet DC motor, a ball screw and a nut, is considered to be analyzed as a passive damper. The main objective pursued in the paper is to determine the EMD characteristics in order to improve the vehicle performance. The effects of the EMD characteristics on ride comfort and road handling are investigated first, and then, the effect of a spring installed in series with the EMD to alter the EMD performance is observed. In order to study energy regeneration, the nonlinear equations of the modified passive electromagnetic suspension system (PEMSS) are extracted. The results of simulation show that the designed passive EMD maintains the desired performance while vibration energy from the road excitation can be regenerated and transformed into electric energy. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the stabilization properties of a beam model on a Winkler foundation by using Timoshenko–Ehrenfest-type systems, taking into account the influence of the so-called second spectrum. We consider the well-known classical version of the Timoshenko–Ehrenfest beam model as well as the truncated (or simplified) version of the same beam model according to the approach given by Elishakoff (in: Banks-Sills (ed.), Advances in mathematical modelling and experimental methods for materials and structures, solid mechanics and its applications. Springer, Berlin, pp 249–254, 2010). The main novelty of our approach is the concept of applying Ostrogradsky's energy to both beam models to highlight the physics issues arising in the frequency spectra. Our ideas are an attempt to fill the gap regarding the consequences of the second spectrum in the stabilization scenario for dissipative Timoshenko systems that are partially damped. [ABSTRACT FROM AUTHOR]

The appropriate consideration of non-material volumes at the level of analytical mechanics is an ongoing research field. In the present paper, we aim at demonstrating the principle of stationary action that is able to yield the proper form of Lagrange's equation in the context, namely the Lagrange's equation in the form derived by Irschik and Holl (Acta Mech 153(3-4):231-248, ). Such issue will here be interpreted as being the inverse problem of Lagrangian mechanics for a non-material volume. The classical method of Darboux (Leçons sur la Théorie Générale des Surfaces. Gauthier-Villars, Paris, ) will be used as the solution technique. This means that our discussion will be restricted to the case of a single degree of freedom. Having such principle of stationary action at hand, the corresponding Hamiltonian formalism will be written in accordance with the classical theory. Furthermore, a conservation law will be demonstrated for the time-independent case. At last, two simple examples will be addressed in order to illustrate the applicability of the proposed formulation. The reader may find some mathematical analogies between the upcoming content and that discussed by Casetta and Pesce (Acta Mech, 2013. doi:) in considering the inverse problem of Lagrangian mechanics for Meshchersky's equation. The mathematical formulation which will be outlined in the present paper is thus expected to consistently situate non-material volumes within the classical variational approach of mechanics. [ABSTRACT FROM AUTHOR]

This paper provides the transfer matrix method for the solution of multiple elliptic layers with different elastic properties. In the study, the medium is composed of an elliptic inclusion and many confocal elliptic layers. In the present study, the exterior layer is a finite confocal elliptic layer. Some derivations in the present study are similar to those in Chen (Acta Mech ). However, some derivations in the present study are quite different from those in Chen (Acta Mech ). Equations for evaluating the coefficients in the Laurent series for complex potentials are suggested, which are derived from the transfer matrix and the boundary condition. A numerical example for the case of an elliptic inclusion and two confocal elliptic layers is provided in this paper. [ABSTRACT FROM AUTHOR]

Poroelasticity refers to the study of the mechanics of porous elastic materials that are saturated with compressible or incompressible fluids. When considering saturated poroelastic geomaterials, their consolidation response can be influenced by the evolution of damage in the porous skeleton. The objective of this paper is to examine the problem of consolidation response of damage-susceptible poroelastic geomaterials. Firstly, a new constitutive model of soft soils expressed by isotropic double scalar damage variables is developed and incorporated into Biot's consolidation finite element equations via EDAPD program. Then, the EDAPD program is applied to analyze a soft subgrade reinforced by surcharge preloading technology. The comparison between the numerical predictions and the experimental data shows that the isotropic double scalar damage model presented in this paper is effective and feasible in analyzing the consolidation problem of damaged porous media. [ABSTRACT FROM AUTHOR]

