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Analyzing the viscoelastic characteristics of materials, especially polymers, is essential for understanding their mechanical properties and their capacity to function in different conditions. This paper presents a novel viscoelastic heat transfer model that integrates a memory-based derivative with the Moore–Gibson–Thomson (MGT) equation. The purpose is to examine the viscoelastic characteristics of materials and assess their response to external stresses and deformations over a certain period of time. In addition to incorporating the third-type thermoelastic model that Green and Naghdi provided, the derivation of this thermo-viscoelastic model included the integration of heat flow and its time derivative into Fourier's equation. To verify and understand the proposed model, it was applied to consider an unbounded viscoelastic semi-space immersed in a uniform magnetic field and exposed to non-Gaussian laser radiation as a heat source. An analysis of computational results was conducted to evaluate how the behavior of the field variables under consideration is affected by viscoelastic coefficients and memory-based derived factors. [ABSTRACT FROM AUTHOR]

For the particular case of an elastic multibody system (MBS) that can be modeled using one-dimensional finite elements, the main methods offered by analytical mechanics in its classical form for analysis are presented in a unitary description. The aim of the work is to present in a unitary form the main methods offered by classical mechanics for the analysis of solid systems. There is also a review of the literature that uses and highlights these methods, which need to be reconsidered considering the progress of the industry and the complexity of the studied systems. Thus, the kinematics of a finite element is described for the calculation of the main quantities used in the modeling of multibody systems and in analytical mechanics. The main methods used in the research of MBS systems are presented and analyzed. Thus, Lagrange's equations, Gibbs–Appell equations, Maggi's formalism, Kane's equations and Hamilton's equations are studied in turn. This presentation is determined by the advantages that alternatives to Lagrange's equations can offer, which currently represent the method most used by researchers. [ABSTRACT FROM AUTHOR]

In this present study, we intend to obtain a new criterion for the analyticity of a complex function. More exactly, we will deduce some concrete restrictions that must be performed by a function that is complex, is defined on the disc centred at the origin that has radius 1 (hereinafter referred to as the unit disc), which, in addition, is continuous on this disc, including its border, to be analytic on the open unit disc. After that, as applications, we will deduce the Schwartz–Villat's formula in this context, and we will obtain the known Joukowski's function. [ABSTRACT FROM AUTHOR]

In our study we construct a boundary value problem in elasticity of porous piezoelectric bodies with a dipolar structure To construct an eigenvalue problem in this context, we consider two operators defined on adequate Hilbert spaces. We prove that the two operators are positive and self adjoint, which allowed us to show that any eigenvalue is a real number and two eigenfunctions which correspond to two distinct eigenvalues are orthogonal. With the help of a Rayleigh quotient type functional, a variational formulation for the eigenvalue problem is given. Finally, we consider a disturbation analysis in a particular case. It must be emphasized that the porous piezoelectric bodies with dipolar structure addressed in this study are considered in their general form, i.e.,inhomogeneous and anisotropic. [ABSTRACT FROM AUTHOR]

First we construct the boundary value problem in the context of the elastostatics of elastic orthotropic beams, which are loaded on the ends and on the lateral surface. Then we determine the solution of this problem with the help of some functions of stress. In this way we find an extension of Prandtl's method and, in the same time, an natural extension of the known Almansi's problem from the classical plane problem of torsion. [ABSTRACT FROM AUTHOR]

In this article, a modified Moore–Gibson–Thompson heat transfer equation with a memory-dependent derivative is utilized to investigate the thermoelastic interaction induced by non-Gaussian lasers in an infinitely elastic nonlocal medium. A memory-based derivative is also examined, and it was discovered to be superior at predicting the pattern of real-life challenges. This finding is part of the conviction that is currently analyzed. The idea of a memory-dependent derivative is attractive since it has some peculiarities. These characteristics include remarkable components as the kernel function and time lag, both of which can be freely selected according to the specifications of the problem. In addition, the non-local concept of Eringen was utilized in the research project so that the small-scale influence could be understood. Using the Laplace transform as a method, analytical–numerical solutions to problems involving thermo-physical fields, such as dimensionless temperature and deformation, as well as nonlocal physical stress, can be analyzed and compared. Numerical solutions have been used to explore the influence of memory-dependent derivative components such as the kernel function and the time delay coefficient on the studied domain variables of the medium. The computational outcomes of the studied fields are also used to find out the role of the non-local index. [ABSTRACT FROM AUTHOR]

We consider a thermoelastic Cosserat body with dual-phase lag. In order to formulate a dual-phase-lag model, an equation is introduced, of the time differential type, to characterize the thermal effects and the coupling with the deformation from an elastic point of view. We associate with this model a mixed problem with initial data and conditions to the limit. We then obtain some qualitative estimates on the solutions of this mixed problem, without resorting to restrictive conditions on the thermoelastic coefficients. In order to obtain the uniqueness of the solution, we appeal to a Lagrange-type identity, easily obtained in the given context, and to a law of conservation, previously demonstrated. Then, we establish an inequality which is of the Gronwall's type, that is useful for proving the continuous dependence of the solutions in relation to initial values and loads, which is another important result of our study. [ABSTRACT FROM AUTHOR]

