This paper addresses the question to which extent the stiffness of an elastic foundation in general, and of a discontinuity occurring in the foundation in particular, affects the stresses to which a beam resting on such a foundation is exposed to. This is particularly relevant for tramway rails, where foundation discontinuities may be generated in the course of maintenance works. In the presented work

In this paper, a novel analytically method for analyzing the dynamic behavior of beams, under different boundary conditions and in presence of cracks, is proposed. Applying the Timoshenko beam theory and introducing the auxiliary functions, the equation of motion is derived using the Hamiltonian approach. The natural frequencies are obtained by applying the Euler–Bernoulli method and are derived by

In this study, the stability of sandwich conical shells covered by functionally graded and uniform distributed carbon nanotube-reinforced composite coatings under external pressures is carried out. The mechanical properties of the carbon nanotube and matrix are assumed to be graded through the thickness of the coatings via three types of grading rule. The basic relationships and stability equations

In the present contribution Castigliano’s theorem is extended to find more accurate results for the deflection curves of beam-type structures. The notion extension in the context of the second Castigliano’s theorem means that all stress components are included for the computation of the complementary strain energy, and not only the dominant axial stress and the shear stress. The derivation shows that

An imperfection sensitivity analysis for the nonlinear post-buckling behavior of functionally graded (FG) porous micro-tubes is performed in this research. The case of geometrically imperfect micro-tubes surrounded by a nonlinear elastic medium under axial compressive load is analyzed. Properties of the micro-tube with uniform distributed porosity are FG across the radius of the cross-section. Two

It is of great significance in the design and evaluation of anti-impact protective structures to investigate the dynamic mechanical properties of lightweight concrete structures. The present work aims to address this challenging task by the development of an improved large-diameter split Hopkinson pressure bar that can accurately predict the dynamic compressive strength and impact failure characteristics

The Payne effect, the nonlinear mechanical behavior of filled elastomers in oscillatory loading conditions, has received considerable attention in the literature. This is because of the extensive use of these materials in different industrial applications. While experimental investigations of the Payne effect have been comprehensive, the models developed to describe the behavior and predict the response

This paper presents two numerical models (Model L and Model N) and its application in the analysis of dynamic stability of beam-type structures. Both numerical models use two-noded rotation-free finite elements and take into account the exact formulation for finite displacement, finite rotations, and finite strains. Model L was previously developed and is intended for linear elastic material behavior

The dynamic response of an elastic thin plate resting on a cross-anisotropic elastic half-space to a rectangular load moving on its surface with constant speed is analytically obtained. The moving load and the plate and soil displacements are expanded in double complex Fourier series involving the two horizontal coordinates x and y as well as the time and the load velocity. Thus, the plate equation

Phenomenological constitutive equations contain material parameters which cannot be measured directly in the experiment. We address the problem of error-resistant parameter identification for models of large strain elasto-plasticity. The identification is based on tests with a heterogeneous stress state. A methodology is presented which allows us to assess the reliability of identification strategies

Solid solution strengthening plays a key role in the strength increasing of alloying metals, due to that a solid solution of alloying element causes lattice distortion to a certain extent. In the paper, the effect of solid solution magnesium additions on the edge dislocation emission from a blunted crack tip in aluminum alloys is investigated. The critical stress intensity factor for the dislocation

This paper addresses a conservative system describing the motion of a smooth body in an ideal fluid under the action of an external periodic torque with nonzero mean and of an external periodic force. It is shown that, in the case where the body is circular in shape, the angular velocity of the body increases indefinitely (linearly in time), and the projection of the phase trajectory onto the plane

A shear-lag model is developed for discontinuous fiber-reinforced composites with a membrane-type imperfect interface, across which the displacement vector is continuous but the traction vector suffers a jump that is governed by the generalized Young–Laplace equation. Closed-form expressions are obtained for the stress fields in both the fiber-reinforced region and the pure matrix regions and for the

The plane problem of a non-circular rigid inhomogeneity embedded in an infinite thermoelectric matrix under a uniform remote electric current is investigated based on the complex variable method. The inclusion is assumed to be electrically insulated and thermally conductive. Techniques of Faber and Fourier series are used to solve the corresponding boundary value problems. The obtained results show

In this paper, a locally-defined stabilized adaptive explicit approach is considered to analyse generalized coupled thermo-mechanical models. In this sense, a modified central difference method is applied, which performs adapting itself along the solution process, considering the properties and results of the model, as well as the relations between the adopted temporal and spatial discretizations.