A new approach to the derivation of the theory of thermoviscoelasticity is proposed. Neither the hypothesis of fading memory nor rheological models are used within the framework of this approach. The proposed approach is based on the mechanical model of a one-rotor gyrostat continuum. In special cases, the mathematical description of this model is proved to reduce to the equations of the coupled problem of thermoelasticity, the self-diffusion equation, and the equation describing the flow of a viscous incompressible fluid. In the context of this model, we consider the original treatment of the physical nature of the mechanism of thermal conduction and internal damping. The first part of the paper contains the aforesaid theoretical results. The second part of the paper is devoted to the determination of some parameters of the model. On the base of the proposed theory, we obtain the dependence of the acoustic wave attenuation factor on a signal frequency. This dependence is in close agreement with the classical dependence in the low-frequency range and agrees with the dependence obtained on the base of the phonon theory in the hypersonic frequency range. We discuss some ways of determining of the volume and shear viscosities and the heat flow relaxation timescale by using known values of the sound velocity and the acoustic wave attenuation factor. The obtained values of the heat flow relaxation timescale are compared with the values derived from the phonon theory. [ABSTRACT FROM AUTHOR]

Polymer networks usually have many entanglements as well as a finite extensibility due to the uncrossability and the full stretching of the network chains. In this paper, the nonaffine model proposed by Davidson and Goulbourne is adopted to characterize the influence of entanglements and finite extensibility of the polymer chains on the mechanical behavior of hydrogels. The Davidson-Goulbourne model only contains three material parameters and has a simpler mathematical form than the Edwards-Vilgis slip-link model, which is the only model that has been adopted to characterize the influence of entanglements on the swelling deformation of polymeric gels so far. Some benchmark problems such as free swelling, constrained swelling, uniaxial tension, equibiaxial tension in the immersed state and uniaxial compression in the isolated state are analyzed, respectively, based on the new constitutive equations. The results show that entanglements as well as chain extensibility have important influences on the mechanical response of hydrogels. [ABSTRACT FROM AUTHOR]

In this paper, we reveal the uncertainty and its fractional generalized Hamiltonian representation for the fractional and nonlinear problem and find general methods of constructing a family of fractional dynamical models. By using the definition of combined fractional derivative, we construct a unified fractional generalized Hamiltonian equation, a fractional generalized Hamiltonian equation with combined Riemann-Liouville derivative, and a fractional generalized Hamiltonian equation with combined Caputo derivative; also, as special cases, under the different definitions of fractional derivatives, we, respectively, obtain a series of different kinds of fractional generalized Hamiltonian equations. In particular, we present a new concept of the family of fractional dynamical models, and it is found that, using the fractional generalized Hamiltonian method, we can construct a series of families of fractional dynamical models. And then, as the new method's application, we construct three new kinds of families of fractional dynamical models, which include a family of fractional Lorentz-Dirac models, a family of fractional Lotka-Volterra models and a family of fractional Hénon-Heiles models. [ABSTRACT FROM AUTHOR]

Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii, efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the generalized Hamilton's principle for a non-material volume. First studies on the subject go back at least four decades with the article of McIver (J Eng Math 7(3):249-261, ). However, it is curious to note that the extended form of Hamilton's principle that is derived by McIver does not recover the Lagrange's equation for a non-material volume which is demonstrated by Irschik and Holl (Acta Mech 153(3-4):231-248, ). This does suggest additional theoretical investigations. In the upcoming discussion, Reynolds' transport theorem is consistently considered regarding the original form of the principle of virtual work, and so the generalized Hamilton's principle for a non-material volume is properly derived. It is finally shown that the generalization of Hamilton's principle that is here proposed is in harmony with the Lagrange's equation which is demonstrated by Irschik and Holl. [ABSTRACT FROM AUTHOR]

In this paper, a new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of heat conduction with fractional orders. The two-temperature Lord-Shulman (2TLS) model and two-temperature Green-Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation using the unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by using a state-space approach. The inversions of Laplace transforms are computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter. [ABSTRACT FROM AUTHOR]

In this paper, advanced concepts for the identification of complex nonlinear systems are discussed. Three major problems are addressed: The nonlinearity of the system, noise in the data upon which the model has to be built, and the potential to incorporate qualitative and quantitative prior knowledge about the system. As an integrated solution approach, local model networks (LMNs) with appropriate parameter estimation schemes are proposed. LMNs generally offer a versatile structure for the identification of nonlinear dynamic systems. In order to account for a realistic situation when noise is present both in input and output data, an equality constrained generalised total least squares algorithm for the local model parameter estimation of the LMN is presented; the incorporation of equality constraints allows to mathematically enforce desired system properties. As an application and benchmark problem, the vertical dynamics of a vehicle is considered. After training the LMN on a rough road, excellent predictions of the behaviour of the vehicle at crossing a single obstacle are obtained, thus proving the effectiveness of the proposed algorithm. It is illustrated how both the application of a proper parameter estimation scheme and the integration of system constraints systematically improve the performance of the model. [ABSTRACT FROM AUTHOR]

