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The purpose of this study is to apply the Meshless Local Petrov–Galerkin (MLPG) method to solve the bending problems of linear viscoelastic plates, considering Reissner’s theory.

The weak formulation for the set of equations that govern Reissner’s plate theory is implemented in conjunction with the integral formulation applied to viscoelastic constitutive expressions. A meshless method based on the Moving Least Squares (MLS) approximation is considered in the numerical implementation. The final equation system is assembled by adopting simple and efficient schemes for numerical integration, considering a simplified formulation through centralization of the local interpolation domains and Gaussian quadrature at the same field point. The results obtained are compared with available solutions to demonstrate the efficiency of the proposed formulation.

The hereditary integral approach proved to be the most general way to analyze the viscoelastic problem, especially when applied together with the modified scheme for numerical integration. In addition, the variable changing technique is demonstrated to be an efficient formulation for solving shear-locking effects in thin plate problems.

The differential of the present study is related to the manner in which the properties of linear viscoelastic materials are considered in the formulation. Although most authors consider this point through the application of the correspondence principle, the present study works with a hereditary integral formulation. In addition, the variable changing technique is applied to solve the shear-locking effects, and an alternative approximation technique is considered to speed up the numerical integration process.

The purpose of this paper is to investigate a two dimensional problem in magneto-micropolar thermoelastic half-space with fractional order derivative in the presence of combined effects of hall current and rotation subjected to ramp-type heating.

The fractional order theory of thermoelasticity with one relaxation time derived by Sherief et al. (2010) has been used to investigate the problem. Laplace and Fourier transform technique has been used to solve the resulting non-dimensional coupled field equations to obtain displacement, stress components and temperature distribution. A numerical inversion technique has been applied to obtain the solution in the physical domain.

Numerical computed results of all the considered variables have been shown graphically to depict the combined effect of hall current and rotation. Some particular cases of interest are also deduced from the present study.

Comparison are made in the presence and absence of hall current and rotation in a magneto-micropolar thermoelastic solid with fractional order derivative.

The purpose of this paper is to review the advances in mechanics and tribology of polymers and polymer-based materials. It is focused on the understanding of the correlation of contact mechanics and the tribological behavior of polymers and polymer composites by taking account of surface forces and adhesion in the contact.

Mechanical behavior of polymers is considered a viscoelasticity. Tribological performance is estimated while considering the parts of deformation and adhesion in friction arising in the contact. Surface energy, roughness, load and temperature effects on the tribological behavior of polymers are evaluated. Polymer composites produced by reinforcing and by the addition of functional additives are considered as materials for various applications in tribology. Particular attention is given to polymer-based nanocomposites.

A review of studies in tribology has shown that polymer-based materials can be most successfully used as self-lubricating components of sliding bearings. The use of the fillers provides changes in the tribological performance of neat polymers and widens their areas of application in the industry. Thin polymer films were found to be prospective lubricants for memory storage devices, micro-electro-mechanical systems and precision mechanisms. Further progress in polymer tribology should be achieved on solving the problems of contact mechanics, surface physics and tribochemistry by taking account of the scale factor.

The review is based on the experience of the authors in polymer mechanics and tribology, their research data and on data of many other literature sources published in this area. It can be useful for specialists in polymer research and industrial engineers working in tribology and industrial lubrication.

This purpose of this paper is to discuss certain aspects of five-parameter viscoelastic models to study harmonic waves in the non-homogeneous polymer rods of varying density. There are two sections of this paper, in first section, the rheological behaviour of the model is discussed numerically and then it is solved analytically with the help of Friedlander Series using Eikonal equation of optics. In another section, the applicability of the developed model is studied through harmonic wave propagation in polymer non-homogeneous rods. The authors have used linear partial differential equations for finding the dispersion equation of harmonic waves in the polymers. All the cases taken in this study are discussed analytically and numerically with MATLAB.

