This paper shows the development of a displacement potential function based on the Galerkin potential using complex variables. The displacement potential function results in a more suitable method for numerical calculations since it avoids the strenuous integration process associated with stress potential methods. Completeness of the displacement potential function is demonstrated. The displacement

We derive here a fundamental solution for the harmonic vibration of thick asymmetrically laminated composite plates. The kinematics of the plate is based on Reddy’s third-order shear deformation theory (J Appl Mech 51:745–752, 1984). The fundamental solution is derived via the Fourier transform, and its final form is given in terms of definite integrals, which are evaluated numerically. All spatial

Vibration chains are of interest in many fields of practical applications. In this contribution, a modal analysis of the rather special Mikota’s vibration chain is performed. Herein, focus is set on the mode shapes of this multibody oscillator, which was firstly introduced by Mikota as a solid body compensator in hydraulic systems for filtering out fluid flow pulsations. The mode shapes show interesting

Forced longitudinal vibration response of nonlocal strain gradient (NLSG) rods is scrutinized and compared with nonlocal (NL), strain gradient (SG), and classical (CL) rods. In this respect, size-dependent kinematics and extended Hamilton’s principle are utilized to derive governing equations of motion. For the first time, forced longitudinal vibratory behavior of non-classical and classical rods is

During tandem cold rolling mill process, strip tearing reduces production rate, damages the rollers, and consequently decreases efficiency of production. Predicting and postponing of this phenomenon leads to less expensive trial and errors in rolling industries. In this research first, DIN1623 St12 steel which is frequently applied in metal forming industries and also Bao–Wierzbicki ductile damage

In this study, stability loss research has been made for composite material containing a locally curved one double-walled carbon nanotube and one triple-walled carbon nanotube separately. The research has been made within the scope of piecewise-homogenous body model by the use of three-dimensional linearized theory of stability (TDLTS). The carbon nanotubes are resistant to tension, but as they contain

In the present work, solutions are recapitulated according to the theory of elasticity for the deformations of an adhesive spherical inhomogeneity in an infinite matrix under remote uniform axial and axial-symmetrical radial tension. Stress fields in the inhomogeneity and at the interface in the matrix are provided, too. It is shown that the sphere is deformed to a spheroid under any of the loading

In production engineering, current research focuses on the induction of targeted residual stress states in components in order to improve their properties. Therein, the combination of experiment and simulation plays an important role. In this contribution, a focus is laid on the investigation of hot forming processes with subsequent cooling. A numerical approach is presented to analyze the distribution

The major goal of this work is to analyze the magnetic effect on the creeping viscous flow past a porous spheroidal particle, a particle of slightly deformed spherical shape. Brinkman’s model is proposed to govern the flow in the porous media. Boundary value problem considers the conditions of continuity of velocity components, continuity of normal stresses, and stress jump boundary condition for tangential

This paper studies the plane constrained shear problem for single crystals having one active slip system and subjected to loading in both directions within the small strain thermodynamic dislocation theory proposed by Le (J Mech Phys Solids 111:157–169, 2018). The numerical solution of the boundary value problem shows the combined isotropic and kinematic work hardening, the sensitivity of the stress–strain

We study the flow past a rough sphere considering the rugosity as a parameter and its effect on the drag coefficient. The numerical implementation is carried out via a novel approach using Galerkin’s method combined with an asymptotic expansion for the stream function. The amplitude of the spatial fluctuation is used as the perturbation parameter. The numerical results for the size of the vortex ring

The evaluation of the parameters of multilayered foundations (pavements, runway strips, etc.) plays an important role in ensuring the safe movement of vehicles. An approach of model construction for estimating the mechanical and geometric parameters of such foundations based on the solutions of inverse problems for multilayered elastic packets is proposed. As input data for such problems the measured

This paper aims to conduct the free vibration analysis of single-layer and laminated composite plates with multiple cutouts based on the scaled boundary finite element method (SBFEM) incorporated with the precise integration method (PIM) and the technique of the degree of freedom transform. It is applicable to a variety of shaped plates containing cordiform, circular and other complicated cutouts.