The current paper presents a two degree of freedom model for the problem of micromirrors under capillary force. The principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the micromirror. Then, using the implicit function theorem, a coupled bending-torsion model is presented for pull-in characteristics of micromirrors under capillary force and the concept of instability mode is introduced. It is observed that with increasing ratio of bending and torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. In order to verify the accuracy of the coupled model, static behavior of a group of micromirrors is investigated both analytically using the presented model and numerically using the commercial finite element software ANSYS. It is observed that results of the coupled model match well with the results of finite element simulations, but they both deviate considerably from the results of the pure torsion model. The presented coupled model can be used for safe and stable design of micromirrors under capillary force. [ABSTRACT FROM AUTHOR]

In this paper, the effect of the system parameters on the flutter of a curved skin panel forced by a supersonic/hypersonic unsteady flow is numerically investigated. The aeroelastic model investigated includes the third-order piston theory aerodynamics for modeling the flow-induced forces and the Von Kármán non-linear strain-displacement relation in conjunction with the Kirchhoff plate hypothesis for the panel structural modeling. Structural non-linearities are considered and are due to the non-linear coupling between out-of-plane bending and in-plane stretching. The effects of thermal degradation and Kelvin's model of structural damping independent on time and temperature are also considered. The aero-thermo-elastic governing equations are developed from the geometrically imperfect non-linear theory of infinitely long two-dimensional curved panels. Computational analysis and discussion of the finding along with pertinent conclusions are presented. [ABSTRACT FROM AUTHOR]

Linear and nonlinear stability analyses of penetrative double-diffusive convection in a porous medium are performed. Adopting a standard energy method approach yields a nonlinear threshold which is independent of the salt field. An adaptation of a new operative method by Mulone and Straughan (ZAMM 86: 507–520, 2006) is used to construct a nonlinear threshold which is dependent on the salt field, greatly reducing the region of potential subcritical instabilities. The employment of this operative technique for problems with spatially dependent coefficients, as presented in this paper, is unexplored in the present literature. [ABSTRACT FROM AUTHOR]

The paper deals with the prediction of coupled sway-roll-yaw motions of a ship with constant forward speed, subject to regular wave force. The governing equations derived in time domain after balancing the hydrodynamic and exciting forces are solved analytically while considering the motion variables, wave frequency and external force are complex quantities. Numerical experiments were carried out for a Panamax container ship under the action of a sinusoidal wave of periodicity 11.2 sec with the variations of speed and wave height. The effect of various parameters on motion responses and system stability is investigated. [ABSTRACT FROM AUTHOR]

The paper analyses the problem of elastic waves propagation through the material reinforced by two families of extensible fibers using high-order shear deformation theories. The material reinforced with two families of fibers can be seen as a material made of an arbitrary number of plies reinforced with one family of fibers, which are at angles $$\phi $$ and $$-\phi $$ , in relation to the lines of symmetry, so that it can be considered to be a composite laminate. Elasticity constants are derived using strain energy and the theory of invariants. The second-order shear deformation theory was used for creating dynamic equations of motion. Using analytical methods, dispersion curves and diagrams of phase velocities in the polar coordinate system were obtained. The emergence of quasi-modes, in the forms of quasi- bending qA, quasi-extensional qS and quasi-horizontally polarized modes qSH, was shown. The numerical part was done in MATLAB software using combinations of symbolic and numeric values. [ABSTRACT FROM AUTHOR]

Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and flexible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the field. [ABSTRACT FROM AUTHOR]

In this paper, a mesh-free strong-form solution is used to investigate the static response of beams made of functionally graded materials. Thanks to a compact notation, the a priori expansion order of the three-dimensional displacement field upon the cross-section can be assumed as a free parameter resulting in a hierarchical kinematic modelling. Several higher-order theories as well as Timoshenko's classical model can be formulated straightforwardly. The governing differential equations and boundary conditions are obtained as a fundamental nucleus, and an algebraic system is derived via collocation with multiquadric radial basis functions. Results are validated towards three-dimensional FEM models and also against an analytical Navier-type solution. The numerical investigations demonstrate that the presented approach yields accurate results. [ABSTRACT FROM AUTHOR]