A five-parameter viscoelastic model constituting of three dash-pots D ₂(η ₂), D _2′(η _2′), D ₃(η ₃) and two springs S ₁(G ₁), S ₂(G ₂) is considered. Where, G ₁, G ₂ are the modulli of elasticity and η ₂, η _2′, η ₃ are the Newtonian viscosity coefficients of the considered model, respectively. The parameters of the model are non-homogeneous in nature, i.e. module of elasticity and viscosity coefficients are space dependent. 1D problem is formed by taking the material in the form of rod of inhomogeneous polymer material by taking one end at x=0. The co-ordinate x is measured positive in the direction of the axis of the filament.

When the density, rigidity and viscosity all are equal for the first material specimen, the sound speed is constant, i.e. non-homogeneous has no effect on speed and phase of the wave is given. So it becomes the case of semi non-homogeneous medium (a medium when characteristics are space dependent while the speed is independent of space variable). The use of five-parameter models is mostly restricted in the field of rock mechanics. Thus, these models can be used in determining the time-dependent behaviour of a polymer medium.

The paper is original and it is not published elsewhere.

The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.

For normal loading, the contact between rough surfaces can often be modeled as the contact of an effective surface with a rigid fiat surface. A solution for the deformation of such equivalent surface, generated using fractal geometry, can be modified. However, in this study only the case of a single rough surface in contact with a rigid flat surface is considered. In the interface, the material is assumed to follow the idealized constitutive viscoelastic standard linear solid (SLS) model. Fractal geometry, through Cantor set theory, is utilized to model the roughness of the surface.

An asymptotic time series power law is obtained, which associates the creep load, the buck temperature and the creep of the fractal surface.

This law is only valid as long as the creep is of the size of the surface roughness. The modified model admits an analytical solution for the case when the behavior is linear viscoelastic. The proposed model shows a good agreement when compared with experimental results available in the literature.

The objective of this paper is to construct a continuous model for the viscoelastic contact of a nominal flat punch and a smooth surface of a rigid half‐space. The considered model aims at studying the normal approach as a function of the applied load. The proposed model assumes the punch surface material to behave according to Kelvin‐Voigt viscoelastic material. The punch surface, which is known to be fractal in nature, is modelled in this work using a deterministic Cantor structure. An asymptotic power law, deduced using iterative relations, is used to express the punch surface approach as a function of the remote force when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.

Aims to propose a new dynamic model for the solution of the three‐dimensional structural analysis problem of a non‐linear (non‐symmetrical) structure which is subjected under seismic forces.

This problem is reduced to the solution of a system of ordinary differential equations of the second kind and such a system is numerically solved by using a special kind of finite elements and by solving the corresponding eigenvalues‐eigenvectors problem.

The proposed finite element method is much smaller in degree of freedom size than commercial software, as classical linear stiffness matrices of three‐dimensional beam element have six degrees of freedom per node.

Future research should concentrate on the application of the new dynamic model to solve more complicated forms of non‐symmetrical structures.

Practical implications are given to structural analysis problems to the determination of the eigenvalues‐eigenvectors. As an example, an application is given to the determination of the eigenvalues and eigenvectors of a 15‐floor building consisting of reinforced concrete and subjected to an horizontal seismic vibration.

The new dynamic model which is proposed is addressed to researchers of dynamic analysis and civil engineers.

The objective of this paper is to construct a continuous model for the thermo‐visco‐elastic contact of a nominal flat, non‐smooth, punch and a smooth surface of a rigid half‐space. The considered model aims at studying the normal approach as a function of the applied loads and temperatures. The proposed model assumes the punch surface material to behave according to the linear Kelvin‐Voigt visco‐elastic material. The punch surface, which is known to be fractal in nature, is modeled in this work using a deterministic Cantor structure. An asymptotic power low, deduced using approximate iterative relations, is used to express the punch surface approach as a function of the remote forces and bulk temperatures when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.

