Abstract: It is well known in planar kinematics of rigid bodies that the acceleration of the material point coinciding with the instantaneous center of rotation (or pole) is perpendicular to the so-called pole changing velocity. In the present paper, the concept of pole changing velocity is generalized to spatial motions. Using this result, the acceleration of the material points along the instantaneous screw axis can be expressed in a straightforward way, without the tools of advanced differential geometry. PubDate: 2019-07-01

Abstract: When two rough surfaces contact under normal static and dynamic forces, the contact damping is an important parameter for the vibration reduction. In this paper, a normal contact damping model is built by the statistical method, which involves the asperity shoulder-to-shoulder contact and interaction of adjacent asperities. Furthermore, the effects of the normal static force, vibration frequency and amplitude of mean separation on the normal contact damping are studied, respectively. Comparing contact damping of some classical models with the results of the proposed model, the effects of the asperity shoulder-to-shoulder contact and interaction can be revealed. According to the final conclusions, an appropriate normal contact damping can be obtained through changing the normal static force, frequency and amplitude of the mean separation, which has significance in some extent for the machine tool vibration. PubDate: 2019-07-01

Abstract: This work is interested in studying the motion of a rigid body carrying a rotor that rotates with a constant angular velocity about an axis parallel to the axis of dynamical symmetry. This motion is assumed to take place due to the effect of a combination of both uniform fields of gravity and magnetism that do not possess an axis of common symmetry. The equations of motion are constructed, and they are rewritten by means of the Hamiltonian function in the framework of the Lie–Poisson system. The equilibrium positions are inserted. The necessary conditions for the stability are introduced by applying the linear approximation method, while the sufficient conditions for stability are determined by utilizing the energy-Casimir method. PubDate: 2019-07-01

Abstract: Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a piezoelastic half-space due to the influence of a magnetic field in the context of the dual-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The bounding plane of the medium is assumed to be stress free and subjected to a thermal shock. Employing the Laplace transform as a tool, the problem is transformed to the space domain, where the solution in the space–time domain is achieved by applying a suitable numerical technique based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are constructed. Excellent predictive capability is demonstrated due to the presence of electric field, memory-dependent derivative and magnetic field. PubDate: 2019-07-01

Abstract: The classical solutions for straight disclinations in an infinite elastic solid have been obtained by integrating the results for disclination densities. In this paper, the equilibrium equations are solved directly for straight twist and wedge disclinations, subject to the boundary conditions of the defects and rigid body translations/rotations. For a twist or wedge disclination in an infinite solid, the current solutions, based on a core fixed at a point to remove rigid body motion, differ from the classical ones by the constant \(-\hbox {log }r_{i}\) , where \(r_{i }\) is the radius of the disclination core. For a wedge disclination in an infinitely long cylinder, additional terms of the form 1 / r in the radial displacement and \(1/r^{2}\) in the stresses appear in the solutions. The dependence of the current and classical results on the Lamé constants highlights significant differences near the disclination line, which will impact studies of disclination relaxation such as crack nucleation and core amorphization. The energy of a singular wedge disclination in a cylinder without a core mostly underestimates that of a wedge disclination with a core. PubDate: 2019-07-01

Abstract: An archetypal isolation system with rational restoring force and fractional damping is proposed and investigated based on the nonlinear mechanism of geometric kinematics. The equations of motion of this nonlinear isolator subject to nonlinear damping and external excitation are derived based on the Lagrange equation. For the free vibration system, the nonlinear irrational restoring force, nonlinear stiffness behaviors, and fractional damping are investigated to show the complex transitions of multi-stability. For the forced vibration system, the analytical expressions of force transmissibility of the nonlinear isolator with single-well potential under the perturbation of viscous damping and harmonic forcing are formulated by applying the harmonic balance method. The shock response spectra of the perturbed system subject to half-sine input are evaluated by the maximum responses. The Melnikov analysis and empirical method are employed to determine the analytical criteria of chaotic thresholds for the homoclinic orbit of the perturbed system with symmetric double-well characteristics. The numerical simulations are carried out to demonstrate periodic solutions, periodic doubling bifurcation, and chaotic solutions. The maximum displacements have been obtained to show the isolation characteristics in the case of chaotic vibration. PubDate: 2019-07-01

