In this paper, an instability analysis of three-dimensional (3D) beams supported with 3D hinges under axial and torsional loadings is presented in the large displacement and rotation regime. An exact displacement field is proposed based on the central line and orientation of the cross section consisting of nine parameters corresponding to 3D centroid movements and rotations. The Cauchy–Green deformation

The current study develops a 3D constitutive model for photo-thermal sensitive hydrogels based on free energy decomposition. The hydrogel under study is PNIPAM network with copper chlorophyllin nanoparticle agents attached to the network. The effect of light intensity is considered as a rise in temperature since chlorophyllin nanoparticle agents absorb light irradiation and convert it to heat. Moreover

To gain a complete view on the unique spatial attenuation phenomenon arising from the periodicity and the material viscoelasticity of the two-dimensional phononic crystals with finite out-of-plane extension, this paper presents a theoretical study of the viscoelastic phononic crystal slabs to investigate the wave transmission characteristics in terms of the dispersion relations for the propagating

A novel yet simple method is proposed to derive an analytical solution to the interaction problem of a screw dislocation inside an elastic inhomogeneity of arbitrary shape partially penetrated by a semi-infinite crack. The two analytic functions characterizing the elastic fields of stresses and displacement in the two-phase composite are readily obtained. Furthermore, we derive explicit expressions

The paper proposes an efficient sequential edge-smoothed finite element (ES-FE) analysis method enhanced with the smoothed recovery stress field to determine the collapse load limit of inelastic structures. The approach applies a modified concept of elastic compensation algorithm developed within the computationally advantageous ES-FE modelling framework and recovery stress field enhancement. It solely

Dynamic analysis of bidirectional functionally graded sandwich beams under a moving mass with the effect of partial support by a Pasternak foundation is presented on the basis of a quasi-3D theory. The face layers of the sandwich beams are made of bidirectional functionally graded material (FGM), while the core is axially FGM. The material properties of the skin layers are varied smoothly in both the

The flutter of a thin flexible plate in uniform flow is an interesting theoretical problem in fluid–structure interaction phenomena, as well as an important engineering problem. Therefore, understanding of the instability mechanism is crucial to preventing fatal defects caused by the flutter. In this study, the instability mechanism of a flexible plate in three-dimensional uniform flow is investigated

In this paper, a systematic approach is presented to obtain the stress fields in a linear elastic body where a spherical inclusion surrounded by a spherical annulus is embedded in an unbounded matrix phase. The entire body is subject to far-field uniform strain. A formulation is carried out for the hydrostatic part and the deviatoric part of the far field strain separately. The obtained formula for

An analytical model for a two-layer Timoshenko beam with a compliant interface is presented. A family of closed-form solutions is given for several cases of contact conditions at the interface that can include or exclude interlayer slip and relative rotations of the layers’ cross sections (distortion), with particular attention devoted to the latter. Each kinematic field at the interface is related

This paper is concerned with free vibration analyses of a circular transversely isotropic elastic plate based on Reddy plate theory and modified higher-order shear deformation plate theory (MHSDT). Hamilton’s principle is used to derive the equations of motion and boundary conditions of the circular plate. Natural frequencies are determined from the solution of the governing equations and boundary

Small superimposed radial oscillations for a class of damaged limited elastic, incompressible, isotropic and homogeneous thick-walled circular cylindrical tube are examined. Both the damage function and the considered limited elastic class depend only on the first invariant \( I_{1} \) of the left Cauchy–Green deformation tensor. The present work puts some light in the context of the surgical procedure

Exhaustion of a supersonic underexpanded air jet into air–helium and air–sulfur hexafluoride mixtures is studied experimentally. The air jet escapes from a convergent circular nozzle in the range of moderate Reynolds numbers covering the laminar and transitional regimes of the jet flow. The experiments are performed with “cold” and heated jets in a low-pressure jet setup, which allows the Reynolds

This paper investigates the fracture characteristics of a Yoffe conductive crack moving along the interface of piezoelectric (PE)/piezomagnetic (PM) bimaterials. By assuming that the tangential electric- and magnetic-fields along the crack surface are zero and that the speed of the moving crack is lower than the minimum shear wave speed of the bimaterial system, the considered problem can be transformed

In this study, an efficient 1D finite element model (FEM) is presented for the axial–flexural buckling, post-buckling and geometrically nonlinear analyses of thin-walled beams. The non-classical effects like transverse shear and normal flexibilities are incorporated in the formulation by adopting a new structural concept called equivalent layered composite cross-sectional (ELCS) modeling. In the framework

