Abstract: Abstract A mode III electrically conductive crack between two different piezoelectric materials under the action of anti-plane mechanical and in-plane electric loadings is analyzed. The strip dielectric breakdown (DB) model, which is free from the electric field singularity, is developed for this crack. According to this model, the electric field along a DB-zone situated in continuation of a crack is assumed to be equal to the electric breakdown strength. The DB-zone lengths are found from the condition of a finite electric field at the end point of such a zone. Using special representations of field variables via sectionally analytic functions, an inhomogeneous combined Dirichlet–Riemann boundary value problem is formulated and solved analytically. Explicit expressions for the shear stress, the electric field and the crack faces’ sliding displacement jump are derived. The stress intensity factor is determined as well. The dependencies of the mentioned values on the magnitude of the external electromechanical loading are presented. PubDate: 2020-05-01

Abstract: Abstract This article presents a new approach for the nonlinear dynamic behavior of an Euler–Bernoulli beam under a moving mass. The governing equations for the behavior of the beam under a moving mass in large oscillations including the effect of horizontal and vertical beam displacements are considered via energy method. The systems of governing equations are solved in the condition of external and autoparametric resonance using Galerkin and perturbation methods. In order to validate the solution, the results are compared with a numerical solution and those available in the literature. The governing equations are used for the stability analysis of the beam in different points that will result in spectral responses in stable circumstances. PubDate: 2020-05-01

Abstract: Abstract In this paper, we explore the use of micromorphic-type interface conditions for the modeling of a finite-sized metamaterial. We show how finite-domain boundary value problems can be approached in the framework of enriched continuum mechanics (relaxed micromorphic model) by imposing continuity of macroscopic displacement and of generalized tractions, as well as additional conditions on the micro-distortion tensor and on the double-traction. The case of a metamaterial slab of finite width is presented, its scattering properties are studied via a semi-analytical solution of the relaxed micromorphic model and compared to a direct finite-element simulation encoding all details of the selected microstructure. The reflection and transmission coefficients obtained via the two methods are presented as a function of the frequency and of the direction of propagation of the incident wave. We find excellent agreement for a large range of frequencies going from the long-wave limit to frequencies beyond the first band-gap and for angles of incidence ranging from normal to near-parallel incidence. The present paper sets the basis for a new viewpoint on finite-size metamaterial modeling enabling the exploration of meta-structures at large scales. PubDate: 2020-05-01

Abstract: Abstract The directional motion of a continuous worm induced by travelling the mass center of its body is studied in this paper. To this end, a new locomotion gait is constructed to derive the condition that the worm can move forward in one period. The interaction force between the worm body and environment is an anisotropic dry friction. The governing equation describing worm-like motion is firstly considered as a quasi-static case for a slow actuation history or for a larger friction. Then the solution of this equation is derived based on the specific form of the tension and its continuous distribution along the worm body. Furthermore, through the method of piecewise analysis of the motion, the expressions of the tension and the displacement along its body in each stage are specifically calculated. The net displacement over one period is further obtained. As a result, the condition that the directed motion of the worm can be effectively achieved. The results show that the worm can keep the body length unchanged by means of the given locomotion gait during the motion process. PubDate: 2020-05-01

Abstract: Abstract Circular and annular elastic plates have wide applications as essential elements in various engineering structures and products demanding accurate analysis of their vibrations. At higher frequencies, the analysis of vibrations needs appropriate equations, as shown by the Mindlin plate equations for rectangular plates with tailored applications for the analysis of quartz crystal resonators. Naturally, there are equally strong demands for the equations and applications in circular and annular plates with the consideration of higher-order vibration modes. By following the procedure established by Mindlin based on displacement expansion in the thickness coordinate, a set of higher-order equations of vibrations of circular and annular plates are derived and truncated for comparisons with classical and first-order plate equations of circular plates. By utilizing these equations, coupled thickness-shear and flexural vibrations of circular and annular plates are analyzed for vibration frequencies and mode shapes. PubDate: 2020-05-01

