Abstract: Abstract The buckling and parametric resonance characteristics of laminated composite spherical sandwich shell panels with viscoelastic material (VEM) core are investigated in the present analysis considering full geometric nonlinearity in the Green–Lagrange sense. The study includes the longitudinal strain and normal strain in the transverse direction along with transverse shear deformation of the VEM core. The core displacements are considered to be varying linearly along the thickness and those of the face sheets follow first-order shear deformation theory. An eight-noded sandwich shell finite element of the serendipity family is adopted to discretize the sandwich shell panel domain. The finite element-based equation of motion is derived using Hamilton’s principle in the form of the Mathieu–Hill-type equation. The dynamic instability regions are obtained by applying Hsu’s criteria-based Saito–Otomi conditions to the transformed equation motion. An in-house finite element-based code is developed in the MATLAB platform to solve the stability problem and to establish the stability regions. A parametric study is carried out to investigate the influence of different system parameters on the critical buckling load and the parametric resonance of the sandwich shell panels. It is noted that an increase in core and constraining layer thicknesses increases the critical buckling load of the sandwich shell panels. The stability boundaries are observed to shift toward a higher-excitation-frequency region in the stability diagram with an increase in constraining layer thickness and a decrease in aspect ratio. PubDate: 2020-02-14

Abstract: Abstract In this article, buckling analysis of a porous nanocomposite cylindrical shell reinforced with graphene platelets (GPLs) using first-order shear deformation theory is carried out. Internal pores and GPLs are scattered uniformly and/or nonuniformly in the thickness direction. The mechanical properties such as the effective modulus of elasticity through the thickness direction are computed by the modified Halpin–Tsai micromechanics approach, whereas density and Poisson ratio are in accordance with the rule of mixtures. The Rayleigh–Ritz method is employed to obtain a critical buckling load of the graphene-reinforced porous cylindrical shell. The accuracy of the obtained formulation is validated by comparing the numerical results with those reported in the available literature as well as with the software ABAQUS. Moreover, the effects of patterns of internal pores and GPLs distribution, GPLs weight fraction, density and size of internal pores, different boundary conditions, geometric factors such as mid-radius to thickness ratio and shape of graphene platelets on the buckling performance of the functionally graded graphene platelet-reinforced composite porous cylindrical shell are explored. PubDate: 2020-02-12

Abstract: Abstract Noncentral force is an exemplary example of curl force and in general this is not an integrable system. The purpose of this note is twofold. First, we study a different reduction in the noncentral force compared to Berry and Shukla, and this leads to the generalized Emden–Fowler (GEF) equation, which in turn can be mapped to the Thomas–Fermi equation. Second, we compute the first integrals of the integrable standard Emden–Fowler (EF) and the generalized EF equations associated with the reduced noncentral dynamics using old results and new techniques. Finally, we compute the reduction in the nonpolynomial noncentral forces, which also leads to generalized EF equations. PubDate: 2020-02-12

Abstract: Abstract We present new nonlinear, one-dimensional equations of extended thermodynamics for temperature and heat flux that describe damped heat wave propagation and predict dependence of the second sound velocity on temperature and heat flux in a rigid thermal conductor. The aim of the present work is to investigate the implications of the considered nonlinearities on the process of heat propagation, especially that such nonlinear effects cannot be disregarded for nanosystems and in small-sized heat conductors, when temperature or heat flux variations are not always proportional to gradients. The characteristics of the nonlinear system of equations are investigated, and a formula for the breaking distance is obtained. For illustration, these equations are solved in the linear approximation by separation of variables, then in the nonlinear case by the homotopy perturbation method in the half-space, and numerically in a bounded interval under concrete initial and boundary conditions. The solutions are discussed in detail and presented graphically. They illustrate the effect of the different material parameters on the propagation of thermal waves and may be used to evaluate some material parameters. The proposed equations provide a closer insight into the thermal interactions in rigid thermal conductors. PubDate: 2020-02-08