The study on reliability of an aging structure requires taking into account the influence of time. Typical approaches for performing time-variant reliability assessment are always based upon the random process model, where the dynamic distributions of uncertain parameters are determined by a substantial number of samples. In this paper, a new time-variant reliability measurement based on a non-probabilistic interval process model is proposed, in which we describe the time-varying uncertain variables at any time as intervals and define the corresponding auto-covariance function and correlation coefficient function to characterize the correlation between limit states at different times. By combining with the set-theory approach and the classical first-passage theory, a new non-probabilistic model of safety evaluation for time-dependent structures is established, and its measure index is then analytically calculated. The proposed model of time-variant reliability is suitable for both the cases of stationary process and non-stationary process. Moreover, the Monte Carlo method is also presented as a means of verification. The comparison between the presented model and the Monte Carlo-based model is eventually carried out on two application examples; the usage, efficiency and accuracy of the developed approach can be demonstrated. [ABSTRACT FROM AUTHOR]

This is the first work to study the influence of elastic modulus on the kinetic performance of smart hydrogels responsive to the stimulus of the ionic strength of the environmental solution, via a multiphysics transient model, which was developed by the present authors and is known as the multi-effect-coupling ionic-strength-stimulus model. It is based on the conservation laws of momentum and mass, and considers the poroelasticity of the hydrogel with coupling the chemical, electrical and mechanical energy domains together. After the model is further validated in this paper via a good comparison with experimental data for the case of kinetics of HMDT hydrogel, it is employed as an accurate theoretical platform to investigate the influence of elastic modulus of the smart hydrogel in transient state. The discussion is detailed for the influence on the hydrogel deformation, the distributions of fixed charge and diffusive ionic concentrations, and the chemical and electric fields over both the hydrogel and surrounding solution, in order to make a fundamental understanding of the kinetics mechanism of the ionic-strength-sensitive hydrogel, especially how the Young's modulus influences the performance of the hydrogel in transient state. [ABSTRACT FROM AUTHOR]

In this paper, the concept of Dugdale crack model and Yoffe model is extended to propose a moving Dugdale interfacial crack model, and the interfacial crack between dissimilar magnetoelectroelastic materials under anti-plane shear and in-plane electric and magnetic loadings is investigated considering the magneto-electro-mechanical nonlinearity. It is assumed that the constant moving crack is magneto-electrically permeable and the length of the crack keeps constant. Fourier transform is applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. The explicit expression of the size of the yield zone is derived, and the crack sliding displacement (CSD) is explicitly expressed. The result shows that the stress, electric and magnetic fields in the cracked magnetoelectroelastic material are no longer singular and the CSD is dependent on the loading, material properties and crack moving velocity. The current model can be reduced to the static interfacial crack case when the crack moving velocity is zero. [ABSTRACT FROM AUTHOR]

In the present paper, a new nonlocal treatment for micro-mechanical damage modeling is introduced based on the background cell concept. The nonlocal damage variable in the modified GTN damage model is defined as the weighted porosity in analogy to the element-free Galerkin method. The evolution of the damage variable is related to the support domain surrounds the integration point. The efficient computational algorithm is taken from the regular background cell and implemented into the commercial finite element code ABAQUS via the user interface UMAT for both two-dimensional and three-dimensional problems. To verify the nonlocal damage model, extensive computational simulations of 2D and 3D cracked as well as holed specimens are presented and confirmed that the nonlocal damage overcomes mesh sensitivity and is computationally more efficient than other nonlocal treatment methods. The computational simulation of a compact-tension shear specimen reveals that the nonlocal damage model is able to predict mixed-mode crack growth independently of the element orientation. [ABSTRACT FROM AUTHOR]