During the launch and subsequent life of a spacecraft, there are various transient loads due to stage separation and micro-meteorite impact which a spacecraft structure must be designed to withstand. However, the force histories for these transients at these locations are not available to design the structure due to practical considerations like mounting of instrumentation. To address this problem

In many controlled acoustics applications, it is desirable to engineer passive-adaptive manipulation of mechanical waves through waveguides based solely on varying dynamic input. We investigate the potential of achieving this using experiments on several types of nonlinear acoustic metamaterial plates. By tuning the amplitude-dependent response of locally resonant attachments and tailoring their patterning

In the version of the article originally

The semi-analytical finite element (SAFE) method is widely used for studying properties of guided waves along composite waveguides. However, evaluating the modes associated to high wave numbers requires important mesh refinements and may significantly increase the computational cost. This paper presents a semi-analytical isogeometric analysis (SAIGA) to calculate the dispersion relation of functionally

The paper presents models to characterize the dependence of hardening and strength characteristics of composite materials on damage and strain rate. The results of experimental studies of the behavior of composite materials in a wide range of strain rates are analyzed, and some regularities are determined. On the base of a failure criterion which includes the dependence of failure characteristics on

In this work, by constructing the equivalent viscoelasticity between a fractional Zener model and a time-varying viscosity Zener model, we obtain the time-varying viscosity of creep and relaxation response. The derived time-varying viscosity can well interpret the physical meaning of the evolution of material from Hooke body to Newtonian fluid body. With the relaxation time gradually becoming larger

The paper reports the results of a study of the strength of fragments of a lithospheric plate with a fault under the assumption that a granite lithospheric plate is rigidly connected to a basalt base along the Conrad border. In this case, one vertical and two horizontal contact stress components arise in the contact zone. Two types of faults are considered. In the first case, the fault banks are at

In this work, we have investigated the nonlinear instability behavior of a thin laminated composite circular plate subjected to a tensile periodic load. A nonlinear system with quadratic and cubic nonlinear terms, referred to the effect of large deflection, is obtained. The method of multiple time scales is used to obtain periodic solutions for the second- and third-order systems, which directly leads

Size-dependent bending analysis of Timoshenko curved beams is performed with a modified nonlocal strain gradient integral model, in which the integral constitutive equation is transformed into an equivalent differential form equipped with two constitutive boundary equations. The governing equations and boundary conditions are derived via the minimum total potential energy principle and solved analytically

A second-order plate theory for a lithium niobate piezoelectric plate with a ferroelectric inversion layer is established. The theory describes coupled extensional, thickness-stretch and symmetric thickness-shear motions of the plate. The two-dimensional theory obtained is validated by comparing the dispersion relations of the relevant waves with the three-dimensional exact theory. For long waves with

Particle-resolved, three-dimensional, time-dependent simulations of rigid and flexible cylinders fluidized by a liquid flow in fully periodic domains have been performed by means of the lattice-Boltzmann method supplemented with immersed boundaries. The solids volume fraction ranges from 0.10 to 0.48 and the length-over-diameter aspect ratio of the cylinders from 4 to 12. The bending stiffness of the

The presented paper investigates the nonlinear vibration of a nanobeam with a piezoelectric layer bounded to its top surface considering the nonlocal piezoelectricity theory. To do this, Hamilton’s principle is implemented to derive the governing nonlinear vibration equations of the nanobeam by assumption of nonlocal piezoelectricity and a nonlinear strain–displacement relation. Then, the Galerkin

Two ways of incorporating moderate rotations of planes normal to the axis of a straight beam into the Euler–Bernoulli and the Timoshenko micropolar beam theories are presented. In the first case, the von Kármán nonlinear strains are used to incorporate the moderate rotations of normal planes into the beam theories. In the second case, appropriate approximations are made on the nonlinear Cosserat deformation

The dynamic analysis of contact problems is related to great mathematical difficulties and, thus, unsurprisingly has to date not been solved completely. In this work, a semi-analytical method is proposed to evaluate some integrals of Green’s function used in the dynamic analysis of a rectangular plate resting on the surface of an elastic foundation of inertial properties (Lamb’s model). The great challenge

The thermally insulated inclined or circular arc cracks problems subjected to axial stress in the upper part of bonded two half planes are considered. The modified complex potential function method with the continuity conditions of the resultant force, displacement, and heat conduction functions is used to develop the new system of hypersingular integral equations (HSIEs) for the problems. The new

A unified procedure is presented to investigate the dispersion and damping behavior of Love waves in a double-layered structure. The double-layered structure is comprised of a viscoelastic fiber-reinforced medium (Medium I) embedded between a viscoelastic sandy layer (Medium II) and a viscoelastic porous semi-infinite medium (Medium III). The displacement vectors for the respective medium have been