Abstract: Abstract Concrete materials show a very complex macroscopic deformation behavior under tension and compression, accompanied by crack opening and crack closing phenomena under cyclic loading. The continuum damage mechanics offers a promising framework for the description of the damage deformation behavior. This paper proposes a continuum damage model, which is formulated based on energy equivalence using a unified equivalent strain. The evolution of isotropic damage is governed by two independent history variables to describe the crack opening and closing behavior, i.e., unilateral behavior, of concrete. The evolution of damage and inelastic strains are described by a single damage function and a modified failure surface, respectively. Moreover, the implicit gradient method is applied to the equivalent strains to achieve proper localization of deformation. The stiffness recovery and crack opening/closing mechanisms are simulated considering the thermodynamically consistent framework. Validation of numerical results with experimental data and the previous models demonstrates the efficiency of the model to simulate concrete behavior under monotonic and cyclic/reverse loadings. PubDate: 2020-05-01

Abstract: Abstract In this study, we investigate the induction field and the phonon and phason stress fields of a spheroidal inclusion embedded within an infinite matrix of a one-dimensional (1D) hexagonal piezoelectric quasicrystal subjected to the following three prescribed uniform traction boundary conditions: axisymmetric loading, out-of-plane and in-plane shear. The explicit expressions are derived in the surrounding matrix and the inclusions by setting the correct potential function. The reduced results show that the stresses exhibit a singularity on the crack faces. The obtained results can also serve as a reference for exploring other 1D piezoelectric quasicrystals reinforced by spheroidal inclusions. PubDate: 2020-05-01

Abstract: Abstract Rod fastening rotor (RFR) is characterized by discontinuity of contact interface and unbalance of multiple disks. There are few researches that focus on unbalance effect including magnitude and phase difference on the nonlinear dynamic characteristics of RFR considering contact feature. A typical RFR model is proposed to investigate the nonlinear dynamic characteristics. The nonlinear motion governing equation considering unbalance excitation, nonlinear oil-film force and nonlinear contact characteristics between disks is derived by D’Alembert principle. The contact effects are simulated by bending spring with nonlinear stiffness. The research focuses on the effects of unbalance on the onset of low-frequency instability and nonlinear response of RFR. The obtained results evidently show the distinct phenomena brought about by the variations of unbalance, which confirms that unbalance magnitude and phase difference are critical parameters for the RFR system response. To restrain large amplitude of nonsynchronous vibration and retard the occurrence of instability, the unbalance magnitude of rotor is suggested to be kept at range from U5 to U6. Meaningfully, RFR can operate relatively well with small vibration and higher instability threshold when the residual unbalance between disks is controlled at an enough-reasonable unbalance phase difference. Phase difference adjustment can accomplish active balance. The total vibration and nonsynchronous components could be reduced, and onset speed of instability could be delayed effectively by using the proposed method, which is helpful for the dynamic design, assembly, balance and vibration control of such RFR. PubDate: 2020-05-01

Abstract: Abstract Determination of stress–strain state in an elastic domain of a particular form is considered. In order to determine the stress–strain state for these or other problems of elasticity theory in such a complex domain, the function that maps the given domain S onto the exterior of a unique circle (or onto a half-plane) \(\gamma \) is determined first. Then, using the complex variable methods and Kolosov—Muskheleshvili potentials, stress components (of normal and tangential stresses) at characteristic cross-sectional points under the action of applied loads are defined. Some problems of theory of elasticity are considered. Therewith, at first, the boundary value problem of plane theory of elasticity is solved by means of the obtained conformal mapping function. Further, this function is applied to solve the boundary condition of a beam, thus introducing the solution of bending problems of theory of elasticity. This study presents the novelty by introducing a new mapping function (suitable for inversion) which was discovered by the author for the first time in the scientific world. The paper then makes an application of the mapping function to solve a class of elasticity theory problems for such complex domains in much simpler way. The necessity to solve the considered problems is substantiated by a broadening use of such complex elements in different fields of science and engineering (crane girders—for traveling cranes, in multi-story buildings—basis of foundations, concrete and reinforced concrete supports, floorings, etc.), as well as in pipe-line saddles, underground, underwater, ground floorings for pipes, offshore platforms, etc. Therefore, the mapping function presented in this paper has a theoretical and practical significance. The complex elements are presented in compression or in bend. The proposed solution is illustrated by numerical examples. PubDate: 2020-05-01