In this paper, we present a new fractional dynamical theory, i.e., the dynamics of a Birkhoffian system with fractional derivatives (the fractional Birkhoffian mechanics), which gives a general method for constructing a fractional dynamical model of the actual problem. By using the definition of combined fractional derivative, we present a unified fractional Pfaff action and a unified fractional Pfaff-Birkhoff principle, and give four kinds of fractional Pfaff-Birkhoff principles under the different definitions of fractional derivative. And then, by using the fractional Pfaff-Birkhoff principles, we establish a series of fractional Birkhoffian equations with different fractional derivatives and construct the tensor representation of autonomous fractional Birkhoffian equations. Further, we study the relationship among the fractional Bikhoffian system, the fractional Hamiltonian system and the fractional Lagrangian system and give the transformation conditions. And furthermore, as applications of the fractional Birkhoffian method, we construct five kinds of fractional dynamical models, which include the fractional Lotka biochemical oscillator model, the fractional Whittaker model, the fractional Hojman-Urrutia model, the fractional Hénon-Heiles model and the fractional Emden model. [ABSTRACT FROM AUTHOR]

In this paper, the stability of delay differential equations (DDEs), describing self-excited vibrations in a micro-milling process, is investigated based on semi-discretization (SD) method. Due to the stubby geometry of micro-tools, the shear deformation and rotary inertia effects are considered for modeling the structure. The extended Hamilton's principle is used to derive a detailed dynamical model of the spinning micro-tool with the support of misalignment in which the gyroscopic effects cause coupling of equations. Considering the actual geometry of the micro-end mill, exact dynamic stiffness (DS) formulations are developed to investigate the tool's free vibration characteristics. The extracted mode shapes obtained from DS method are utilized as base functions in a Galerkin approach. Having considered regenerative cutting force, imposing the Galerkin method reduces the governing PDEs of the system to a set of DDEs. The resulting equations are discretized by means of SD procedure. Finally, numerical Floquet theory is utilized to investigate the stability of the system. Also, the effects of process damping on the stability diagrams are explored. The results show the efficiency of the proposed model and delineate the considerable influence of process damping on the stability borders of the system especially at low spindle speed. [ABSTRACT FROM AUTHOR]

In the paper, the reinforcement of no-tension structures by the application of superposed high-strength sheets, or by the insertion of tensile bars, has been considered with the purpose to set up a design path aiming at the positioning of the new material according to some optimal criterion. In detail, no-tension models are adopted which are recognized as an effective tool for analyzing a wide class of structures (e.g., masonry and reinforced concrete members), and the equilibrium and the failure analysis of the reinforced body are developed with particular reference to its ultimate limit state of collapse. Finally, an approach through the 'topologic optimization' is proposed for the identification of the optimal distribution of the reinforcement, and some of the obtained results are shown. [ABSTRACT FROM AUTHOR]

In this paper, thermal buckling properties of a nanoplate with small-scale effects are studied. Based on the nonlocal continuum theory, critical temperatures for the nonlocal Kirchhoff and Mindlin plate theories are derived. The thermal buckling characteristics are presented with different models. The influences of the scale coefficients, half-wave numbers, width ratios, and the ratios of the width to the thickness are discussed. From this work, it can be observed that the small-scale effects are significant for the thermal buckling properties. Both the half-wave number and width ratio have influence. The nonlocal Kirchhoff plate theory is valid for the thin nanoplate, and the nonlocal Mindlin plate theory is more appropriate for simulating the mechanical behaviors of the thick nanoplate. [ABSTRACT FROM AUTHOR]

A magneto-mechanical-thermal model based on a domain rotation mechanism is developed in this paper. An energy distribution parameter related to prestress and temperature is induced, which can be determined by simple experiments. Magnetization and magnetostriction of Terfenol-D at different temperatures and prestresses are calculated and estimated, which are consistent with experiments. The model can be applied to estimate prestress effects to magnetization. The results show that compressive prestress can increase to maximum using temperature of giant magnetostrictive materials. [ABSTRACT FROM AUTHOR]

High-aspect-ratio microstructures have been found, in the literature, to collapse due to capillary forces of liquids. In this paper, mathematical models are developed to study the collapse of a microstructure represented by a double cantilever beam (DCB) with a liquid droplet located at the free end. Formulations are presented using the classical Bernoulli-Euler beam theory as well as an analysis that accounts for geometrical nonlinearity. The models introduce rigorous coupling between the DCB deformation, the capillary forces, and the meniscus position, and have predicted interesting nonlinear behaviors that previous models could not. Parameters governing the capillary collapse of the DCB are identified, and their influence is discussed. A single dimensionless number that controls the condition for collapse is proposed and validated against numerical results. Comparison between the linear and nonlinear beam analyses shows that linear analysis generally suffices for the description of capillary collapse of microstructures. [ABSTRACT FROM AUTHOR]