Soft-landing buffer systems with spherical curvature outer shells are widely used in the aerospace field, which not only requires its efficient and smooth buffer performance, but also that the shell of the landing buffer system is compact and lightweight. This paper presents a novel design method for the spherical honeycomb core structure for a soft-landing device buffer shell. The proposed method

The theoretical analysis of thick plate vibration behavior has been investigated in the literature, but most of the studies were focused on flexural dynamic characteristics and lack experimental verification. In this study, the analytical solutions based on the superposition method for both the flexural and extensional vibrations are presented to obtain resonant frequencies and associated mode shapes

The paper deals with Rayleigh wave propagation in a nonlocal thermoelastic layer, and the layer is lying over a nonlocal thermoelastic half-space. The problem is treated in the context of Eringen’s nonlocal thermoelasticity and Green–Naghdi model type III of hyperbolic thermoelasticity. The frequency equation of Rayleigh waves is derived, and different cases are also discussed. The effect of the nonlocal

A loading–unloading fractal contact model between two three-dimensional spherical rough surfaces with regard to friction is developed. The contact model of single asperity for the load–unload cycle with regard to friction is obtained. The expressions between contact load and real contact area in the loading and unloading processes in different deformation stages of three-dimensional spherical contact

Oceans crossing the Solar System attract people’s attention: the Earth, Enceladus, and Titan. On a variable-coefficient nonlinear dispersive-wave system for the shallow oceanic environment, our symbolic computation yields two non-auto-Bäcklund transformations and auto-Bäcklund transformations with some solitons, with regard to the wave elevation and surface velocity of the water wave, which depend

A new model for anisotropic magneto-electro-elastic Mindlin plates is developed by using an extended modified couple stress theory. The equations of motion and complete boundary conditions are simultaneously obtained by a variational formulation based on Hamilton’s principle. The new anisotropic magneto-electro-elastic plate model includes the models for orthotropic and transversely isotropic magneto-electro-elastic

The surface stress-induced deflection of a microcantilever beam with arbitrary axial nonhomogeneity and varying cross section is investigated. The surface stresses are assumed to be uniformly distributed on the upper surface of the beam. Based on the small deformation and Euler–Bernoulli beam theory, the second-order integral–differential governing equation is derived. A simple Taylor series expansion

This paper develops a microstructure-based numerical model to simulate the mechanical behavior of homogeneous coarse-grained (CG) and harmonic-structured (HS) Ti–6Al–4V under monotonic and cyclic simple shear loading conditions. This model incorporates a crystal plasticity model describing the deformation behavior of lamellar \(\alpha +\beta \) colonies and a scale transition rule called ‘\(\beta \)-rule’

The effective properties of the fiber-reinforced composite materials with fibers of circular cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For analytical solution of the periodically repeated cell problem, the Schwarz alternating process is

Secondary resonance effects in the spherical motion of a heavy asymmetrical rigid body with moving masses are reviewed in the case close to the Lagrange top. It is known that perturbations acting on the body, particularly a small displacement of the center of mass with respect to axis of symmetry and a small perturbing moment in a connected system of coordinates, lead to non-resonant evolutions of

To study the dynamic behavior of cable-stayed bridges, a linear multi-cable-stayed beam model is developed to investigate its in-plane and out-of-plane transverse vibrations. From the full-bridge perspective, an in-plane nonlinear single-mode discrete model is established. First, the in-plane and out-of-plane motion equations of the system and their boundary conditions are derived. Second, by employing

Under asymmetrical stress-controlled cyclic loading accompanied by ratcheting, the evolution of microscopic substructures of stainless steel 304 (SS304), a face-centered cubic metal, was detected using transmission electron microscopy (TEM). This observation demonstrates that dislocation slip is the main mechanism of uniaxial ratcheting in the non-steady stage (stage I). Dislocation proliferate rapidly

Based on the differential variational principle of Herglotz type, we reveal the internal relation between the perturbation and the adiabatic invariants for fractional Hamiltonian system with combined Caputo derivatives. First, based on the Herglotz variational problem, the Herglotz differential variational principle for fractional Hamiltonian systems is derived, and the fractional Hamilton canonical

Tensegrity structures are self-equilibrated statically and kinematically indeterminate structures. Cellular morphogenesis represents a generative process for the composition of complex tensegrity structures based on elementary cells. This article discusses the mechanism creation by the integration of mobility conditions in the generation of tensegrity structures using cellular morphogenesis. The creation