Abstract: In this paper, an interface crack between dissimilar one-dimensional (1D) hexagonal quasicrystals with piezoelectric effect under anti-plane shear and in-plane electric loadings is studied. By using integral transform techniques, the mixed boundary value problem for the interface crack is reduced to the solution of singular integral equations, which can be further reduced to solving Riemann–Hilbert problems with an exact solution. An analytical full-field solution for phonon and phason stresses, electric fields and electric displacement in the cracked bi-materials is given, and of particular interest, the analytical expression of the phonon and phason stresses and electric displacements along the interface is obtained. The crack sliding displacements of the interface crack are provided, and it is found that the phonon and phason stress distributions inside the dissimilar quasicrystal material are independent of the material properties under the anti-plane shear and in-plane electric loadings. The results of the stress intensity factors energy release rate indicate that the crack propagation can either be enhanced or retarded depending on the magnitude and direction of the electric loadings. PubDate: 2019-07-01

Abstract: Based on the complex variable method, the decoupled thermoelastic problem of an infinite matrix containing an arbitrarily shaped inclusion subjected to plane deformations and uniform remote heat flux is studied in this paper. The shape of the inclusion is defined by a polynomial conformal mapping. Faber series and Fourier expansion techniques are used to solve the corresponding boundary value problems. Several numerical examples are presented to study the influence of the hardness and the heat conductivity of the inclusion on the concentration of the interfacial Von Mises stress and tangential stress in the matrix for a uniform remote uniaxial heat flux. It is shown that for given thermal expansion coefficients and given heat conductivities of the inclusion–matrix system, the Von Mises stress and the tangential stress in the matrix around the inclusion both increase significantly with increasing hardness of the inclusion whether the inclusion is softer or harder than the matrix. On the other hand, it is found that for given thermal expansion coefficients of the inclusion–matrix system, the Von Mises stress in the matrix around the inclusion decreases significantly with increasing heat conductivity of the inclusion, while the tangential stress concentration first decreases and then increases with increasing heat conductivity of the inclusion whether the inclusion is softer or harder than the matrix. PubDate: 2019-07-01

Abstract: This paper is concerned with the study of the high-frequency modes resulting from the use of the finite element absolute nodal coordinate formulation (ANCF) in multibody system (MBS) applications. The coupling between the cross-sectional deformations and bending and extension of ANCF beam and plate elements produces high-frequency modes which negatively impact the computational efficiency. In this paper, two new and fundamentally different approaches are proposed to efficiently solve stiff systems of differential/algebraic equations by filtering and/or damping out ANCF high-frequency modes. A new objective large rotation and large deformation viscoelastic constitutive model defined by the Navier–Stokes equations, widely used for fluids, is proposed for ANCF solids. The proposed Navier–Stokes viscoelastic constitutive model is formulated in terms of a diagonal damping matrix, allows damping out insignificant high-frequency modes, and leads to zero energy dissipation in the case of rigid body motion. The second approach, however, is numerical and is based on enhancing the two-loop implicit sparse matrix numerical integration (TLISMNI) method by introducing a new stiffness detection error control criterion. The new criterion avoids unnecessary reductions in the time step and minimizes the number of TLISMNI outer loop iterations required to achieve convergence. The TLISMNI method ensures that the MBS algebraic constraint equations are satisfied at the position, velocity, and acceleration levels, efficiently exploits sparse matrix techniques, and avoids numerical force differentiation. The performance of the TLISMNI/Adams algorithm using the proposed error criterion is evaluated by comparison with the TLISMNI/HHT method and the explicit predictor–corrector, variable-order, and variable step-size Adams methods. Several numerical examples are used to evaluate the accuracy, efficiency, and damping characteristics of the new nonlinear viscoelastic constitutive model and the TLISMNI procedure. PubDate: 2019-07-01

Abstract: A new concept in building construction is introduced. Arches or vaults with rigid members can be designed with zero moments at the joints (funicular), thus greatly decreasing the need for rigid joints. The lengths and inclinations of these members are determined for the optimum funicular arch which has maximum enclosed area. Analytic solutions are found for arches with five segments or less. PubDate: 2019-07-01

Abstract: We analyze the compression of a right cylinder made of an elastomeric material, sliding on a rigid plate in the framework of linear elasticity theory. Lubrication seems to reduce the heterogeneous effects of lateral bulging so that the deformations can be considered as “quasi-homogeneous.” As a result, we show that the ratio between the transversal deformation and axial strain is not a Poisson’s ratio but a Poisson’s function. PubDate: 2019-07-01