Abstract: Abstract Surface-treated bodies are considered under the assumption that the plastic strain distribution is uniform along the surface and changes only with depth. The elastic problem of the surface-treated plate is solved. The obtained solution is used to derive the explicit exact reconstruction formulas for distributions of main tangential components of the plastic strain tensor. It has been proved that the deflection of the surface-treated strip does not depend on the width of the strip. These results are intended for use in destructive testing methods and for numerical prediction of strength. The following initial data were used: (a) the dependence of the deflection on the thickness of the removed material layer obtained by the Davidenkov method, (b) the dependence of the tangential residual stress components on the depth, and (c) the dependence of the surface tangential stress components or elastic strain tangential components on the thickness of the removed material layer obtained by the X-ray diffraction method. The obtained formulas were analyzed and approved for all types of initial data, wherefore two experiments were conducted. A way to incorporate the plastic strain distribution into a model of a machine part of complex geometry to take into account the residual stress field in fatigue, wear, cracking, the and corrosion strength predictions is presented. PubDate: 2020-02-06

Abstract: Abstract The design equations of a neutral coated inhomogeneity with confocal elliptic interfaces are derived, when the elastic matrix is subjected to a longitudinal shear. The neutrality of such an inhomogeneity is achieved by inserting an appropriate coating between inhomogeneity and matrix provided that the longitudinal shear applied to the matrix is parallel to one of the elliptical semi-axes. The above general results are verified numerically by designing specific neutral inhomogeneities using finite elements. PubDate: 2020-02-05

Abstract: Abstract Main theoretical results concerning bulk piezoelectric wave propagation subjected to the action of electric bias and rotation are presented, in which the higher-order tensors of piezoelectric, elastic, dielectric and electrostrictive constants are necessary. Some calculations for lithium niobate are performed revealing that the application of electric bias and rotation has considerable influence on the wave dispersion parameters. PubDate: 2020-02-05

Abstract: Abstract It is likely that in surging glaciers so-called selected dynamic states occur in a zone extending from the surge front upwards to a cross section in the region of extreme velocity. Selected dynamic states of glacier zones are determined mathematically by requirements for the three external longitudinal forces, which are exerted on its lower bounding plane (the front), its base and its upper bounding plane (the rear). In this paper, ‘base’ denotes the whole area of contact with the ground. Such selected dynamic states are analysed. Quasi-hydrostatic forces are defined mathematically as ‘natural’ reference forces, and the forces in the considered state are described by their fractional changes with respect to these reference forces. These fractional changes are the ‘dimensionless dynamic quantities’ of the front, of the base, and of the rear, but the latter quantity is zero due to the requirements mentioned above. A dynamic–geometric relation between the dynamic quantity of the front and a dimensionless geometric quantity of the glacier zone is established, and consequently, a critical length is introduced, which must be exceeded by the length of the zone for it to exist. Finally, a method of calculation of the dimensionless dynamic and geometric quantities from data of strain rates, temperatures and geometry is developed. PubDate: 2020-02-04

Abstract: Abstract In the present paper, a study is performed in an irregular earth crust, layered over a semi-infinite half-space under the effect of gravity. The irregularities at the interface are possible combinations of geometric shapes such as rectangular, paraboic and triangular notches. The aim of the study is to come up with the influence of these irregularities on the phase velocity of shear horizontal waves. The current work also explores how inhomogeneities affect SH-wave propagation. The medium is assumed to exhibit inhomogeneities as a function of depth. These functions are the product of a linear algebraic function and an exponential function of depth. By means of separation of variables and the substitution method, the equation of motion is reduced to the hypergeometric equation. Suitable boundary conditions are employed to derive a closed form of the dispersion equation. Numerical computations are performed to visualize the impact of irregularity and inhomogeneity. It is observed that the irregular interfaces and the inhomogeneity involved in the medium have a significant effect on SH-wave propagation. PubDate: 2020-02-04

Abstract: Abstract The linear boundary value problem for the stress tensor field \({\mathbf {S}}\) in a glacier is considered. This problem is determined by the balance of forces and of torques inside the glacier and by vanishing stresses at the free surface. A mathematically exact two-dimensional general solution \({\mathbf {S}}\) of this problem is developed, depending on its arbitrarily prescribed deviatoric longitudinal stress component. We complement a paper ‘Surging Glaciers I’ (Halfar in Acta Mech, 2020) and detail results spelled out there. Furthermore, an alternative exact expression of \({\mathbf {S}}\) is outlined, depending on the arbitrarily prescribed longitudinal stress component. PubDate: 2020-02-04