In this paper, the complete explicit solution for physical fields around a micro-hole is solved with the simultaneous consideration of the strain gradient elasticity, the direct flexoelectricity, and the converse flexoelectricity. First, the higher-order Navier-like governing equations are proposed for an isotropic flexoelectric solid by using an extended linear theory of flexoelectric materials considering

The aim of this work is to show how the moving frames method can be applied for reducing and solving two nonlinear mechanical systems: a bead on a rotating wire hoop and a spinning top. Once both problems are adequately formulated, we explicitly determine the corresponding moving frames associated to the symmetry group of transformations admitted by the systems. The knowledge of the moving frames for

This paper investigates the influence of the material properties on the deceleration dynamics of a deformable cylinder rolling with slipping on a half-space of the same material. The interaction of the cylinder and the half-space is described by the 2D quasistatic contact problem of viscoelasticity (Goryacheva: J Appl Math Mech 37(5):877–885, 1973; Contact mechanics in tribology. Kluwer, Dordrecht

This paper aims to enhance and tune wave-propagation characteristics of periodic architected structures by adding auxiliary resonators made of functionally graded materials (FGMs). For this purpose, cantilever FGM beams are added to periodic metamaterials with square and hexagonal topologies, and the effects of the material distribution of the added resonators on their wave-attenuation performance

Surface layers with microstructures are widely used in many engineering fields. The mechanical behavior of microstructures in solids can be described by gradient elasticity theories. [One of them is the couple stress theory (Mindlin and Tiersten in Arch. Ration. Mech. Anal. 11:415–448, 1962).] In the present paper, we study the in-plane surface wave propagating in a classical elastic half-space covered

Biaxial simulation tests with flexible membrane boundaries and Cosserat theory are used to investigate the effect of the particle shape on the properties of a shear band of granular materials. Three kinds of special particle shapes are quantified by the aspect ratio (AR) and the AR values for disks, squared, and elongated grains which are 1.00, 0.88, and 0.50, respectively. The peak and residual stress

The paper is devoted to simply supported beams under three-point bending. Their mechanical properties symmetrically vary in the depth direction. The individual shear deformation theory for beams of such features is proposed. Based on the principle of stationary total potential energy the differential equations of equilibrium are obtained. The system of the equations is analytically solved, and the

In this paper, the governing differential equation of a beam with axial force is studied using the Lie symmetry method. Considering the inhomogeneous beam and non-uniform axial load, the governing equation is a fourth-order linear partial differential equation with variable coefficients with no closed-form solution. We search for a favourable coordinate system where the governing equation has a simpler-form

A nonlocal Kirchhoff plate model with fourth-order strain gradient theory is firstly proposed to study variations with band gap frequencies and vibration energy distribution. The temperature rise is supposed to vary linearly through the thickness of the periodic nanoplate structures. The dynamic equations of finite periodic nanoplate structures under thermal load with the small-scale effect and the

In this paper, we analyze a linear problem describing the vibrations of a coupled suspension bridge. The single-span roadbed is modeled as an extensible thermoelastic beam of Timoshenko type. The main cable is modeled as an elastic string and is connected to the roadbed by a distributed system of elastic springs. For this linear model, we obtain the existence and uniqueness of solutions by using the

A novel active elastic metamaterial plate is proposed, with tunable vibration band-gap characteristics is by using the periodically placed piezoelectric actuator and sensor pairs along one direction of the plate. Active control strategies are employed to actively adjust the band-gap properties of the metamaterial plate. Displacement and acceleration feedback control methods are applied to design the

We first characterize strain solitary waves propagating in a fluid-filled membrane tube when the fluid is stationary prior to wave propagation and the tube is also subjected to a finite stretch. We consider the parameter regime where all traveling waves admitted by the linearized governing equations have nonzero speed. Solitary waves are viewed as waves of finite amplitude that bifurcate from the quiescent

We consider the axisymmetric contact problem of a multi-elastic layer with various elastic constants bonded to an elastic semi-infinite substrate indented by rigid flat-ended cylindrical and spherical indenters. The transfer matrix method is applied to each elastic layer, and dual integral equations are reduced to an infinite system of simultaneous equations by expressing the normal contact stress

In this paper, we deal with the numerical analysis of the Lord–Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness

The transversely isotropic response of pristine as well as defective boron nitride nanotubes (BNNTs) containing Stone–Wales (SW) defects was comprehensively studied via molecular dynamic simulations with a three-body Tersoff force field. The elastic properties and the failure behavior of BNNTs were studied under the transversely isotropic loading conditions, namely uniaxial tension, twisting moment