Knitted fabrics have been widely used in a wide range of applications such as apparel industry. Since these fabrics are continuously subjected to the long-term tensile stresses or tensile creep in real conditions, investigation of viscoelastic behavior of sewn knitted fabrics would be important especially at the seamed area. The paper aims to discuss this issue.

A lockstitch machine was used to produce sewn samples by knitted fabric. Factors such as stitch per inch (SPI), thread tension and thread type were variables of the model. Tensile creep tests under constant load of 200 N were conducted, and creep compliance parameter D(t) of samples was obtained as a response variable. A successive residual method (SRM) was also used to characterize viscoelastic properties of sewn-seamed fabrics.

The instantaneous elastic responses of the seamed samples were less than those of the neat fabric (fabric with no seam). An increase in sewing thread strength increases the instantaneous elastic response of the sample. SPI and thread tension have an optimum value to increase E₀. High tenacity polyester thread, due to its higher elastic modulus, caused a larger E₀ than polyester/cotton thread in sewn knitted fabric. Characteristics of seam including sewing thread type, SPI and sewing tension have significant influence on T₀. Sewn-seamed fabric by high modulus thread shows less viscous strain T₀ than the neat fabric (fabric with no seam). Viscous strain T₀ decreases as SPI changes from 8 to 4 and/or 12. SPI and thread tension have an optimum value to increase the viscous strain T₀. E1 is the same for optimum seamed fabric and fabric sample but T1 is about two times greater for seamed fabric. Retarded time for creep recovery increases by sewing process but characteristics of seam have significant influence on E1 and T1. All sewn knitted fabric samples used in this study could be described by Burger’s model, which is a Maxwell model paralleled with a Kelvin one.

This paper is going to use a different method named successive residuals to model the creep behavior of seamed knitted fabric. On the whole, this paper paved a way to obtain viscoelastic constants of sewn-seamed knitted fabrics based on different sewing parameters such as the modulus of elasticity of the sewing thread, SPI and sewing thread tension.

This mathematical analysis has been accomplished for the purpose of understanding the propagation behaviour like phase velocity and attenuation of Love-type waves through visco-micropolar composite Earth’s structure.

The considered geometry of this problem involves a micropolar Voigt-type viscoelastic stratum imperfectly bonded to a heterogeneous Voigt-type viscoelastic substratum. With the aid of governing equations of motion of each individual medium and method of separation of variable, the components of micro-rotation and displacement have been obtained.

The boundary conditions of the presumed geometry at the free surface and at the interface, together with the obtained components of micro-rotation, displacement and mechanical stresses give rise to the determinant form of the dispersion relation. Moreover, some noteworthy cases have also been extrapolated in detail. Graphical interpretation irradiating the impact of viscoelasticity, micropolarity, heterogeneity and imperfectness on the phase velocity and attenuation of Love-type waves is the principal highlight of the present study.

In this study, the influence of the considered parameters such as micropolarity, viscoelasticity, heterogeneity, and imperfectness has been elucidated graphically on the phase velocity and attenuation of Love-type waves. It has been noticed from the graphs that with the rising magnitude of micropolarity and heterogeneity, the attenuation curves shift upwards, that is the loss of energy of these waves takes place in a rapid way. Hence, from the outcomes of the present analysis, it can be concluded that heterogeneous micropolar stratified media can serve as a helpful tool in increasing the attenuation or in other words, loss of energy of Love-type waves, thus reducing the devastating behaviour of these waves.

Till date, the mathematical modelling as well as vibrational analysis of Love-type waves in a viscoelastic substrate overloaded by visco-micropolar composite Earth’s structure with mechanical interfacial imperfection remain unattempted by researchers round the globe. The current analysis is an approach for studying the traversal traits of surface waves (here, Love-type waves) in a realistic stratified model of the Earth’s crust and may thus, serves as a dynamic paraphernalia in various domains like earthquake and geotechnical engineering; exploration geology and soil mechanics and many more, both in a conceptual as well as pragmatic manner.