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In addition to the prediction of effective elastic properties of random media, the statistical variations of these properties for finite size specimens are of practical interest. From finite element method calculations on simulated 2D random media, size effects are studied and modelled. They enable us to draw practical conclusions for finite element applications to elastic random media.

To provide an explicit representation for wide‐sense stationary stochastic fields which can be used in stochastic finite element modelling to describe random material properties.

This method represents wide‐sense stationary stochastic fields in terms of multiple Fourier series and a vector of mutually uncorrelated random variables, which are obtained by minimizing the mean‐squared error of a characteristic equation and solving a standard algebraic eigenvalue problem. The result can be treated as a semi‐analytic solution of the Karhunen‐Loève expansion.

According to the Karhunen‐Loève theorem, a second‐order stochastic field can be decomposed into a random part and a deterministic part. Owing to the harmonic essence of wide‐sense stationary stochastic fields, the decomposition can be effectively obtained with the assistance of multiple Fourier series.

The proposed explicit representation of wide‐sense stationary stochastic fields is accurate, efficient and independent of the real shape of the random structure in consideration. Therefore, it can be readily applied in a variety of stochastic finite element formulations to describe random material properties.

This paper discloses the connection between the spectral representation theory of wide‐sense stationary stochastic fields and the Karhunen‐Loève theorem of general second‐order stochastic fields, and obtains a Fourier‐Karhunen‐Loève representation for the former stochastic fields.

This paper aims to introduce an efficient time-domain formulation of adjustable accuracy for a consistent and trustworthy computation of electromagnetic field characteristics in randomly varying configurations. The developed methodology is carefully certified via comprehensive comparisons with the corresponding outcomes obtained by the Monte Carlo approach.

The presented methodology uses higher-order approximations of Taylor series expansions of stochastic multivariable functions for the rapid estimation of the electromagnetic field component mean value and confidence intervals of their variance. Toward this objective, new time-update equations for the mean value and the variance of the involved electromagnetic field are elaborately derived.

The featured technique presents an efficient alternative to the excessively resource-consuming Monte Carlo finite-difference time-domain (MC–FDTD) implementation, which requires an unduly number of realizations to achieve a satisfying convergence. The higher-order stochastic algorithm retrieves accurately the statistical properties of all electromagnetic field in a single simulation, presenting promising accuracy, stability and convergence.

The adjustable-accuracy higher-order scheme introduces a new framework for the derivation of the stochastic explicit time-update equations and precisely computes the required confidence intervals for the electromagnetic field variance instead of the variance itself, which can be deemed a key advantage over existing schemes. This fully controllable formulation results in significantly more accurate calculations of the electromagnetic field variance, especially for larger fluctuations of the involved electromagnetic media parameters.

The main purpose of the paper is to propose a new approach to stochastic computational modeling of interface defects in fiber‐reinforced composites. Interface defects with random radius and total number at the fiber‐matrix interface are modeled as an interphase between original composite components with the thickness obeying all the discontinuities and material parameters of this new, fictitious material are obtained by modified spatial averaging method. Such a model is used in the stochastic finite element analysis of composites in their original configuration. Next, the probabilistic moments of global effective properties of the entire composite are estimated, thanks to the traditional Monte Carlo simulation method implementation. Numerical experiments show that introduction of the interface defects results in significant increase of randomness level of the composite displacements and the homogenized elastic characteristics. Computer programs implemented can find their applications in digital image‐based analysis and the reliability analyses for fiber‐reinforced composites.

The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media..

The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB.

In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix.

The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.

The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

The present discussed problem deals with the torsional surface wave scattering in an initially stressed inhomogeneous medium. The assumed model consists of tri-mediums resting over a viscoelastic semi-infinite medium and the considered tri-mediums are transversely isotropic, porous, and heterogeneous respectively under the impression of initial stress.

Heterogeneities are associated with density and rigidity in the intermediate layer and considered heterogeneities are of the trigonometric form. Displacement components are derived for mediums by applying separable variables.

Frequency equation is deduced by using suitable boundary conditions, defined at the free surface of the uppermost medium, and on the interfaces between mediums. The derived equation is of the complex form, real and imaginary parts direct the phase/damped velocities respectively. Additional results are considered in particular cases. Numerical examples are adopted for computing frequency equation and drawn consequences are demonstrated graphically to analyze the significant impact of various parameters on the phase velocity as well as on damped velocity of the surface wave sketched against the wavenumber.