Abstract: Abstract The mechanical model of eigenstrains could not be always taken as uniform distributions in engineering applications when performing micromechanics analysis of the inclusion-matrix system. In the framework of plane strain, this paper presents the analytical solution to an inhomogeneous circular inclusion with a non-uniform eigenstrain concentrically embedded in a finite matrix. First, the equivalent eigenstrain equation is extended to satisfy the condition of the finite matrix through the equivalent eigenstrain principle. The modified equation is used to transform the inhomogeneous inclusion in a finite matrix into the corresponding homogeneous inclusion. Then, the model of the inhomogeneous circular inclusion is accordingly formulated, and the stress and strain distributions are found. Finally, the stresses for the case of the polynomial series distribution of eigenstrains are obtained. The effects of non-uniformity of eigenstrains, the material mismatch and the inclusion size on stress distributions are shown graphically. The results indicate the stiffer inclusion induces the larger stress under the specific eigenstrain distribution. The analytical solutions obtained here also help to predict failure and optimize the designs of composite structures. PubDate: 2020-05-01

Abstract: Abstract This paper aims to analyze large deflections of nanomembranes including surface effects with arbitrary shapes. The nonlinear differential equations of nanomembranes are formulated by using the nonlinear kinematic relations and the surface elasticity theory of Gurtin–Murdoch. The principle of virtual work is applied to establish the three governing partial differential equations of nanomembranes. The coupled boundary element-radial basis functions (BE-RBFs) method is developed to solve the complicated nonlinear problem of nanomembranes. The proposed methodology is based on the analog equation method in conjunction with radial basis functions in order that the boundary line integrals and boundary elements are only involved. The validation and accuracy of the present method are evaluated by comparing the obtained results with those available from other numerical solutions. The proposed formulation can provide the numerical results that correspond to the experimental findings of the monolayer circular graphene membrane by specifying the proper surface properties. The influences of the surface elastic constants and residual surface stress on large deflection responses of nanomembranes are evidently investigated. Moreover, some numerical results of the present formulations could serve as a benchmark for the numerical evaluation of future research. Finally, the interesting results of large deflection analysis of the various nanomembrane shapes using the coupled BE-RBFs method are highlighted. PubDate: 2020-05-01

Abstract: Abstract Observance of Stoneley waves at the guided wave dispersion in stratified plates containing layers with alternating contrast physical properties is analyzed by applying Cauchy sextic formalism coupled with the exponential fundamental matrix method. Additional high-frequency asymptotes related to appearing interfacial Stoneley waves are detected and analyzed. Comparison with the case when Stoneley waves do not exist is presented. PubDate: 2020-05-01

Abstract: Abstract This paper studies the bending behavior of two-dimensional functionally graded (TDFG) beam based on the Timoshenko beam theory, where the material properties of the beam vary both in the length and thickness directions. By introducing a new auxiliary function, we simplify the coupled governing equations for the deflection and rotation to a single governing equation. Moreover, all physical quantities of interest can be expressed in terms of the auxiliary function. Then, the exact analytical solutions for bending of TDFG Timoshenko beams are derived for various boundary conditions. The influence of gradient indexes on the deflection and stress distribution of TDFG Timoshenko beams is discussed subjected to different transverse loadings, including uniformly distributed loading, linearly distributed loading and concentrated external loading. The introduced approach is of benefit to exact bending analysis of TDFG beams by employing other beam theories. PubDate: 2020-05-01

Abstract: Abstract A stabilized finite element formulation is proposed to the study of the finite deformation of a porous solid saturated with a compressible fluid. Unlike previous finite element schemes, the compressibility of the fluid constituent is entirely considered, and particularly, the a porosity-dependent permeability is utilized in the present formulation. As a special case, the formulation for the saturating fluid being an ideal gas is also derived. The displacement of solid skeleton and pore pressure are treated as primary variables to express the resulting coupled nonlinear system of equations. Equal-order \(C^{0}\) elements are employed to approximate displacement and pressure fields. The stability problem caused by the equal-order interpolation is overcome by using the method of polynomial pressure projections. Two examples are provided to demonstrate the effect of fluid compressibility, as well as the porosity-dependent permeability, on the responses of the material. PubDate: 2020-05-01

Abstract: Abstract This work presents an analytical approach to investigate the mechanical buckling of functionally graded material (FGM) thin conical panels surrounded by Winkler–Pasternak foundation and exposed to thermal environments. The material properties of FGMs are assumed to be temperature-dependent and graded only in the thickness direction according to the power-law, sigmoid and the exponential distribution of volume fraction. Eight well-known types of micromechanical models, namely Voigt, Reuss, Mori–Tanaka, Hashin–Shtrikman, modified Wakashima–Tsukamoto, Halpin–Tsai, Tamura and LRVE estimations, are studied to determine the effective two-phase FGM material properties as a function of the particles’ volume fraction considering thermal effects. Further, it is been supposed that the FG conical panel is heated uniformly, linearly and nonlinearly through the thickness. The nonlinear temperature distribution is obtained based on Fourier’s law by applying a semi-analytical procedure. The fundamental relations and the basic equations are derived by using Love’s thin shell theory. Finally, the numerical results are provided to reveal the effect of explicit micromechanical model, FGM profile, temperature distribution with various thermal boundary conditions, foundation conditions and the geometric parameters on the stability of these panels. Additionally, the critical buckling load is compared with that of FG truncated conical shells, cylindrical panels and the cylindrical shells. PubDate: 2020-05-01