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell's law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles. [ABSTRACT FROM AUTHOR]

Model reduction has become very important in order to save calculation time. In particular, in structural dynamics, computations become very time-consuming when the critical time step of explicit integrators becomes very small. The main focus of this paper is on the application of the Proper Orthogonal Decomposition (POD) method to a structure subjected to transient earthquake loading. It is shown that based on the information of only a small portion of the transient excitation and the structure ('snapshots'), it is possible to assemble a reduced-order model, which yields a very accurate and time-saving approximation of the response to the entire earthquake. The POD reduction method is applied not only to linear, but also to nonlinear structures under earthquake loading. In the linear case, the POD results can be compared to those obtained by the classical method of modal truncation. In the nonlinear case, base isolation systems (friction pendulum systems) are integrated in the structure. Error estimations are applied in order to assess the solution of the POD-reduced system of the linear and the nonlinear systems. The POD can be applied successfully if the snapshots within the chosen time interval describe the main behavior of the system well. In both the linear and nonlinear cases, the approximation of the system as reduced by the POD is very accurate even if only a few POD modes are used. The advantage over the method of Modal Truncation is not only the optimality of the POD modes concerning their associated energy, but also its applicability to nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, an efficient method is presented for the geometrically nonlinear analysis of circulant structures. A structure is called regular if its model can be formed as the product of two subgraphs, and if one of the subgraphs is a cycle then it is termed circulant. In the present method, we deal with the eigensolution of circulant structures by simply finding the eigenvalues and eigenvectors of the blocks of the stiffness matrix rather than those of the entire structural matrix, leading to a considerable reduction in the computational time. The developed method utilizes concepts from product graphs and linear algebra for the nonlinear analysis of structures. Graph products are used to perform the eigensolution of circulant structures through those of its constituting subgraphs. Here, using the existing numerical methods, nonlinear static and dynamic analyses can be performed. In the presented method instead of solving the characteristic equation in each iteration of each step, the eigensolution of the structure is obtained using the eigensolution of the primary structure (the structure of the first iteration of the first step) together with some simple mathematical operations. In the present method instead of heavy matrix operations such as inverting a matrix and solution of the corresponding equations, one needs only to perform simple matrix multiplications and additions. The advantage of the presented method becomes more apparent when it is applied to the nonlinear analysis of a structure, where analysis should be performed many times. [ABSTRACT FROM AUTHOR]

The charged system search as a recently developed meta-heuristic algorithm has been successfully utilized for optimum design of different examples. In addition, the fields of forces model provides a means to enhance the algorithm, and this results in the enhanced charged system search (ECSS). This paper utilizes positive features of the chaos in the ECSS algorithm to optimize engineering design problems. Simulation results and comparisons based on various well-known mechanical and engineering design problems show the efficiency of the present algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a thermodynamic theory for elastic rods using the model of directed curves. In this model, the thin rod-like bodies are described as deformable curves with a triad of rigidly rotating vectors attached to each point. To account for the thermal effects in rods, we introduce two independent temperature fields: the absolute temperature field and the temperature deviation field. We present a complete derivation of the non-linear equations of thermoelastic rods, starting from the principles of thermodynamics. Finally, we prove the uniqueness of solution to the linearized equations of thermoelastodynamics for rods. [ABSTRACT FROM AUTHOR]

