Search results

The purpose of this paper is to calculate near field and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method (PVIEM) quantitatively.

The PVIEM is applied for the analysis of elastic wave scattering problems in an unbounded solid containing multiple multilayered anisotropic circular inclusions. It should be noted that this numerical method does not require the use of the Green’s function for the inclusion – only the Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general elastodynamic problems involving inhomogeneous and/or anisotropic inclusions whose shape and number are arbitrary.

A detailed analysis of the SH wave scattering problem is presented for multiple multilayered orthotropic circular inclusions. Numerical results are presented for the displacement fields at the interfaces and the far field scattering patterns for square and hexagonal packing arrays of multilayered circular inclusions in a broad frequency range of practical interest.

To the best of the authors’ knowledge, the solution for scattering of SH waves by multiple multilayered anisotropic circular inclusions in an unbounded isotropic matrix is not currently available in the literature. However, in this paper, calculation of displacements on interfaces and far field scattering patterns of multiple multilayered anisotropic circular inclusions using PVIEM as a pioneer of numerical modeling enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), the multilayer’s geometry, isotropy/anisotropy and softness/hardness.

The purpose of this article is the propagation of Rayleigh waves in a homogeneous, isotropic, initially stressed orthotropic elastic solid half-space lying under a homogeneous, viscous, inviscid liquid layer of finite thickness.

In the presence of both viscous and inviscid liquids, it derives the phase velocity, initial stress, and wave number-dependent frequency equation for an orthotropic elastic solid. With the help of the MATLAB program, the thickness effects of liquid layers, initial stress, and viscosity on the phase velocity and attenuation coefficient of the Rayleigh wave are explained for a particular model.

The phase velocity-dependent dispersion relation of Rayleigh waves at the interface of viscous liquid and solid half-space is a function of initial stress and wave number. Rayleigh waves along the free surface of an orthotropic elastic half-space are also derived as a particular case. The classical results of an inviscid liquid are achieved when the thickness of a viscous liquid approaches zero. Well-known classical results for initially stressed orthotropic elastic solids were also derived.

So far, many researchers have looked into the propagation of surface waves at the interfaces of solid–inviscid liquid, solid–solid, and multilayer interfaces. But in this article, the dispersion behavior of Rayleigh wave propagation in an initially stressed homogeneous orthotropic elastic solid half-space under a double layer of viscous liquid and inviscid liquid is studied.

Frictional sliding contact problems between laterally graded orthotropic half-planes and a flat rigid stamp are investigated. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members.

The solution procedure is based on a finite element (FE) approach which is conducted with an efficient FE analysis software ANSYS. The spatial gradations of the orthotropic stiffness constants through the horizontal axis are enabled utilizing the homogeneous FE approach. The Augmented Lagrangian contact algorithm is used as an iterative non-linear solution method in the contact analysis.

The accuracy of the proposed FE solution method is approved by using the comparisons of the results with those computed using an analytical technique. The prominent results indicate that the surface contact stresses can be mitigated upon increasing the degree of orthotropy and positive lateral gradations.

One can infer from the literature survey that, the contact mechanics analysis of orthotropic laterally graded materials has not been investigated so far. In this study, an FE method-based computational solution procedure for the aforementioned problem is addressed. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members. Additionally, this study provides some useful points related to computational contact mechanics analysis of orthotropic structures.

A two‐step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (a) decomposition of the stiffness matrix into the sum of an orthotropic and non‐orthotropic (anisotropic) parts; and (b) successive application of the finite element method and the classical Rayleigh—Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh—Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero non‐orthotropic matrix and its various‐order derivatives with respect to an anisotropic tracing parameter (identifying the non‐orthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed technique is demonstrated by means of numerical examples and its potential for solving other quasi‐symmetric problems is discussed.

The response of moving load over a surface is a subject of investigation because of its possible applications in determining the strength of a structure. Recently, with the enlargement of high-speed train networks, concern has been expressed about the effects of moving loads on the track, embankment and nearby structures. Earth surface and artificial structure are not always regular in nature. Irregularities are also responsible for structural collapse of long bridge and highway of plateau area under the action of moving loads. The purpose of this paper is to investigate the influence of irregularity on dynamic response due to a moving shear load.

At first the authors developed the mathematical model for the problem which is comprised of equation of motion together with boundary conditions. Perturbation technique has been used to derive the stresses produced in an irregular orthotropic half-space (which is influenced by gravity) due to a moving shear load. MATLAB and MATHEMATICA softwares have been employed for numerical computation as well as graphical illustration.

In this paper the authors have discussed the stresses produced in an irregular gravitating orthotropic half-space due to a moving shear load. The expression for shear stress has been established in closed form. Substantial effects of depth, irregularity factor, maximum depth of irregularity and gravitational parameter on shear stress have been reported. These effects are also exhibited by means of graphical illustration and numerical computation for an orthotropic material T300/5208 graphite/epoxy which is broadly used in aircraft designing. Moreover, comparison made through meticulous examination for different types of irregularity, presence and absence of anisotropy and gravity are highlighted.