High-speed turbocharger rotors are often supported on double film floating ring bearings. In recent times, foil bearings are increasingly used as an alternative to floating ring bearings for supporting such lightweight rotors. Present work aims at the dynamic modeling and stability studies of the automotive turbocharger rotor system supported on the airfoil bearings under varying operating conditions

We study the torsion of a flexoelectric semiconductor rod with a rectangular cross section. The macroscopic theory of flexoelectric semiconductors is used. A one-dimensional model is established from the three-dimensional theory using double power series expansion of the coordinates within the cross section. The angle of twist of the rod and warping of the cross section are taken into consideration

Structural components with arbitrary cross sections play a key role in several engineering fields. Many engineering structures are subjected to torsional moments, so it is important to design and analyze these type of crucial engineering issues. First, this study offers a novel analytical solution for Prandtl’s stress distribution of arbitrary annular wedge-shaped bars under uniform torsion moment

The membrane structures are the potential solution for near term spacecraft systems due to its significant advantages such as lightweight, higher folding and packaging efficiency, ease of deployment, and low on-board volume requirement. For the membrane structures, maintaining the uniform state of stress conditions with a minimum mass penalty of a tensioning system is the most challenging task for

This article presents the design and validation of a regression model for the identification of dynamic parameters in manipulator robots. The model exhibits implementation advantages as it is based on the acquisition of position, speed and voltage data from the actuator in each joint rather than on the calculation of acceleration and torque. Actuators can be direct current and/or servomotor type. The

The current paper discusses the optimum parameter setting of asymmetric high-static low-dynamic stiffness (HSLDS) suspensions to reduce vibrations of a high-speed symmetric rotary system, excited by an unbalance force. The rotating system consists of a shaft that is supported by tilting pad journal bearings on the asymmetric HSLDS suspensions. The Reynolds equation is solved numerically to obtain the

In engineering structures, such as large fluid-filled pipelines, continuous monitoring for damage detection is needed. To address this issue, we study the generation of guided waves in pipes by using a circumferential strip of macro fiber composite transducer to generate and detect torsional and flexural lower modes. The propagated elastic waves and their resulting reflected and mode-converted signals

In the present study, a flapping-wing micro-air vehicle (FWMAV) like a dragonfly is developed by changing the phase shift angle between the fore and hind wings and experimentally tested using the wind tunnel. Two conditions are considered while conducting the experiments; (1) hovering [advance ratio (J) or the inlet velocity of air is kept zero], and (2) forward flight condition (advance ratio J = 0

The primary aim of this study is to establish the theoretical foundations for a solid–fluid biphasic mixture domain that can accommodate inertial effects and a viscous interstitial fluid, which can interface with a dynamic viscous fluid domain. Most mixture formulations consist of constituents that are either all intrinsically incompressible or compressible, thereby introducing inherent limitations

This article deals with heat transfer analysis on the Electro-magnetohydrodynamic Carreau fluid flow through a pair of rectangular plates. A Darcy–Brinkman–Forchheimer medium is considered for physical modeling. The flow is induced due to the Lorentz force, which occurs owing to the presence of an extrinsic imposed magnetic and electric field. The solutions are obtained with the help of numerical and

A solution in finite form for the screw dislocation interacting with the nanocrack incorporating surface piezoelectricity under anti-plane loads is developed. By the boundary integration and the Cauchy’s integral formula to convert the problem into a first-order differential equation, the finite-form solution in physical region is established via the mapping technique. At the crack tip, the results

The martensite structure of steel is of great importance in mechanical engineering and is usually adjusted by heat treatment. Of particular interest is the morphology of martensite, as it has a significant influence on mechanical properties. In this work, a phase field model is presented, where the order parameter is used to describe the evolution of martensite in order to predict the resulting morphology

The present work investigates the traveling wave formulation and their scattering characteristics in a waveguide having splitting expansion chamber. The segments of the chamber contain sandwiched elastic components backed by rigid cavities and absorbent linings. The structure is radiated by a plane wave mode incident which scatter on interaction with the expansion chamber. The mode-matching (MM) solution

This study makes an attempt at analyzing free vibration and transient behavior of advanced composites such as FGM plates by isogeometric approach. A new hybrid-type HSDT capable of taking into account through-thickness expansion for the dynamic analysis is developed and coupled with the NURBS-based IGA method. The quasi-3D theory in which the transverse displacement is divided into the bending and

In this paper, the free vibration of an aluminum beam coated with imperfect and damaged functionally graded material is investigated. The imperfections consist of porosities, while 4 evenly distributed cracks represent the damage profile. A polynomial function is used to vary the density and elasticity through the thickness of the coating, while the effective elastic modulus and density are found with

The present study proposes a new stochastic finite element method. The Karhunen–Loéve expansion is utilized to discretize the stochastic field, while the point estimate method is applied for calculating the random response of the structure. Two illustrative examples, including finite element models with one-dimensional and two-dimensional stochastic fields, are investigated to demonstrate the accuracy

In this study, a nanoscale beam of transversely isotropic thermoelastic (TIT) medium with two temperature and with Green–Naghdi (GN) III theory of thermoelasticity for free vibrations with simply supported boundaries have been examined. Euler–Bernoulli (EB) beam theory is used to formulate a mathematical model of the nanoscale beam in a closed form. The lateral deflection, frequency shift, thermal

