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In this paper, we employ the finite element method based on non-uniform rational B-splines function approximation to solve the nonlinear Brinkman-Forcheimer-Darcy equation in a simply connected and bounded Lipschitz domain. We provide both theoretical and numerical studies of the Dirichlet boundary problem. Utilizing a stream function formulation, we demonstrate the well-posedness of the weak form. Furthermore, we approximate the velocity and pressure fields by linearizing the nonlinear terms, resulting in an algebraic system. This Non-uniform rational B-splines method is more effective in terms of the exact representation of the geometry and the good approximation of the solution compared to the virtual element method. To validate the effectiveness of the non-uniform rational B-splines Finite Element Method, we conduct numerical simulations of fluid flow in porous media. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to study the impact of delay times in a poro-elastic medium using the finite element approach and the three-phase lag thermo-elastic theory. The governing equations were obtained for a three-phase lag model with six delay times. Consideration was given to a one-dimensional application of a poro-elastic half-space. Because of the complex form of the basic equations, the finite element approach was used to solve this problem. Asymmetric and symmetric tensors were used to represent all of the physical quantities. The numerical results were presented in graphical form. The effects of porosity and delays were introduced. Finally, the results were plotted to show the difference between the three-phase delay (TPL) and the Green−Naghdi with and without energy dissipation (GNIII) models.

In this paper, the authors propose the application of the Gibbs–Appell equations to obtain the equations of motion in the case of a mechanical system that has elements with a micro-polar structure, containing voids. Voids can appear as a result of the processing or manufacturing of the parts, or can be intentionally introduced. This research involves a model of the considered solid material containing voids. To determine the dynamic behavior of such a system, the Gibbs–Appell (GA) method is used to obtain the evolution equations, as an alternative to Lagrange's classical description. The proposed method can be applied to any mechanical system consisting of materials with a micro-polar structure and voids. The study of such systems is interesting because the literature shows that even a reduce number of small voids can produce significant variations in physical behavior. The proposed method requires a smaller number of mathematical operations. To apply this method, the acceleration energy is calculated, which is then used to derive the equations. The method comes with advantages in the application to multibody systems having the mentioned properties and, in particular, in the study of robots and manipulators. Using the GA method, it is necessary to do a fewer differentiation operations than applying the Lagrange's equations. This leads to a reduced amount of computation for obtaining the evolution equations. [ABSTRACT FROM AUTHOR]

The aim of this study is to solve a practical problem encountered in the automotive industry, especially the failure of a cracked lower control arm made of al 6062 T6 material during static and crash physical tests, and to characterize the behavior of cracked parts made of aluminum materials using the fracture mechanics parameters. As a first step, we carried out a numerical study and simulation using Abaqus/CAE 2020 software and the finite element method to determine the stress concentration and load limit capacity for different car weight cases. The von Mises stress variation shows crack initiation and propagation to be in the area of the lower control arm's attachment to the vehicle platform, where stress is concentrated. These numerical results are consistent with the experimental test results found by automotive manufacturers. Also, we find that the mechanical load that can support this part is below 4900 N for good performance. In the second step, we use the results of the first section to simulate the failure of a lower control arm with a crack defect. This paper investigates the stress intensity factor KI in mode I for different lengths (L) and depths (a) of the crack in the lower control arm using the extended finite element method (XFEM) under Abaqus/CAE. For crack failure initiation and progression, we relied on the traction separation law, specifically the maximum principal stress (MAXPS) criterion. The KI factor was evaluated for the materials steel and Al 6062 T6. The results obtained from the variation of the KI coefficient as a function of crack depth (a) and the thickness (t) show that the crack remains stable even when a depth ratio (a/t = 0.8) is reached for the steel material. However, the crack in the Aluminum 6062 T6 material becomes unstable at depth (a/t = 0.6), with a high risk of total failure of the lower control arm. [ABSTRACT FROM AUTHOR]

Mechanical systems with structural symmetries present vibration properties that allow the calculation to be easier and the analysis time to decrease. The paper aims to use the properties involved by the symmetries that exist in mechanical systems for the analysis of the forced response to vibrations. Thus, the study of the properties of systems with symmetries or with identical parts is expanded. Based on a classic model, the characteristic properties that appear in this case are obtained and the advantages of using these properties are revealed. On an example consisting of a truck equipped with two identical engines, the way of applying these properties in the calculation and the resulting advantages is presented. [ABSTRACT FROM AUTHOR]

In this work, the finite element technique is employed to evaluate the effects of thermal relaxation durations on temperature, displacements, and stresses in a two-dimensional, polymeric, orthotropic, elastic medium. The problem is considered in a homogeneous, polymeric, orthotropic medium in the context of the Green and Lindsay model with two thermal relaxation times. The bounding surface of the half-space was subjected to a heat flux with an exponentially decaying pulse. Finite element techniques were used to solve the governing formulations, with eight-node isoparametric rectangular elements with three degrees of freedom (DOF) per node. The developed method was calculated using numerical results applied to the polymeric, orthotropic medium. The findings were implemented and visually shown. Finally, the results were displayed to demonstrate the differences between classical dynamic coupling (CT), the Lord–Shulman (LS) and the Green and Lindsay (GL) models.