A description of brick/block masonry by continua equivalent to discrete systems made of blocks of different geometry and texture is proposed in this paper. Here, the reasons for the selection of a micropolar continuum with respect to the classical continuum are discussed. As recent research in various micromorphic multifield formulations shows, the problem of the choice of the most appropriate continuum to model masonry mechanical behavior is still open, and the advantages of non-classical continuum modeling are not yet completely ascertained. Earlier analyses performed on masonry panels in the presence of load and geometrical singularities pointed out the significant role of the additional degree of freedom of the micropolar continuum (microrotation) and of its gradient. The present study aims to expand the investigation into the consequences of changes in blocks' shape, size and arrangement on the response of block masonry panels under shear forces. This analysis points out the greater effectiveness of micropolar models in capturing the gross structural response of masonry, with respect to the classical modeling. The cases analyzed herein show that apart from the very peculiar case of orthotetragonal symmetry, not only the gradient of microrotation but also the relative rotation between the local rigid rotation and the microrotation, to which relevant non-symmetric strains correspond, are predominant in the majority of the performed numerical tests. Models lacking in these strain measures are therefore inappropriate. The results obtained, ascertained by analyses performed on discrete block assemblies, point out that the micropolar continuum provides a proper description of the masonry behavior. Moreover, the differences between micropolar and classical models remain when the internal lengths vanish. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method to model a general system containing cracks and voids in an infinite elastic plate under remote cyclic loads. By extending Bueckner's principle suited for a crack to a general system containing cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus, the results in terms of the stress intensity factors can be calculated by considering the latter problem, which is analyzed easily by using the hybrid displacement discontinuity method (a boundary element method). Further, a fatigue growth technique of a mixed-mode crack is combined with the numerical approach to simulating a void-crack interaction problem under cyclic loads. Test examples are included to illustrate that the numerical method is very simple and effective for analyzing a void-crack interaction problem. [ABSTRACT FROM AUTHOR]

The periodic viaduct in this study was defined as a new kind of periodic structure-the 'open'-type periodic structure-for the first time. Knowledge about the energy bands of this kind of 'open' periodic viaduct is important for its aseismic design. Using the transfer matrix method and the compliances for the pile foundations, the impedances for the piers were obtained. Based on the Bloch theorem and the transfer matrix method, the nonlinear polynomial eigenvalue equation for the energy bands of the periodic viaduct undergoing in-plane motion was derived using the impedance of the piers. Based on the obtained nonlinear eigenvalue equation, the approximate linear eigenvalue equation for the periodic viaduct was obtained, and numerical results for the energy bands of the periodic viaduct were presented. The numerical results in this paper demonstrate that when the periodic viaduct is undergoing in-plane motion, there exist three lattice waves: the first kind of wave is a highly decaying wave; the second kind of lattice wave can propagate only at some frequency ranges; and the third kind of lattice wave can propagate at most frequencies. [ABSTRACT FROM AUTHOR]

This paper develops a semi-analytic model for periodically structured composites, of which each period contains an arbitrary distribution of particles/fibers or inhomogeneities in a three-dimensional space. The inhomogeneities can be of arbitrary shape and have multiple phases. The model is developed using the Equivalent Inclusion Method in conjunction with a fast Fourier Transform algorithm and the Conjugate Gradient Method. The interactions among inhomogeneities within one computational period are fully taken into account. An accurate knowledge of the stress field of the composite is obtained by setting the computational period to contain one or more structural periods of the composite. The effective moduli of the composite are calculated from average stresses and elastic strains. The model is used to analyze the stress field and effective moduli of anisotropic composites that have cubic symmetry. It shows that the bulk and shear moduli predicted by the present model are well located within the Hashin-Shtrikman bounds. The study also shows that the stress field of the composite can be significantly affected by the distribution of inhomogeneities even though the effective moduli are not affected much. [ABSTRACT FROM AUTHOR]

This paper deals with the formulation of an analytical model for the dynamic behavior of anisotropic plates, with an arbitrarily located internal line hinge with elastic supports and piecewise smooth boundaries elastically restrained against rotation and translation among other complicating effects. The equations of motion and its associated boundary and transition conditions are derived using Hamilton's principle. By introducing an adequate change of variables, the energies that correspond to the different elastic restraints are handled in a general framework. The concept of transition conditions and the determination of the analytical expressions are presented. Analytical examples are worked out to illustrate the range of applications of the developed analytical model. One of the essential features of this work is to demonstrate how the commonly formal derivations used in the applications of the calculus of variations can be made rigorous. [ABSTRACT FROM AUTHOR]

In this paper, firstly, the acceleration of the temperature and concentration are assumed to need the extra increment of the heat and energy. The inertial entropy and the inertial chemical potential were proposed by Kuang (Acta Mech 203:1-11, , Acta Mech 214:275-289, ). Secondly, the expressions of dissipative energy produced by the variation of the temperature and concentration are derived by using the second law of thermodynamics. Finally, several variational principles for coupled temperature-diffusion-mechanics are established, and their corresponding governing equations and boundary conditions are naturally presented. Meanwhile, some numerical simulations are carried out to describe the coupled reciprocity, which shows concentration diffusion with a finite velocity. [ABSTRACT FROM AUTHOR]