This presented research work provides a different view over the analysis of torsional surface waves than the earlier investigations. Previously studied problems on the wave generation were conducted in different models under the various affecting parameters. Study on torsional wave generation in the present model is not carried out till now. This study may find its virtue in the theoretical aspect as well as in the possible practical implications. The outcomes are relevant to geology and allied areas; moreover, the concern applications may be implicated in geological exploration, civil engineering, and prediction of Earthquake etc.

The purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent years have witnessed significant progress in optimizing these fluids for enhanced heat transfer within porous (Darcy–Forchheimer) structures, offering promising solutions for various industries seeking improved thermalmanagement and energy efficiency.

The first step is to transform the original partial differential equations into a system of first-order ordinary differential equations (ODEs). The fourth-order Runge–Kutta method is chosen for its accuracy in solving ODEs. The present study investigates the free convective boundary layer flow of hybrid nanofluids over a moving thin inclined needle with the slip flow brought about by inclined Lorentz force and Darcy–Forchheimer porous matrix, viscous dissipation.

It is found that slip conditions (velocity and Thermal) exist for a range of the natural convection boundary layer flow. In the hybrid nanofluid flow, which consists of Al₂O₃ and Fe₃O₄ are nanoparticles, H₂O − C₂H₆O₂ (50:50) are considered as the base fluid. The consequence of the governing parameter on the momentum and temperature profile distribution is graphically depicted. The range of the variables is 1 ≤ M ≤ 4, 1 ≤ d ≤ 2.5, 1 ≤ δ ≤ 4, 1 ≤ Fr ≤ 7, 1 ≤ Kr ≤ 7 and 0.5≤λ ≤ 3.5. The Nusselt number and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in Table 4. These analyses elucidate that upsurges in the value of the Fr noticeably diminish the momentum and temperature. It is investigated to see if the contemporary results are in outstanding promise with the outcomes reported in earlier works.

The results can be very helpful to improve the energy efficiency of thermal systems.

The hybrid nanofluids in heat transfer have the potential to improve the energy efficiency and performance of a wide range of systems.

This study proposes that in the combined effects of hybrid nanofluid properties, the inclined Lorentz force, the Darcy–Forchheimer model for porous media and viscous dissipation on the boundary layer flow of a conducting fluid over a moving thin inclined needle. Assessing the potential practical applications of the hybrid nanofluids in inclined needles, this could involve areas such as biomedical engineering, drug delivery systems or microfluidic devices. In future should explore the benefits and limitations of using hybrid nanofluids in these applications.

This paper aims to study the attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips. Numerical investigations are performed for the phase and damped velocity profiles of the wave. For numerical computation purposes, water-saturated limestone and kerosene oil saturated sandstone for the first and second porous strips, respectively. Some other peculiarities have been observed and discussed.

Dispersion and attenuation characteristic of the shear wave propagations have been studied in an inhomogeneous poro-anelastic strip of finite thickness, which is clamped between an inhomogeneous poroelastic strip of finite thickness and an elastic half-space. Both the strips are initially stressed and the half-space is self-weighted. Analytical methods are used to calculate the interior deformations of the model with the involvement of special functions. The determination of the frequency equation, which includes the Bessel’s and Whittaker functions, has been obtained using the prescribed boundary conditions.

Impacts of attenuation coefficient, dissipation factor, inhomogeneities, initial stresses, Biot’s gravity, porosity and thickness ratio parameters on the velocity profile of the wave have been demonstrated through the graphical visuals. These parameters are playing an important role and working as a catalyst in affecting the propagation behaviour of the wave.

Inclusion of the concept of doubly layered initially stressed inhomogeneous porous structure of elastic and anelastic medium bedded over a self-weighted half-space medium brings a novelty to the existing literature related to the study of shear wave. It may be helpful to geologists, seismologists and structural engineers in the development of theoretical and practical studies.

This paper aims to study photothermal excitation process in an initially stressed semi-infinite double porous thermoelastic semiconductor with voids subjected to Eringen’s nonlocal elasticity theory under the fractional order triple-phase-lag thermoelasticity theory. The considered substrate is governed by the mechanical and thermal loads at the free surface.

The normal mode technique is used to carry out the investigation of photothermal transportation. By virtue of the MATHEMATICA software, each distribution is exhibited graphically.

The expressions of the displacements, temperature, volume fractions of both kinds of voids, carrier density and stresses are determined analytically. With the help of the numerical data for silicon (Si) material, graphical implementations are presented on the basis of initial stress, fractional order, nonlocality and thermoelectric coupling parameters.

The present study fabricates the association of Eringen’s nonlocal theory and the stress analysis in a semiconducting double porous thermoelastic material with voids, which significantly implies the originality of the conducted work.