In this work, a new model for porothermoelastic waves under a fractional time derivative and two time delays is utilized to study temperature increments, stress and the displacement components of the solid and fluid phases in porothermoelastic media. The governing equations are presented under Lord–Shulman theory with thermal relaxation time. The finite element method has been adopted to solve these equations due to the complex formulations of this problem. The effects of fractional parameter and porosity in porothermoelastic media have been studied. The numerical outcomes for the temperatures, the stresses and the displacement of the fluid and the solid are presented graphically. These results will allow future studies to gain a detailed insight into non-simple porothermoelasticity with various phases.

In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments.

The study of multibody systems with elastic elements involves at the moment the reevaluation of the classical methods of analysis offered by analytical mechanics. Modeling this system with the finite element method requires obtaining the motion equation for an element in the circumstances imposed by a multibody system. The paper aims to present the main analysis methods used by researchers, to make a comparative analysis, and to show the advantages or disadvantages offered by different methods. For the presentation of the main methods (namely Lagrange's equations, Gibbs–Appell's equations, Maggi's formalism, Kane's equations, and Hamilton's equations) a unified notation is used. The paper provides a critical evaluation of the studied applications that involved some of these methods, highlighting the reason why it was decided to use them. Also, the paper identifies potential research areas to explore. [ABSTRACT FROM AUTHOR]

The purpose of this study is to provide a method to investigate the effects of thermal relaxation times in a poroelastic material by using the finite element method. The formulations are applied under the Green and Lindsay model, with four thermal relaxation times. Due to the complex governing equation, the finite element method has been used to solve these problems. All physical quantities are presented as symmetric and asymmetric tensors. The effects of thermal relaxation times and porosity in a poro-thermoelastic medium are studied. Numerical computations for temperatures, displacements and stresses for the liquid and the solid are presented graphically.

The aim of this paper is to present some important practical cases in the analysis of the creep response of unidirectional fiber-reinforced composites. Some of the currently used models are described: the micromechanical model, homogenization technics, the Mori–Tanaka method, and the finite element method (FEM). Each method was analyzed to determine its advantages and disadvantages. Regarding the accuracy of the obtained results, comparisons are made with experimental tests. The methods presented here are applied to carbon-fiber-reinforced composites, but these considerations can also be applied to other types of composite materials. [ABSTRACT FROM AUTHOR]

An interesting feature that appears in the thermoelastic interaction in an orthotropic material containing cylindrical cavities is addressed in this study. For this purpose, the Finite Element Method is applied to analyze a generalized thermoelasticity theory with a relaxation time. For the development of the model, a thermal conductivity that is dependent on the temperature of the orthotropic medium was considered. The boundary condition for the internal surface of a cylindrical hollow is defined by the thermal shocks and the traction on the free surface. The nonlinear formulations of thermoelastic based on thermal relaxation time in orthotropic mediums are abbreviated using the Finite Element Method. The nonlinear equations without Kirchhoff's transformations are presented. The results are graphically represented to demonstrate how changing thermal conductivity affects all physical values. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to study the impact of delay times in a poro-elastic medium using the finite element approach and the three-phase lag thermo-elastic theory. The governing equations were obtained for a three-phase lag model with six delay times. Consideration was given to a one-dimensional application of a poro-elastic half-space. Because of the complex form of the basic equations, the finite element approach was used to solve this problem. Asymmetric and symmetric tensors were used to represent all of the physical quantities. The numerical results were presented in graphical form. The effects of porosity and delays were introduced. Finally, the results were plotted to show the difference between the three-phase delay (TPL) and the Green−Naghdi with and without energy dissipation (GNIII) models. [ABSTRACT FROM AUTHOR]

In this work, the finite element technique is employed to evaluate the effects of thermal relaxation durations on temperature, displacements, and stresses in a two-dimensional, polymeric, orthotropic, elastic medium. The problem is considered in a homogeneous, polymeric, orthotropic medium in the context of the Green and Lindsay model with two thermal relaxation times. The bounding surface of the half-space was subjected to a heat flux with an exponentially decaying pulse. Finite element techniques were used to solve the governing formulations, with eight-node isoparametric rectangular elements with three degrees of freedom (DOF) per node. The developed method was calculated using numerical results applied to the polymeric, orthotropic medium. The findings were implemented and visually shown. Finally, the results were displayed to demonstrate the differences between classical dynamic coupling (CT), the Lord–Shulman (LS) and the Green and Lindsay (GL) models. [ABSTRACT FROM AUTHOR]