This paper analyses the thermal and roughness effects on different characteristics of finite rough tilted pad slider bearings. The roughness is assumed to be stochastic, Gaussian randomly distributed. Density and viscosity are assumed to be temperature dependent. In this study, two models of one-dimensional roughness, longitudinal and transverse, are considered. The irregular domain due to roughness is mapped to a regular domain so that the numerical method can be easily applied. The modified Reynolds equation, momentum equation, continuity equation and energy equation are coupled and solved using the finite difference method to yield various bearing characteristics. It is observed that for nonparallel slider bearing the load carrying capacity due to the combined effect is less than the load capacity due to the roughness effect for both longitudinal and transverse roughness models. However, in case of a parallel pad slider bearing, the reverse is true, though the load capacity is not significant. It is also observed that the load carrying capacity due to the combined effect is larger than the load carrying capacity due to the thermal effect for both roughness models. [ABSTRACT FROM AUTHOR]

In this paper, a novel model for a single-storey irregular-plan building, subjected to earthquake and harmonic translational excitation, is presented to consider non-linear inertial coupling terms, which are ignored in conventional linear models. Furthermore, the effect of internal resonance is investigated. The governing equations of motion for a model of this type of structure are achieved in a non-inertial rotational system of reference, attached to the centre of mass of the rigid diaphragm of its floor. Non-linearities are caused by non-linear inertial coupled lateral and torsional responses. Using the method of multiple scales, the non-linear equations are reduced to approximate linear equations, and subsequently the dynamic stability of the steady-state responses near a two-to-one ratio of internal resonant conditions is studied. The difference between the responses of the proposed non-linear model and the conventional linear one is shown in time history and frequency domain analyses. By inspecting the effects of amplitude and frequency detuning parameters in the responses, some non-linear phenomena, such as saturation, hysteretic and jumping, are observed. [ABSTRACT FROM AUTHOR]

This paper addresses numerical modeling of historical brick masonry subjected to in-plane loads. Based on experimentally determined material parameters for the masonry constituents brick and mortar numerical simulations of masonry specimens under various loading conditions are performed. These simulations aim at calibrating and validating parameter sets for historical brick masonry on the meso-scale. For computations on a larger scale, a macro-model in the framework of multi-surface plasticity theory is implemented in a finite element program, which captures the fundamental failure modes of in-plane loaded masonry. Material parameters for the macro-model are derived in a numerical homogenization procedure yielding the transition from the meso-scale to the macro-scale. Results from comparative simulations on discrete and homogenized models show both efficiency and limitations of the proposed methodology. [ABSTRACT FROM AUTHOR]

In the present paper, environmentally motivated numerical modeling for the limestone layered masonry structures has been investigated involving the continuous hygric state field variable, i.e. relative humidity Π. By taking advantage of the Lin et al. assumption pertaining to the relative humidity (independency of the relative humidity and temperature) (Lin MW et al. Build. Environ. 41(5):646-656, (); Khoshbakht M et al. Finite Elem. Anal. Des. 42(5):414-429, (); Khoshbakht M, Lin MW Meas. Sci. Technol 2989-2996, (); Khoshbakht M Finite Elem. Anal. Des., 45(8-9):511-518, ()), we have provided a mathematical model involving hygro-thermo-mechanical aspects as well as the water vapor transfer across the porous limestone masonry walls. The numerical study substantiates the impact of hygric effects as the major key point in the thermo-hygro-mechanical degradation and effect of geometry in the real brick-line of mortar assembly. Furthermore, we have obtained the moisture entrapment at the intersection of the lines of mortar through the layered masonry wall by means of the multidisciplinary nonlinear finite element method (NFEM) for variably saturated porous media. The new outlooks and fresh departure in durability and aging have been briefly discussed. [ABSTRACT FROM AUTHOR]

In this paper, we discuss in detail the derivation of the bi-potential function used to express the flow rule of pressure-dependent non-associated plastic models. In particular, we show that an infinity of equivalent expressions of the bi-potential can be derived for pressure-dependent models. The method consists in applying a transformation to the plastic strain rate or the stress or both to recover the normality rule. Then, the Fenchel inequality is used to derive the bi-potential function. The construction method itself indicates clearly that a class with infinite equivalent expressions of the bi-potential can be derived. [ABSTRACT FROM AUTHOR]