Abstract: Energy harvesting at micro- and nanoscales has recently seen a renewed interest that the flexoelectric effect can counter the inability of piezoelectric energy harvesters to generate enough energy at small scales. Almost all small-scale energy harvesters use uniform rectangular geometries, whereas at the macroscale energy harvesters use a wide array of geometries including tapered rectangular geometries. The incorporation of non-uniform effects into a piezoelectric system considering the flexoelectric effect should give insight into how these systems can benefit from different geometries. A non-uniform flexoelectric Euler–Bernoulli cantilever energy harvester is modeled using classical continuum theories and is examined at the microscale. The non-uniformity of the energy harvester is governed by linear and nonlinear tapering effects, with the nonlinearities represented by high-order polynomials. The system is assumed to be linear, only undergoing harmonic base excitation. The varied tapering ratios and powers of the geometric tapering, considering that only the thickness and the width of the beam are tapered, are compared with uniform systems. The results show that non-uniform beams exhibit more harvested power than their uniform counterparts and also increase the range of resonant frequencies where significant power can be generated. Nonlinear tapering increases the amount of power that could be harvested compared to linear tapering; however, the nonlinearity of the tapering effects is limited to cubic and quadratic forms. It is demonstrated that higher-order tapering effects reduce the amount of harvested power compared to the linear taper counterpart. Non-uniform beams prove to be more effective than their rectangular counterparts within a linear system, whereas optimal resistive loads decrease as the tapering effects increase. PubDate: 2019-07-01

Abstract: In this study, a gradient weighted extended finite element method (GW-XFEM) is presented for the analysis of fracture problems. For this method, the domain discretization is the same as the standard XFEM. However, the gradient field is constructed by considering the influences of the element itself and its adjacent elements. Based on the Shepard interpolation, the weighted strain filed can be obtained, which will be utilized to construct the discretized system equations. The validity of the presented method is fully investigated through several numerical examples. From these results, it is shown that compared with standard XFEM, the presented method can achieve much better accuracy, efficiency and higher convergence, when dealing with fracture analysis. PubDate: 2019-07-01

Abstract: It is shown that a heretofore seemingly unnoticed correspondence (or analogy) exists between the traction boundary value problem for compressible media and the displacement boundary value problem for incompressible media occupying the same domain, in plane, isotropic, linear elastostatics. The Airy stress function, which satisfies equilibrium identically, has to be biharmonic in order to satisfy the compatibility condition in a compressible body. Correspondingly, a displacement potential function, which satisfies the incompressibility condition identically, has to be biharmonic in order to satisfy equilibrium. Since Stokes flow is governed by identical relations as incompressible plane elasticity, if displacement is interpreted as velocity and the shear modulus as dynamic viscosity, the correspondence extends to that between compressible elasticity and Stokes flow for boundary value problems indicated above. This analogy provides a rare example of a constrained system which is equivalent to the same system without the constraint. PubDate: 2019-07-01

Abstract: This paper adopts a meshless method that combines the moving least-squares approximation and Galerkin weak form to investigate the mechanical properties of unidirectional fiber-reinforced composites under a lateral load. The degree of nonuniformity is adopted to quantify the spatial distribution of randomness during simulation, and then the numerical implementation is developed to generate a representative volume element (RVE) model with random distribution of fibers. A statistical analysis is carried out by using three descriptors, that is, inter-fiber distance, second-order intensity function and radial distribution function. Numerical examples are presented to illustrate the accuracy of the proposed multiscale meshless method, and excellent agreement is achieved in comparison with experiments and the finite element method. Finally, the performance of the proposed numerical technique is evaluated by considering the effects of RVE size, node influence domain, degree of nonuniformity and fiber volume fraction separately. PubDate: 2019-07-01