The radial stiffness of rolling bearings is the basis for analyzing the dynamic performance of bearing-rotor systems. The changes of rolling element position may cause continuous change of radial stiffness and relative displacement of inner and outer ring during the operation of the bearing-rotor systems. As a result, the vibration of bearing-rotor systems would be aggravated. In order to accurately

Due to unphysical coupling induced by the material inhomogeneity, FG (functionally graded) nanobeam problems were formulated in a very complex way so that they cannot be analytically solved. In this paper, an uncoupled theory is proposed for FG nanobeams considering their small size effects. First, with the aid of the neutral axis, the axial displacement is expressed in terms of generalized displacements

Motivated by experimental findings on deformation induced microcracks in thin metal films and by their influence on the effective macroscopic electrical conductivity, a computational multiscale formulation for electrical conductors is proposed in this contribution. In particular, averaging theorems for kinematic quantities and for their energetic duals are discussed, an extended version of the Hill–Mandel

In this paper, the dynamics and the buckling loads for an Euler–Bernoulli beam resting on an inhomogeneous elastic, Winkler foundation are studied. An analytical, asymptotic method is proposed to determine the stability of the Euler–Bernoulli beam for various types of inhomogeneities in the elastic foundation taking into account different types of damping models. Based on the Rayleigh variation principle

The geometrical nonlinear effects caused by large displacements and rotations over the cross section of composite thin-walled structures are investigated in this work. The geometrical nonlinear equations are solved within the finite element method framework, adopting the Newton–Raphson scheme and an arc-length method. Inherently, to investigate cross-sectional nonlinear kinematics, low- to higher-order

The dynamic properties of structural and mechanical systems are commonly predicted using frequency response functions (FRFs), which represent the relationship between input forces and the corresponding responses in the frequency domain. Analytically calculated responses seldom coincide with actual responses because of modeling and construction errors, performance deterioration in service, etc. The

We propose an efficient inverse solver for identifying the diffusion coefficient based on few random measurements which can be contaminated with noise. We focus mainly on problems involving solutions with steep heat gradients common with sudden changes in the temperature. Such steep gradients can be a major challenge for numerical solutions of the forward problem as they may involve intensive computations

In the current practice, the one-dimensional nonlocal constitutive relations are always employed to model beam-type structures, regardless of the inherent three-dimensional interactions between atoms, resulting in inaccurately predicted nonlocal structural behaviors. To improve modeling, the present work first reveals and establishes how the nonlocal interactions in beams’ width and height directions

The characteristics of coherent structures in turbulent boundary layers were investigated experimentally using PIV and hydrogen bubble visualisation techniques. Turbulent boundary layers were generated and tested in two flumes with different scale, for two Reynolds numbers: \(\hbox {Re}=32{,}000\) and 71,200, both over a smooth bed. Measurements from the PIV technique and hydrogen bubble visualisation

Cylindrical inclusions with constant cross section in an infinite isotropic matrix are usually treated as plane elasticity problems and solved by complex potential method without considering the longitudinal eigenstrains. This paper provides a closed-form solution for the Eshelby’s circular cylindrical inclusion with eigenstrains which are polynomial in transverse direction and uniform in longitudinal

In this paper, a direct procedure to identify interaction forces between self-adhesive flexible polymeric films is developed. High-resolution photographs of the deformed shape within and outside the zone of adhesive interaction are taken at different instances of the T-peel test. To describe the deformed centerline, an approximate analytical solution to the equations of the nonlinear beam theory is

In this paper, water droplet behavior and its removal process in the anode gas flow channel (GFC) of a proton exchange membrane fuel cell (PEMFC) with partial blockage are numerically investigated using a three-dimensional volume of fluid model. The governing equations are solved using the finite volume method. The effects of the droplet emergence location (\(\alpha )\), blockage ratio (\(\beta )\)

In this paper, size effects exhibited by mechanical metamaterials have been studied. When the sizescale of the metamaterials is reduced, stiffening or softening responses are observed in experiments. In order to capture both the stiffening and softening size effects fully, a second-order asymptotic homogenization method based on strain gradient theory is used. By this method, the metamaterials are

Composite laminates often comprise notch-like features such as drilled assembly holes or geometric discontinuities resulting from damage. These features induce stress concentrations in their vicinities and can, through incompletely understood temperature-dependent damage mechanisms, reduce laminates’ load carrying capacity. Accordingly, this work investigates the effect of elevated temperatures on