Abstract: Abstract The present work focuses on the effect of rotational restraints on the shear buckling of symmetrically laminated curved composite panels. The Sanders–Koiter shell theory and a first-order shear deformation scheme were used for the mathematical representation of the deformation kinematics of cylindrical shells. The eigenvalue buckling equations were obtained using the principle of minimum total potential energy and by employing the Ritz method. The solution for the deformed shape was approximated as a series of trigonometric functions compatible with the essential boundary conditions of the problem. The effect of the rotational and torsional springs was incorporated by adding their corresponding potential energy to the total potential energy of the panel-loading system. Using the developed formulation, the effect of the influential parameters such as aspect ratio, panel curvature and restraint stiffness on the buckling strength of a specific class of laminates was studied extensively. To present the results in a more insightful manner, non-dimensional parameters were used in parametric studies. To normalize the effect of torsional elements, a new non-dimensional parameter was introduced. PubDate: 2020-02-03

Abstract: Abstract In this paper, the rolling contact fatigue crack growth in the presence of multiple cracks and their interactions is studied. The proposed formulation is based on linear elastic fracture mechanics and singular integral equations. The body under the rolling contact is modeled by a half-plane weakened by a set of surface, subsurface and surface–subsurface cracks. Rolling contact is simulated by translational motion of an elliptically distributed force along the half-plane boundary. Several parameters, such as the distance between cracks, the value of initial crack lengths, the value of the friction coefficient, and the initial angle between cracks and the boundary of the half-plane are studied. Results obtained from this investigation are in good agreement in a special case with those reported in the literature. It is observed that in the system of two parallel surface and subsurface cracks with equal lengths, changing the distance between the cracks changes the growth paths, and when this distance increases to a critical value, the cracks grow independently. In addition, in the case of two parallel surface cracks when the left crack is shorter, the cracks have a stronger tendency to join together, which leads to pitting phenomena on the contact surface. Furthermore, in the system of two parallel subsurface cracks, it is seen that fast fracture occurs sooner when the initial angle of the cracks increases. In the system of parallel surface and subsurface cracks, the dominant failure mode is spalling. PubDate: 2020-02-03

Abstract: Abstract The purpose of this paper is to extend and generalize the precise integration method (PIM) and the Wittrick–Williams (W–W) algorithm to analyze the dispersion of guided waves in multilayered anisotropic piezoelectric structures. The analysis shows that the W–W algorithm cannot be directly applied to piezoelectric materials. This is due to the fact that a submatrix of the Hamiltonian matrix is not positive definite for piezoelectric materials such that the eigenvalue count of sublayers is not zero when the divided sublayers are sufficiently small. The reason for this issue is explored by a theoretical analysis, and then, a symplectic transformation is introduced to ensure that the W–W algorithm can conveniently be applied to solve wave propagation problems in multilayered anisotropic piezoelectric structures. The present method not only guarantees that the computation is accurate and stable, but also finds all eigenfrequencies without being missed. Three numerical examples are provided to illustrate the performance of the method, and the results obtained by the method are compared with the published results and the results obtained by the semi-analytical finite element method. The effects of boundary conditions, wave propagation direction, thickness ratios and stacking sequences on the dispersion behavior of guided waves are discussed. PubDate: 2020-02-03

Abstract: Abstract The vibration of a functionally graded axisymmetric nonlocal thermoelastic hollow sphere with dual-phase-lag effect is addressed in this paper. Surfaces of the sphere are assumed to be thermally insulated or isothermal and stress free. According to a simple power law, the material is assumed to be graded in the radial direction. The linear theory of modified thermoelasticity with a dual phase lag based on Eringen’s nonlocal elasticity is employed to model this problem. The Matrix Frobenius method of continued power series is introduced to derive the analytical solutions. The phase velocity relations for the existence of various modes of vibrations in the designed hollow sphere are derived in compact forms. In order to explore the attributes of vibrations, the fixed-point numerical iteration technique is used to solve the secular equations. The numerical computations for the material crust in respect of the natural frequencies, thermoelastic damping and the frequency shifting are presented graphically using MATLAB software tools. PubDate: 2020-02-03