• Displacements, microdeformations, temperature and microtemperatures are coupled in a multiphysics process. • Existence, uniqueness and continuous dependence results are shown for the mathematical model. • The plane strain problem is studied by the finite element method. In this study we formulate the mixed initial boundary value problem for a dipolar thermoelastic material whose micro-particles possess microtemperatures. Then this mixed problem is transformed in a Cauchy problem attached to a temporally equation of evolution on a specific Hilbert space, which will be suitably chosen. As such, we will be able to use certain results specific to the theory of the semigroups of contractions in order to obtain the existence and uniqueness of the solution for our problem. The theory of semigroups also facilitates our approach regarding the continuous dependence of the solution upon initial data and loads. Finally, we reduce our model to the isotropic case and perform numerical simulations for the corresponding system of partial differential equations by means of the finite element method. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the stress and strain states appearing in the elbow of a tube, such as those commonly used in a city's water supply network. The stress field is characterized by the fact that there is a significant stress increase when compared to a straight tube. As a result, the strength of such an elbow must be investigated and guaranteed for such a network to be well designed. A practical solution used is to anchor the elbow in a massive concrete block. The paper compares the stress field that occurs in the elbow when it is free, buried in the ground, and when it is anchored in a massive concrete block. Furthermore, we investigate how a crack appears and propagates in the elbow. This happens especially for the elbow buried in the ground where the stress and strain are higher than when the elbow is anchored in concrete. The results obtained can be used in the current practice in the case of water supply networks made by high-density polyethylene pipes. [ABSTRACT FROM AUTHOR]

Engineering practice imposes an increased rigidity of mechanical elements that are parts of machinery or equipment used in practice. Circular plates are such elements, especially used in many common applications, which is why the increase in mechanical properties of circular plates in engineering is connected with the weight optimization problem. The paper makes a study of such a composite plate, proposes and validates a constructive solution capable of increasing the stiffness of this piece. The finite element method is used for the composite panel analysis, and experimental measurements allow us to take information concerning of the magnitude of this rigidity. [ABSTRACT FROM AUTHOR]

Composite-based polymer materials are manufactured in a wide variety of types with different compositions, structures, geometries, and topological descriptions. Among these, micropolar materials with voids have become increasingly studied in the literature. This paper establishes the equations of motion for such a material for the purpose of dynamic analysis via the finite element method (FEM). The Euler–Lagrangian formalism, based on the expressions of kinetic energy, potential energy, and mechanical work, is used. Hence, it is possible to study the dynamic response of such a system in the most general configuration case. The choice of the shape functions will determine the matrix coefficients for each particular case. An application illustrates the presented results. [ABSTRACT FROM AUTHOR]

The paper studies the vibration response of an elastic solid that has geometric symmetries. These determine special properties of the equations of motion of such a system, presented in the case of a cylindrical body (hollow cylinder). The properties of the eigenvalues and eigenmodes of these systems are theoretically established. A validation of these results is made using the finite element method. The use of the obtained results can lead to an easing of the vibration analysis of such a system and, consequently, to the decrease of the cost related to the design and manufacture of such a structure. The properties presented and demonstrated in the paper can simplify the numerical calculation and experimental verifications of such a structure. Serving these symmetries, the computation cost decrease substantially and will depend not in the number of the identical parts. [ABSTRACT FROM AUTHOR]

In the manufacture of commercial trucks, used in oil installations or the army, two identical engines are used on a single chassis, whose power is summed by a gearbox, a compact metal construction, which must meet multiple operating requirements. The paper studies the behavior of such an adding box, currently used in manufacturing, and an improved, welded solution that produces less noise and has a lower weight. The finite element method is used for modeling the gearbox in order to analyze stresses and strains and obtain a modal analysis of the system. The results obtained from the calculation are then verified by experimental measurements. The two versions are analyzed in parallel to highlight the advantages of the second version. [ABSTRACT FROM AUTHOR]

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton's equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method. [ABSTRACT FROM AUTHOR]

The main method used to determine the equations of motion of a multibody system (MBS) with elastic elements is the method of Lagrange's multipliers. The assembly of equations for the whole system represents an important step in the elastodynamic analysis of such a system. This paper presents a new method of approaching this stage, by applying Maggi's equations. In this way, the links that exist between the finite elements and the connections that exist between different bodies of the MBS system are conveniently taken into account, each body having a distinct velocity and acceleration field. Although Maggi's equations have been used, sporadically, in some applications so far, we are not aware that they have been used in the study of elastic systems using the finite element method. Finally, an algorithm is presented that uses the Maggi formalism to obtain the equations of motion for an MBS system. [ABSTRACT FROM AUTHOR]