Abstract: Abstract In practical conditions, turbochargers are supported by floating ring bearings and mounted on engines. In this paper, the effect of rotating unbalance and engine excitations on turbocharger is studied. The finite element model of turbocharger system is developed considering flexible rotor, using Timoshenko beam elements. The nonlinear fluid film forces generated in floating ring bearings are derived analytically in dimensional form using short bearing approximation. A new \(\hbox {MATLAB}^{{\circledR }}\) code has been constructed to solve the governing differential equations of motion of system using implicit Newmark-\(\upbeta \) numerical integration scheme along with Newton–Raphson convergence method, and dynamic response of the system is computed. The orbital plots, Poincare maps, and frequency spectrum are developed to show the nonlinear behaviour of the turbocharger system. At low rotor speeds, the system exhibits chaotic behaviour and has a wide range of sub-synchronous vibrations. As the speed of turbocharger increases, the forces due to unbalance dominate over engine excitations and nonlinear bearing forces and frequency spectrum become narrow. The behaviour of compressor and turbine disc centre is governed by their respective bearing nodes. PubDate: 2020-05-01

Abstract: Abstract Using the sextic Stroh formalism, we show that the strains and stresses inside an anisotropic elastic parabolic inhomogeneity are uniform when the surrounding anisotropic elastic matrix is subjected to uniform loading at infinity. All of the uniform strains and stresses inside the inhomogeneity are independent of the single geometric parameter characterizing the two-phase structure. In addition, some strain and stress components within the inhomogeneity simply coincide with their remotely prescribed counterparts in the matrix. PubDate: 2020-05-01

Abstract: Abstract The present paper can be considered as an extension of the work (Charalambopoulos and Polyzos in Arch Appl Mech 85:1421–1438, 2015). The simplest possible elastostatic version of Mindlin’s strain gradient elastic (SGE) theory is employed for the solution of a SGE rectangle in bending under plane strain conditions. The equilibrium equations as well as expressions for all types of stresses and boundary conditions appearing in the considered rectangle are explicitly provided. An improved version of Mindlin’s solution procedure via potentials is proposed. Besides, an elegant solution representation that contains the solution of the corresponding classical elastic problem is demonstrated. Results of six plane strain bending problems, which reveal a significant diversification from the classical elasticity theory and specific features of the underlying microstructure, are addressed and discussed. PubDate: 2020-05-01

Abstract: Abstract A novel family of composite sub-step algorithms with controllable numerical dissipations is proposed in this paper to obtain reliable numerical responses in structural dynamics. The new scheme is a self-starting, unconditionally stable and second-order-accurate two-sub-step algorithm with the same computational cost as the Bathe algorithm. The new algorithm can control continuously numerical dissipations in the high-frequency range in an intuitive way, and the ability of numerical dissipations can range from the non-dissipative trapezoidal rule to the asymptotic annihilating Bathe algorithm. Besides, the new algorithm only involves one free parameter and always achieves the identical effective stiffness matrices inside two sub-steps, which is not always achieved in three Bathe-type algorithms, to reduce the computational cost in the analysis of linear systems. Some numerical examples are given to show the superiority of the new algorithm over the Bathe algorithm and the CH-\(\alpha \) algorithm. PubDate: 2020-04-01

Abstract: Abstract In this work, we further develop a newly proposed interval algebraic approach for analysis or design of structures involving uncertain interval-valued parameters. The methodology is based on an algebraic extension of classical interval arithmetic, namely Kaucher arithmetic, and within it the interval equilibrium equations can be completely satisfied by the primary unknown variables (displacements). Here this method is expanded to derived (secondary) variables—forces, strains and stresses which are of particular practical interest in design and strength of materials. Numerical examples are presented to illustrate the proposed methodology and to compare the algebraic interval approach to that based on classical interval arithmetic. PubDate: 2020-04-01