Abstract: Based on the modified couple stress theory, nonlinear thermally induced large deflection analysis of shallow sandwich arches is studied. A functionally graded material (FGM) micro-arch with piezoelectric layers integrated into the surfaces and with immovable pinned and fixed edges is analyzed. Temperature and position dependence of the thermomechanical properties for an FGM micro-arch are taken into account. The piezo-FGM arches are subjected to different types of thermal loads such as uniform temperature, linear temperature, and heat conduction. A modified couple stress theory is combined with the uncoupled thermoelasticity assumptions to derive the governing equations of the arch by using the virtual displacement principle. The von Kármán type of geometrical nonlinearity and first-order shear deformation theory are also used to obtain the equilibrium equations. The nonlinear governing equilibrium equations of the piezo-FGM sandwich arch under different thermal loads are solved analytically. The solutions of the system of ordinary differential equations for both cases of boundary conditions are established by employing the two-step perturbation technique. Comparison is made with the existing results for the cases of FGM arch without couple stress and piezoelectric layers under uniform temperature rise, and good agreement is obtained. Also, parametric studies are proposed to show the effects of couple stress, piezoelectric layers, volume fraction index, geometrical parameters, and temperature dependence, the thermally induced deflection of the piezo-FGM sandwich arch. PubDate: 2019-07-01

Abstract: In an attempt to correct the unrealistic material stiffness predicted by elastoplastic models which adopt an associative flow rule, this paper introduces an innovative technique for the computation of the inelastic contributions generated in a non-proportional loading path. The formulation of these inelastic contributions takes into account the plastic response along the direction normal to the plastic potential, neglecting the irreversible stretch caused by the tangential component of the stress rate. Here, the introduction of tangential plasticity, in combination with the return mapping technique, eliminates this drawback, allowing fast and accurate computation. The present paper focuses on the evaluation of the load-carrying capacity of a steel bridge pier, indicating the necessity of considering the additional tangential plasticity term for a correct description of the structural response. PubDate: 2019-07-01

Abstract: Application of the principle of energy balance to a rigid indenter in contact with a thin elastic layer on a flat rigid substrate provides a very simple derivation of the detachment criterion which earlier has been obtained by much more complicated asymptotic analysis. The simple criterion is additionally confirmed by the fully three-dimensional simulations of contact with a coated rigid substrate using the recently developed formulation of the boundary element method for coated media. The found detachment criterion is applied to contact of indenters of various shape. In the case of flat-ended indenters, the adhesive strength occurs to be proportional to the area of the face of the indenter (independently of the shape). The asymptotic criterion is also used for calculation of the adhesion strength of indenters having arbitrary shape and is illustrated with a case study of a contact of a rough indenter with a coated substrate. PubDate: 2019-07-01

Abstract: This article contributes to an understanding of the pathway from regular to chaotic traveling wave fronts over periodically undulated inclines in thin films. In order to investigate the transition from regular to chaotic waves, we used various undulation forms and varied the Reynolds number and the inclination angle in the measurements. Thereby, we revealed the first partially chaotic waves on a gravity-driven thin film channel flow. The wave is subdivided into: (i) the chaotic wave front and (ii) a regular wave tail. The area of the chaotic part can be increased by increasing the inertia of the system. Various phenomena on the flow were revealed: (a) bubble formation, (b) fingering, (c) splashes, and (d) pinch-offs. Our investigation leads to the conclusion that wave breaking over obstacles is a necessary condition for the transition from regular to chaotic wave fronts. PubDate: 2019-07-01

Abstract: In this paper, a semi-analytical formulation is developed to examine the swelling-induced finite bending of a functionally graded hydrogel strip, when the strip is embedded in a solvent bath of an assigned chemical potential. The cross-link density of the hydrogel polymeric network varies through the strip thickness either linearly or exponentially. As a result of inhomogeneous swelling ratio through the hydrogel strip thickness, the strip bends in a circle. In contrast to earlier solution methods, the initial configuration is mapped to the deformed state without assuming any intermediary virtual state, using a total deformation gradient tensor. The swelling response of the hydrogel is studied utilizing the Flory–Huggins model for the free energy changes due to the mixing and deformation of the hydrogel network. In order to validate the presented method, FEM is employed to solve the finite bending of the functionally graded hydrogel strip. Using the presented method, the effects of the hydrogel network cross-link density distribution on the radial and tangential stress fields, strip bending curvature, and semi-angle are studied. In contrast to hydrogel-based multilayers, continuous stress and deformation field are found for the functionally graded hydrogel strip. Also, multiple tangential stress-free axes are observed for functionally graded hydrogel strips under bending configuration. PubDate: 2019-07-01