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The present work aims to study the influence of variable thermal conductivity in generalized thermoelastic solid with microstretch within the framework of the Green‐Naghdi theory. The analytical methodology is adopted for obtaining exact expressions of displacement components, stresses, couple stresses, micro stress distribution and temperature distribution. The effect of variable thermal conductivity...
This paper proposes a mathematical model that can be used to quantify the effects of a polarized electric field on the mechanical properties of a polar dielectric in the framework of mechanics of deformable solids. The physical essence of the phenomenon is known. However, its direct use in practical calculations may cause difficulties due to the complexity of the composition and structure of materials...
A review of publications on stability of mechanical equilibrium of multicomponent mixtures in gases and liquids under non‐isothermal and isothermal conditions is given. Studies where diffusion in binary and multicomponent mixtures led to the occurrence of instability of mechanical equilibrium of the system have been analyzed. The main attention is paid to the description of approaches predicting the...
The present article considers an anti‐plane stress problem of three cracks at different orthotropic materials' interfaces. According to the geometry of the problem, the governing equations and mixed boundary conditions have been formulated. Fourier integral transformation is used to convert the mixed boundary value problem into dual integral equations, which gives two equations containing infinite...
This article offers the first investigation into the thermoelectric vibration of microscale Euler‐Bernoulli beams resting on an elastic Winkler base. We developed the system of equations for thermoelastic microbeams using elastic basis theory and the generalized Moore–Gibson–Thompson (MGT) thermal transport framework with a single‐phase delay. At the front of the microbeam, a graphene strip connected...
A current topic in the photovoltaic industry is the analysis and evaluation of possible structural and material properties. This requires the effective material characteristics of polycrystalline silicon, which is an important component for the functional performance of the photovoltaic modules in use. Since this assessment is associated with high costs, it is to be carried out already in the product...
This article is concerned with developing a method to find a numerical solution of a one‐dimensional variable‐order non‐linear partial integro‐differential equation (PIDE) viz., reaction–advection–diffusion equation with initial and boundary conditions. The proposed numerical scheme shifted Legendre collocation method is based on operational matrices. The operational matrices using one‐dimensional...
Peridynamics (PD) has been introduced to account for long range internal force/moment interactions and to extend the classical continuum mechanics (CCM). PD equations of motion are derived in the form of integro‐differential equations and only few analytical solutions to these equations are presented in the literature. The aim of this paper is to present analytical solutions to PD beam equations for...
The article deals with the problem of three thermally insulated cracks embedded in a fibrous composite material subjected to thermo‐mechanical loading. Orthotropy is ensured by the unidirectional reinforcement of fiber. The considered infinite orthotropic plane is divided mathematically into three parts. The present mathematical model comprises of a central crack parallel to two symmetric collinear...
This investigation aims to examine the impact of the time‐harmonic laser pulse on the vibration phenomenon in 2D homogeneous transversely isotropic homogeneous visco‐thermoelastic nanobeam with a new modified three‐phase lag Green Nagdhi (TPL‐GN) model. The ends of the nanobeam are considered to be simply supported and held at a constant temperature. The mathematical model so formed is solved to derive...
A non-linear mechanical model with a linear spring, a linear dashpot and a non-linear dashpot is used for studying the non-linear viscoelastic behaviour of a multi-layered inhomogeneous beam with a delamination crack. The beam with a circular cross-section is under a torsion moment that increases at a constant speed. The non-linear stress-strain-time constitutive law of the model is obtained by adding...
The inverse Hooke's law and complementary strain energy density has been examined in the context of the theory of coupled gradient elasticity for second gradient materials. To this end, it was assumed that the potential energy density is a quadratic form of the strain and of the second gradient of displacement. Existence of the coupling term significantly complicates the problem. To avoid this complication...
In this paper, we present the model of continuum mechanics for an analysis of the size‐dependent elastic state of the wrinkled thin film coating with the nanosized thickness. For this purpose, we formulate the two‐dimensional boundary value problem for the film‐on‐substrate system under plane strain conditions in terms of the complex variable. To analyse the effect of surface and interface elasticity,...
The article deals with the collinear Griffith cracks under the time‐harmonic waves, situated in an orthotropic strip sandwiched between two identical half‐planes. The outer cracks are considered to be situated on either sides of the central crack. The mathematical model is solved by applying the Fourier transform and then the unknown functions have been determined using Schmidt method. The approximate...
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