The paper focuses on the problem of evaluating analytically the electric and elastic fields in a piezoelectric material of the symmetry class 6 containing a penny-shaped crack loaded by both normal and tangential tractions and by electric charges. A solution of this kind has been developed for symmetry class 6 mm by Karapetian et al. (Arch. Appl. Mech. 70: 201–229, 2000). To the best of our knowledge

This paper presents an enstrophy-resolved simulation of the phase inversion problem using the volume of fluid (VOF) method. This well-known benchmark for modeling multiphase flows features a buoyancy-driven unsteady motion of a light fluid into a heavy one followed by several large- and small-scale interfacial processes such as deformation, ligament formation, interface breakup, and coalescence. A

In this paper, we use an implicit generalization of the celebrated Kelvin–Voigt solid constitutive equation to study the problem of circumferential shearing of a cylindrical annulus of viscoelastic material. This generalization of the Kelvin–Voigt model allows one to take into consideration the possibility of the body undergoing shear thinning or shear thickening and allows the material moduli to depend

Bulge testing is an experimental technique applied to the characterization of thin films, with which the mechanical properties are obtained employing numerical and analytical approaches. For rectangular and circular thin films, classical methods have been well adopted to calculate the stresses and strains at the central point without the dependency of its properties. It is due to that the equilibrium

We study the buckling of flexoelectric semiconductor beams using one-dimensional equations based on the macroscopic theory of flexoelectric semiconductors. Simple solutions for a beam with sliding ends and a simply supported beam with hinged ends are obtained. Results show that when buckling occurs, the mobile charges in the beams redistribute themselves driven by the electric polarization or field

An enhanced multi-fiber beam–column element suitable for the analysis of reinforced concrete members including the torsional effect is presented in this paper. The model is developed based on displacement formulation with the assumptions of small displacement. The section kinematics is based on the assumptions of a two-node Timoshenko beam and enhanced by introducing additional degrees of freedom at

Elastostatic problems of Bernoulli–Euler nanobeams, involving internal kinematic constraints and discontinuous and/or concentrated force systems, are investigated by the stress-driven nonlocal elasticity model. The field of elastic curvature is output by the convolution integral with a special averaging kernel and a piecewise smooth source field of elastic curvature, pointwise generated by the bending

The shimmy phenomenon is a significant concern in aircraft landing gear dynamics. The prediction of the shimmy instability is an essential issue in landing gear design to develop a passive or active suppression method. This work investigates the application of the nonlinear energy sink (NES) concept to mitigate the effects of shimmy in landing gears. The NES concept has been used in recent research

Mapping an irregular domain into a square one is a common technique in analyzing problems of plates and shells with irregular shapes. For the irregular shape without four corners such as the elliptical shape, the difficulty arises that the Jacobian determinant is zero at the corner points. An efficient quadrature method is presented to analyze the transverse vibration of thin plates with an elliptical

A method for identification of multiple transverse cracks and other localized defects in a rod by means of two spectra of longitudinal vibrations that correspond to free–free and fixed–free end conditions is presented. A numerical algorithm is developed that implements the method. The algorithm was tested on experimental data obtained on a cylindrical sample of aluminum alloy D16 with the created localized

This work presents a framework to study the quasi-static brittle fracture in functionally graded materials with random material properties using a non-intrusive phase field method. The model accounts for variation in the material and fracture properties. Further, the effective Young’s modulus, the gradient index and the fracture properties of the constituent materials are considered as random input

Researchers usually simplify their simulations by considering the Newtonian fluid assumption in microfluidic devices. However, it is essential to study the behavior of real non-Newtonian fluids in such systems. Moreover, using the external electric or magnetic fields in these systems can be very beneficial for manipulating the droplet size. This study considers the simulation of the process of non-Newtonian

In this article, a quadtree element-free Galerkin method (QEFGM) is proposed for automatically configuring background cells. The QEFGM is then employed in the fracture analysis of a piezoelectric elliptical tube subjected to internal pressure and thermal loading. The stress intensity factor (SIF) is calculated by the QEFGM and the traditional element-free Galerkin method (EFGM). By investigating an

Considering the piezoelectric effect, the electro-elastic field of an infinite one-dimensional quasicrystal medium with two circular cylindrical inclusions is derived under antiplane shear and inplane electric loading. The boundary value problem of the composite material with circular cylindrical inclusions is analytically solved by the use of the conformal mapping technique and analytical continuation

The characteristic equations of Rayleigh waves in monoclinic materials have already been derived by various prominent researchers. This paper revisits all these studies with special attention on numerical solutions of the characteristic equation. In this work, the propagation of a Rayleigh surface wave in a rotating monoclinic half-plane is studied. The boundary conditions on the surface of the half-space