A planar mechanism represents a mechanism that is frequently used in engineering, and very often, the elasticity of some elements of the mechanism cannot be neglected. Consideration of all rigid elements does not allow the analysis of vibrations or situations of loss of stability of some elements. Gibbs–Appell's generalized equations are used in this paper to obtain the governing equations for a two-dimensional finite element, which is in plane motion. Using Lagrange's equations is the most widely used way for researchers to address such a problem. This is mainly due to the familiarity of researchers with this robust calculation method. There are two major advantages of applying this formalism: a smaller number of differentiation operations is needed to be performed and, by eliminating Lagrange multipliers, the number of unknowns decreases significantly. The method is applied for the plane multibody systems with elastic elements. We hope that this method, due to its simplicity, will be interesting for mechanical designers. [ABSTRACT FROM AUTHOR]

A matrix-based representation of the inertial characteristics with possible used in multibody dynamics is presented in the paper. The paper aims to develop a unitary formalism that will help to model multibody systems, for the purpose of kinematic and dynamic analysis. Properties of the inertia matrix due to the symmetry of this matrix are presented. The points with spherical and cylindrical symmetry are identified, which allow the easier writing of the equations of motion. The form of the inertia matrix from any body of a multibody system in the global reference system is shown. [ABSTRACT FROM AUTHOR]

Our study is a generalization of some results obtained by Synge in the classical theory of elasticity. By this extension, we wish to cover the theory of micropolar elastic bodies. More precisely, we approach the electroacoustic energy flux in the case of plane waves of harmonic type which propagate in piezoelectric crystals which are supposed to be prepolarized and prestressed. [ABSTRACT FROM AUTHOR]

In this study it is approached a linear model for the mixture of two Cosserat bodies having pores. It is formulated the mixed problem with initial and boundary data in this context. The main goal is to show that the coefficients that realize the coupling of the elastic effect with the one due to voids can vary, without the mixture being essentially affected. In a more precise formulation, this means that a small variation of the coefficients in the constitutive equations of the two continua causes only a small variation of the solutions of the corresponding mixed problems, that is, the continuous dependence of the solutions in relation to these coefficients is ensured. The considered mixture model is consistent because all estimates, specific to continuous dependence, are made based on rigorous mathematical relationships. [ABSTRACT FROM AUTHOR]

The paper aims to study, using the finite element method, the elastic behavior of a cylinder made by a material with micropolar structure, containing (as the results of the processing or introduced intentionally) voids. To study such a type of problem, a theoretical model of a continuous solid body with voids in the material is presented, after which, in order to determine the effect that these voids have, a model with finite elements is made, using Lagrange's equations. This model can be applied to any type of elastic solid with voids. In the paper study the elastic response of a hollow cylinder made by a material with voids. Finally, comparative results are obtained to show the influence of voids on the elastic behavior of the body in some classic cases. These results are compared with the values obtained in the literature by experimental methods. It is found that a small percentage of voids can lead to significant variations on the mechanical properties. [ABSTRACT FROM AUTHOR]

In this study, we consider the final boundary value problem for a thermoelastic Cosserat material. With the help of a simple translation, our final problem is transformed in a usual mixed problem with boundary relations and initial data. For this new problem, we obtain some theorems of uniqueness of solutions. For this, we do not use any law of conservation of energy, as is usually done to obtain a result of uniqueness. Moreover, we do not need assumptions to ensure the boundedness of the tensors which characterize thermoelastic coefficients. [ABSTRACT FROM AUTHOR]

Our study deals with a thermoelastic body with pores. We have added a new independent variable, namely the time derivative of the voidage. Within the theory of such media, we analyze the spatial and temporal evolution of solutions. For the spatial behavior, we will prove certain estimations of the Saint-Venant type, in the situation the bodies are bounded. In the case the bodies are unbounded bodies, to describe the spatial evolution we consider certain estimations of the Phragmén–Lindelöf type. [ABSTRACT FROM AUTHOR]

We study the linear theory of thermo-electro-viscoelasticity of Green–Naghdi type for the case of a one-dimensional body. For the corresponding mathematical model, we prove a uniqueness theorem of the solution to the mixed boundary-initial-value problem by means of the Laplace transform after rewriting the constitutive equations in an appropriate form. Moreover, we derive a result of continuous dependence upon the supply terms. [ABSTRACT FROM AUTHOR]