A plane elastic–plastic problem of stress distribution in a circular hole thin plate involving initiation and propagation of cracks in an elastic zone, is considered. It is assumed that the stress level is such that the circular hole is entirely enclosed by the plastic deformations zone. The plate material satisfies the Tresca–Saint Venant plasticity condition. It is supposed that cracks initiation

Within this work, we utilize the framework of phase field modeling for fracture in order to handle a very crucial issue in terms of designing technical structures, namely the phenomenon of fatigue crack growth. So far, phase field fracture models were applied to a number of problems in the field of fracture mechanics and were proven to yield reliable results even for complex crack problems. For crack

Time-harmonic SH-wave scattering by a nanocrack in a continuously inhomogeneous magnetoelectroelastic (MEE) plane with exponentially dependent material parameters and under conditions of anti-plane strain is studied. A non-hypersingular, traction-based boundary integral equation method (BIEM) for solution of the problem under consideration is presented. The BIEM formulation combines classical elastodynamic

In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem of three bodies, ER3BP (with Keplerian elliptic trajectories of primaries Sun and planet around each other). A new type of the solving procedure is implemented here

The main aim of this work is to track the evolution of the stiffness tetrad during large plastic strain. Therefore, the framework of a general finite plasticity theory is developed. Some special cases are examined, and the case of a material plasticity theory is considered more closely. Its main feature is that the elasticity law changes during plastic deformations, for which we develop an approach

The coupling of two rotating spherical magnets is investigated experimentally. For two specific angles between the input and output rotation axes, a cogging-free coupling is observed, where the driven magnet is phase-locked to the driving one. The striking difference between these two modes of operation is the reversed sense of rotation of the driven magnet. For other angles, the experiments reveal

In this paper, an analysis is given about dynamic characteristics for a quasi-zero-stiffness isolator coupled with mechanical disturbance from a view of engineering application. In addition to traditional Columbo friction and linear damping in the vertical direction, the influence of other disturbing parameters such as geometrically nonlinear damping, friction and inertia of rods is also taken into

Hexagonal close-packed (HCP) metals show highly anisotropic mechanical responses due to twinning, slip and the interaction among various slip and twin systems. Each HCP metal shows different sets of activated slip and twin systems. The interaction among slip and twin systems causes highly nonlinear and rapidly changing hardening behaviors in the critical resolved shear stress (CRSS) of each slip/twin

Cylindrical rotating components have been of special interest in different industries and due to their wide applications such as grinding wheel, drive shaft; the analyses of elastic and plastic stress and strains have been an interesting topic for investigation. Therefore, in this study an analytical elastic and elasto-plastic solution to evaluate the stress field in axisymmetric thick-double-walled

The antiplane dynamic flexoelectric problem is stated as a dielectric solid that incorporates gradients of electric polarization and flexoelectricity due to strain gradients. The work examines dielectric materials without piezoelectric coupling or nonlinear ferroelectric switching and considers the inverse flexoelectric effect. It is shown that the coupling of the mechanical with the electrical problem

In this study, the discontinuous contact problem between a functionally graded (FG) layer, which is loaded symmetrically with point load P through a rigid block, and a homogeneous half-space was solved using the theory of elasticity and integral transform techniques. The shear modulus and density of the layer addressed in the problem vary with an exponential function along with its height. The half-space

A new numerical approach for the time-dependent wave and heat equations as well as for the time-independent Poisson equation developed in Part 1 is applied to the simulation of 1-D and 2-D test problems on regular and irregular domains. Trivial conforming and non-conforming Cartesian meshes with 3-point stencils in the 1-D case and 9-point stencils in the 2-D case are used in calculations. The numerical

The authors regret to have made an implementation error in their simulation code.

In this study, the squeezing flows between parallel disks, which one disk is impermeable and the other is porous, in the presence of magnetic field are investigated by Gegenbauer Wavelet Collocation Method (GWCM). Appropriate similarity transformations may be used to convert the governing non-linear partial differential equations into non-linear ordinary differential equations. The resultant non-linear

In this paper, the formulation of post-buckling of end-supported nanorods under self-weight was developed by the variational method. The surface stress effect was considered following the surface elasticity theory of Gurtin–Murdoch. The variational formulation involving the strain energy in the bulk material, the strain energy of the surface layer, and the potential energy due to self-weight was expressed

Scale-dependent stress intensity factors in an anti-plane cracked orthotropic material layer are evaluated using strain gradient theory. Both volumetric and surface strain gradient material characteristic lengths represented as l and \(l^{'}\), respectively, are employed to obtain semi-analytical solutions. The surface strain gradient effect is considered for both positive and negative \(l^{'}\) values