Estimation of the effective homogenized properties is an essential step in the application of carbon nanotube (CNT)-reinforced composites. The difference between the experimental results and continuum-based homogenization schemes has motivated this work to present a modified Mori–Tanaka homogenization approach for CNT-reinforced nanocomposites. The agglomeration of CNT fibres in the matrix phase and

A simulation model for the flexural dynamics of a slender ship undergoing heave and pitch in regular waves is presented. The heave and pitch motions are found from the strip theory of Gerritsma and Beukelman [1] which is known to be experimentally validated. It is assumed that the ship structure is sufficiently stiff so that bending deformations do not significantly alter the wave field and hence the

Recent research extended the non-adhesive contact problems between an incompressible layer and a rigid indenter to adhesive cases in the limit of the Johnson–Kendall–Roberts (JKR) model, where it simply changes the boundary condition. The governing equation of this problem is in the form of Poisson’s equation, and there are two boundary conditions, one of which serves to determine the extent of the

The present work discusses the impact of the back coupling of the fiber orientation distribution on the base flow and on the fiber orientation itself during mold filling simulations. Flows through a channel and over a backward-facing step are investigated. Different closure approximations are considered for modeling the flow-induced evolution of anisotropy. The results corresponding to the decoupled

In this work, a time domain spectral element-based wave finite element method is proposed to analyze periodic structures. Time domain spectral element-based formulation reduces the total degrees of freedom and also renders a diagonal mass matrix resulting in substantial reduction in computation time for the wave finite element method. The formulation is then considered to obtain the stop band characteristics

A non-classical model for circular cylindrical thin shells is developed by using a modified couple stress theory and a surface elasticity theory. The equations of motion and boundary conditions are simultaneously obtained by a variational formulation based on Hamilton’s principle, which provides a unified treatment of the microstructure and surface energy effects. The new non-classical shell model

This study deals with two general solutions for a simply supported linear elastic Bernoulli–Euler beam with a stochastic bending flexibility, subjected to a deterministic loading. Two model problems are considered. The first problem is associated with a trapezoidally distributed load, whereas the second problem treats a sinusoidally distributed load. The importance of the solution for the trapezoidal

The kinetic theory is widely used in the description of thermal transport at the micro- and nanoscale. In the theory, it is assumed that heat is carried by quasi-particles, obeying the Boltzmann transport equation. These quasi-particles are sometimes associated with phonons. However, since phonons are not localized in physical space, they cannot play the role of the quasi-particles used in the kinetic

In this paper, a nonlinear formulation for beam-type structures is presented within the framework of two-phase stress-driven (SD) nonlocal theory. Various boundary conditions are considered for the beams, and it is assumed that they are on the Winkler- and Pasternak-type elastic foundations. It is considered that the beams are made of laminated functionally graded-graphene platelet-reinforced composite

This paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure

Material properties are inevitably stochastic due to the manufacturing process and the measurement procedure. In case of a cracked domain, the stochasticity of material properties (as stochastic variables) may manifest in the stress intensity factors (SIFs). Having the stochastic representation of the material properties, Young modulus and Poisson ratio (isotropic material), we approximate the SIFs

The three-dimensional model of the hyperelastic body under large strains is researched. A new strain measure, based on the QR-decomposition of the deformation gradient, is discussed. It is shown that this strain measure allows for more explicit analytical connections between different parameters of the stress–strain condition then the traditional approach. An example method of introducing this measure

The work presents a general strategy to design high-order conservative co-located finite-difference approximations of viscous/diffusion terms for flows featuring extreme variations of diffusive properties. The proposed scheme becomes equivalent to central finite-difference derivatives with corresponding order in the case of uniform flow properties, while in variable viscosity/diffusion conditions it

The self-similarity of characteristic stages of damage-failure transition has been studied both theoretically and experimentally, with the damage localization kinetics analyzed according to the nonlinearity of free energy release of solids with defects: Free energy in the generalized Ginzburg–Landau form reflecting the specific criticality of solids with defects, and the structural-scaling transition

The vibration of a rotor with variable mass as a one-mass system with two degrees of freedom is investigated. An analytical procedure for solving of the system of two coupled second-order differential equations with slow time variable parameters is developed. The trajectory of the rotor center for various initial conditions is obtained. The method developed in the paper is applied for determining the

A Timoshenko beam model is applied for the analysis of the flexoelectric effect for a curved nano-beam. This theory transforms the beam to a 1-d problem along the beam axis. The electric intensity vector for the open-circuit condition can be expressed by mechanical quantities, namely strains and strain gradients. The variational principle is applied to derive the system of ordinary differential equations