In this study, we approach the strain gradient thermoelasticity of bodies with microtemperatures. We define the internal energy corresponding to an arbitrary solution of the mixed problem with boundary and initial values, considered in the context of strain gradient thermoelasticity of bodies with microtemperatures. The Cesaro means of different parts of the internal energy are considered. In our main result, we prove the asymptotic equipartition of the strain and kinetic energies, in the case t → ∞ . [ABSTRACT FROM AUTHOR]

Lagrange's equations represent the common approach in finite element analysis of an elastic multibody system. The most important step in this case is to write the governing equations. The work develops an alternative method to obtain these equations, using so-called Gibbs–Appell formalism. The advantage of this method is the decrease in the number of calculations to be made. The acceleration energy will be calculated first for a one-dimensional finite element, and then Gibbs–Appell equations are applied in the classical form. The number of differentiations required, compared to the method of Lagrange's equations, decreases significantly, with effects on the computational time required to solve such a problem. We can assume that, due to its simplicity, this method will determine the interest of researchers in the case of large industrial applications. [ABSTRACT FROM AUTHOR]

In our present paper, we approach the mixed problem with initial and boundary conditions, in the context of thermoelasticity without energy dissipation of bodies with a dipolar structure. Our first result is a reciprocal relation for the mixed problem which is reformulated by including the initial data into the field equations. Then, we deduce a generalization of Gurtin's variational principle, which covers our generalized theory for bodies with a dipolar structure. It is important to emphasize that both results are obtained in a very general context, namely that of anisotropic and inhomogeneous environments, having a center of symmetry at each point. [ABSTRACT FROM AUTHOR]

This study is concerned with the linear elasticity theory for bodies with a dipolar structure. In this context, we approach transient elastic processes and the steady state in a cylinder consisting of such kind of body which is only subjected to some boundary restrictions at a plane end. We will show that at a certain distance d = d (t) , which can be calculated, from the loaded plan, the deformation of the body vanishes. For the points of the cylinder located at a distance less than d, we will use an appropriate measure to assess the decreasing of the deformation relative to the distance from the loaded plane end. The fact that the measure, that assess the deformation, decays with respect to the distance at the loaded end is the essence of the principle of Saint-Venant. [ABSTRACT FROM AUTHOR]

In our study, we consider the linear mixed initial boundary value problem for a porous elastic body having a dipolar structure. The equations that describe the elastic dipolar deformations are coupled with the equations which describe the evolution of the voids by means of certain coefficients. Our main result proves the continuous dependence of solutions for the mixed problem with regard to the coefficients which perform this coupling. Using an adequate measure, we can evaluate the continuous dependence by means of some estimate regarding the gradient of deformations and the gradient of the function that describes the evolution of the voids. [ABSTRACT FROM AUTHOR]

We develop a thermo-electro-mechanical continuum theory for a bone remodeling model in order to understand and predict the features of the remodeling process under the control of the strain for a normal living bone. Bone remodeling refers to the continual processes of growth, reinforcement and resorption which arise in living bone. Unlike other approaches to the subject, we follow the Green–Naghdi approach to thermodynamics that employs the concept of thermal displacement and an entropy equality instead of an entropy inequality. We study the bone remodeling process in the context of thermo-electro-elasticity and introduce new balance laws of momentum, energy and entropy. Then, we derive the local balance laws, the constitutive assumptions, the constitutive restrictions and finally focus on the case of transversely isotropic bodies. Last but not least, we prove that the mathematical model is well posed in the nonlinear case. [ABSTRACT FROM AUTHOR]

In our paper, we consider a combination of two sub-cylinders coupled by an interface in a semi-infinite cylinder. Both sub-cylinders are made of dipolar elastic materials. For one of the two sub-cylinders, we will consider the elastostatic problem, and for the other the elastodynamic problem. Thus, the spatial behaviors of the sub-cylinders are of different kind and the question arises whether the evolution of this combination can be controlled. By using a polynomial way, we prove that the decay of solutions for the two problems can be controlled. [ABSTRACT FROM AUTHOR]

This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved. [ABSTRACT FROM AUTHOR]

This study is concerned with the mixed initial boundary value problem for a dipolar body in the context of the thermoelastic theory proposed by Green and Naghdi. For the solutions of this problem we prove a result of Hölder's-type stability on the supply terms. We impose middle restrictions on the thermoelastic coefficients, which are common in continuum mechanics. For the same conditions we propose a continuous dependence result with regard to the initial data. [ABSTRACT FROM AUTHOR]

The current investigation deals with the deformation of a non-homogeneous thermoelastic half space under hydrostatic initial stress for the Green–Naghdi model III. The medium is supposed to be rotating with a constant angular velocity. The non-homogeneous properties of the material are along the x-direction. At the first instance, the problem has been solved analytically to obtain stress and displacement components. Further, the numerical values of these expressions are evaluated using a computer program for a particular medium. The numerical values obtained are then presented graphically to show the effect of initial stress parameter and non-homogeneity parameter on the quantities. [ABSTRACT FROM AUTHOR]