Abstract: Abstract In the present paper, constitutive equations accounting for coupled damage-thermo-elasto-(visco)plastic and diffusion at small deformation are proposed in the standard thermodynamics of irreversible processes framework. One main objective is to include the diffusion phenomenon in the models with ductile damage. The model is developed in the framework of thermodynamics of irreversible processes with a set of internal state variables. For illustration, we consider hydrogen diffusion in both normal interstitial lattice sites and trapping sites. The damage modelling of microvoids or microcracks is introduced by the use of Continuum Damage Mechanics framework leading to the definition of effective state variables on fictive undamaged configuration based on the total energy equivalence assumption. Consequently, the full coupling concerns not only the elastic and inelastic behaviour with hardening (isotopic and kinematic), but also the thermal and diffusion phenomena. The concept of the total energy equivalence is thus extended to define effective temperature, entropy, and effective state variables associated with diffusion. It enables to obtain different couplings between thermal phenomena, diffusion phenomena, and the mechanical behaviour, especially isotropic ductile damage. Such a full coupled model is then applied to a representative volume element subject to some typical simple loading paths for illustration and test of such couplings. PubDate: 2020-01-31

Abstract: Abstract In this paper, a weak form quadrature element formulation of a geometrically nonlinear shell model is proposed and applied for analysis of laminated composite shell structures. Thickness stretch parameters of the shell are incorporated for introducing 3D constitutive relations in the formulation. A drilling rotation constraint on the basis of polar decomposition of a modified deformation gradient is enforced by the Lagrange multiplier method and employed for implementing spatial finite rotations. The present formulation is shown to be feasible to model complex structures and circumvent locking problems naturally. A series of numerical benchmark examples are presented to demonstrate the validity of the formulation. PubDate: 2020-01-30

Abstract: Abstract A biologically microscopic system presenting a highly scientific interest is the microtubule (MT). Our research endeavor revolves around the eigenfrequencies’ analysis of an MT embedded in the cytoplasm of the cell by means of the nonlocal integral elasticity for the first time. The MT is simulated as a beam and the cytoplasm as a Pasternak-type elastic foundation, respectively. The responses of the nonlocal integral stress models show to have a softening behavior in comparison with that of the classic model. Unlike the nonlocal differential model, no paradoxes and inconsistencies are raised for the nonlocal integral models. Our research conclusions are a hopeful sign for the applications of biomaterials and bioengineering structures. PubDate: 2020-01-30

Abstract: Abstract In the present paper, the linear theory of viscoelasticity for binary porous mixtures is considered. The fundamental solution of the system of steady vibration equations is constructed, and its basic properties are established. Green’s identities of this theory are obtained. The uniqueness theorems for classical solutions of the internal and external basic boundary value problems (BVPs) of steady vibrations are proved. The surface and volume potentials are introduced, and their basic properties are established. The determinants of symbolic matrices of the singular integral operators are calculated explicitly, and the BVPs are reduced to the always solvable singular integral equations for which Fredholm’s theorems are valid. Finally, the existence theorems for classical solutions of the internal and external BVPs of steady vibrations are proved by means of the potential method and the theory of singular integral equations. PubDate: 2020-01-30

Abstract: Abstract In this paper, the generalized Noether’s theorem for mechanical systems is extended to the classical fields with variable mass, i.e., to the corresponding continuous systems. Noether’s theorem is based on the modified Lagrangian, which, besides time derivatives of the field function, contains its partial derivatives with respect to the space coordinates. The generalized Noether’s theorem for the classical fields systems with variable mass enables us to find transformations of field functions and independent variables for which there are some integrals of motion. In the paper, Noether’s theorem is adopted for non-conservative fields, and energy integrals in a broader sense are determined. In the case of non-conservative fields, a complementary approach to the problem is introduced by applying so-called pseudo-conservative fields. It has been demonstrated that the pseudo-conservative systems have the same energy laws as the non-conservative fields where the laws are obtained by means of this generalized Noether’s theorem. As the special case, the natural classical fields with standard Lagrangian are considered. PubDate: 2020-01-29

Abstract: Abstract In this study, an effective model is proposed to predict the effect of nanoparticle agglomeration on the thermal conductivity of three-phase nanocomposites/polymers. In order to better describe this effect, the concept of agglomeration degree is introduced. The effect of particle volume fraction on thermal conductivity of composites is also studied by considering the interphase and agglomeration degree of particles. First, the relationship between agglomeration degree and particle volume fraction is discussed. Then, the effects of particle volume fraction, agglomeration degree and interphase thickness on thermal conductivity of composites are studied. The obtained results show that the agglomeration degree increases with increasing particle volume fraction. The thermal conductivity of composites increases first and then decreases with increasing particle agglomeration degree, and is also affected by the different thermal conductivity of particles and matrix, and the thickness of interphase. PubDate: 2020-01-28