An analytical model for predicting the vibrations from an underground railway tunnel embedded in an unsaturated half-space is proposed. The tunnel lining is modeled as an infinite Flügge cylindrical shell, and the unsaturated soil is modeled as a three-phase medium comprising solid grains and pores containing water and air. By using the transformation properties between the plane wave functions and

The dynamics of micro-/nanoscale plates are extremely sensitive to external conditions. Here, the vibration of a submicron-thick circular plate exposed to its ambient environment was investigated. The obtained results indicate that the vibration behavior of circular plates shows a strong dependence on the surrounding conditions. Mode pair splitting was observed in a vibration experiment. One crucial

Stability analysis of soils prone to static liquefaction based on their monotonic undrained shear strength characteristics is an indispensable challenge in earthquake geotechnical engineering. This paper presents a laboratory study on the static behavior of Chlef sand–silt mixtures (with a silt content fc range from 0 to 50%); under low confining pressures. The experimental program includes undrained

A sequentially coupled shape and topology optimization framework is presented in which the outer geometry and the internal topological layout of beam-type structures are optimized simultaneously. The outer geometry of the beam-type structures is parametrically described by non-uniform rational B-splines (NURBS), which guarantees a highly accurate description of the structural shape and enable an efficient

We seek to understand the behavior of a pendulum under parametric excitation coupled with a nonlinear absorber. First, the reference system without any coupled absorber, i.e., a simple pendulum, is analyzed with a multiple scale method thanks to supposed assumptions about the excitation. The equilibrium points of the system are calculated, and their stability is determined. The phase portraits are

The classical Kapitsa’s problem of stability of an inverted pendulum subjected to vertical vibration of the support and some generalizations are investigated. The asymptotic method of two-scale expansions allows one to determine the level of vibrations that stabilizes the vertical position of the rod. The cases of inextensible and extensible rod are studied, and a benchmark of results is carried out

In this study, the inelastic buckling equation of a thin plate subjected to all in-plane loads is analytically solved and the inelastic buckling coefficient is explicitly estimated. Using the deformation theory of plasticity, a multiaxial nonlinear stress–strain curve is supposed which is described by the Ramberg–Osgood representation and the von Mises criterion. Due to buckling, the variations are

Identifying the exactly or approximately explicit expression of the stationary response probability density for general nonlinear stochastic dynamical systems is of great significance in the fields of stochastic dynamics and control. Almost all the existing methods are devoted to determine the exact or approximate solution for specific values of system and excitation parameters. Herein, aimed at stochastic

Taking the randomness of parameters into account, probabilistic dynamic stability analysis is carried out for a rotating tapered beam made of bidirectional functionally graded (BDFG) materials with time-dependent rotation speed. Hamilton’s principle is adopted to establish the equations of motion. The dynamic instability problem due to parametrical excitation is solved by Bolotin’s method with higher-order

A six-node co-rotational curved triangular shell finite element with a novel rotation treatment for folded and multi-shell structures is presented. Different from other co-rotational triangular element formulations, rotations are not represented by axial (pseudo) vectors, but by components of polar (proper) vectors, of which additivity and commutativity lead to symmetry of the tangent stiffness matrices

For structures with both random and fuzzy uncertainty parameters, a novel method for obtaining the membership function of reliability in the fuzziness failure criterion is presented using a Random Fuzzy Support Vector Machine based on the Particle Swarm Optimization method (PSO-RFSVM). The proposed method is used to solve the structural reliability problem with implicit limit state function in the

Indentation scaling relationships provide normalized guidance for measuring and predicting mechanical properties in indentation experiments. At the nano-scale, the material size-effect is significant, while conventional scaling relationships fail to depict this phenomenon in nanoindentation precisely. In the present research, cross-scale indentation scaling relationships are investigated using a strain

A simplified second strain gradient Euler–Bernoulli beam theory with two non-classical elastic coefficients in addition to the classical constants is presented. The governing equation and the associated classical and non-classical boundary conditions are derived with the aid of variational principles. The simplified second strain gradient theory is governed by an eighth-order differential equation

Existing continuum multiphase tumor growth models typically do not include microvasculature, or if present, this is modeled as a non-deformable network of vessels. Vasculature behavior and blood flow are usually non-coupled with the underlying tumor phenomenology from the mechanical viewpoint; hence, phenomena like vessel compression/occlusion modifying microcirculation and oxygen supply cannot be

The objective of this work is to study the effect of strain gradient, electric field gradient, and magnetic field gradient on the potential and field distributions of multiferroic fibrous composites subjected to generalized anti-plane shear deformation. A detailed energy variational formulation with strain, strain gradient, electric field, electric field gradient, magnetic field, and magnetic field