A number of classical fatigue failures occur in aircraft structures. The moving load responsible for such fatigue failure may occur during manufacturing process, servicing, etc. Apart from these the aircraft structures may also experience load because of environmental damages (such as lightning strike, overheat) and mechanical damages (like impact damage, overload/bearing failure). Therefore the present study is likely to find application in the field of construction of highways, airport runways and earthquake engineering.

To the best of the authors’ knowledge no problem related to moving load on irregular orthotropic half-space under influence of gravity has been attempted by any author till date. Furthermore comparative study for different types of irregularity, presence and absence of anisotropy and influence of gravity on the dynamic response of moving load are novel and major highlights of the present study.

This paper introduces a closed-form solution for analyzing the buckling behavior of orthotropic plates using a refined plate theory with four variable parameters, leveraging a new hyperbolic shear displacement model.

The proposed theory incorporates a quadratic variation of transverse shear strains across the plate’s thickness and satisfies zero traction boundary conditions on both the upper and lower surfaces without employing shear correction factors. The governing equations are derived from the principle of minimum total potential energy. Closed-form solutions for rectangular plates, with two opposite edges simply supported and the remaining two edges subjected to arbitrary boundary conditions, are obtained using the state space approach to the Levy-type solution. Comparative studies are conducted to validate the accuracy of the obtained results.

The paper successfully examines and discusses in detail the effects of boundary conditions, loading conditions, variations in modulus ratio and thickness ratio on the critical buckling load of orthotropic plates.

This study presents a novel and precise method for evaluating the buckling behavior of orthotropic plates. The refined plate theory, without the need for shear correction factors, offers significant insights and improvements in understanding the critical buckling load under various conditions, contributing valuable knowledge to the field of structural analysis.

The purpose of the current manuscript is to investigate the reflection of plane waves in a rotating, two-dimensional homogeneous, initially stressed, nonlocal orthotropic thermoelastic solid half-space based on dual-phase-lag model.

The reflection phenomenon has been utilized to study the effects of initial stress, rotation and nonlocal parameter on the amplitude ratios. During the reflection phenomenon three coupled waves, namely quasi displacement primary wave (qP), quasi thermal wave (qT) and quasi displacement secondary wave (qSV) have been observed in the medium, propagating with distinct velocities. After imposing the suitable boundary conditions, amplitude and energy ratios of the reflected waves are obtained in explicit form.

With the support of MATLAB programming, the amplitude ratios and energy ratios are plotted graphically to display the effects of rotation, initial stress and nonlocal parameters. Moreover, the impact of anisotropy and phase lags is also observed on the reflection coefficients of the propagating waves.

In the current work, we have considered rotation and nonlocality parameters in an initially stressed orthotropic thermoelastic half-space, which is lacking in the published literature in this field. The introduction of these parameters in a nonlocal orthotropic thermoelastic medium provides a more realistic model for these studies. The present work is valuable for the analysis of orthotropic thermoelastic problems involving rotation, initial stress and nonlocality parameters.

This study aims to examine the plane wave reflection problem in micropolar orthotropic magneto-thermoelastic half space, considering the influence of impedance as a boundary in a nonlocal elasticity.

This study presents the novel formulation of governing partial differential equations for micropolar orthotropic medium with impact of nonlocal thermo-elasticity under magnetic field.

This study provides the numerical results validation for a particular numerical data and expression for the amplitude ratios of reflected waves and identifies the existence of four different waves, namely, quasi longitudinal displacement qCLD-wave, quasi thermal wave qCT-wave, quasi transverse displacement qCTD-wave and quasi-transverse micro-rotational qCTM-wave. The study derives the velocity equation giving the speed and phase velocity of these waves. The study also shows that the small-scale size effect gives significant impact on phase velocity.

The graphical analysis examines the variation of speeds and coefficients of attenuation of these waves due to frequency, magnetic field and nonlocal parameters. Also, significant conclusions on the variation of reflection coefficient against nonlocal parameter, frequency, impedance parameter and angle of incidence are provided graphically.

The creation of more effective micropolar orthotropic anisotropic materials which are very useful in the daily life and their applications in earth science are greatly impacted by the findings of this study.

The authors of the submitted document initiated and produced it collectively, with equal contributions from all members.

The purpose of this paper is to present the basic solution of two collinear mode-I cracks in the orthotropic medium by the use of the non-local theory.

Meanwhile, the generalized Almansi’s theorem and the Schmidt method are used. By the Fourier transform, it is converted to a pair of dual integral equations.

Numerical examples are provided to show the effects of the crack length, the distance between the two collinear cracks and the lattice parameter on the stress field near the crack tips in the orthotropic medium.

The present solution exhibits no stress singularity at the crack tips in the orthotropic medium.

The constitutive relationship of a four‐node flat shell finite element with six degrees of freedom per node and a modified five‐point quadrature, previously presented by the authors, is extended to include symmetric and unsymmetric orthotropy. Through manipulation of the kinematic assumptions, provision is made for out‐of‐plane warp. A wide range of membrane and thin to moderately thick plate and shell examples are used to demonstrate the accuracy and robustness of the resulting element.