Article
Mathematics, Applied
Bienvenido Barraza Martinez, Robert Denk, Jonathan Gonzalez Ospino, Jairo Hernandez Monzon, Sophia Rau
Summary: This paper considers a transmission problem for a system of a thermoelastic plate with (or without) rotational inertia term coupled with a membrane with different variants of damping. The well-posedness of the problem, higher regularity of the solution, and the asymptotic behavior of the solution are proven, depending on the damping and on the presence of the rotational term.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Yajing Zhang, Lujuan Liu
Summary: In this paper, the stabilization problem of a 1D coupled string-riser system with partial frictional damping is considered. It is shown that the coupled system is not exponentially stable, but polynomial decay rates for the energy functionals are obtained using a semigroup approach combined with the multipliers technique. The results also demonstrate that simultaneous damping on both the string and riser equations leads to exponential stability, while damping on either the string or riser equation alone results in polynomial stability.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Jian Jiang, Wenjun Liu
Summary: In this paper, we study a coupled system involving fluid and thermoelastic plate. The heat effects are modeled using Cattaneo's law, which introduces a second sound effect. We prove the existence of a unique global mild solution for the coupled system. Additionally, we construct a second-order energy to control the term ||del theta||L-2(Gamma 0), leading to exponential decay of the solutions.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics, Applied
Aissa Guesmia, Mohammad Kafini, Nasser Eddine Tatar
Summary: This article investigates a Timoshenko system coupled with heat equations modeled by Cattaneo's law, where the coupling is through transverse displacement. The authors design a feedback control method at the base to stabilize the system, and prove stability results using the multiplier technique.
APPLICABLE ANALYSIS
(2023)
Article
Thermodynamics
Ahmed Keddi, Salim A. Messaoudi, Mohamed Alahyane
Summary: In this work, we analyze the well-posedness and asymptotic stability of a linear thermoelastic Timoshenko system that is free of second spectrum, with Cattaneo's law governing the heat conduction. We provide a detailed proof of the well-posedness using semigroup theory, and establish the exponential stability of the system regardless of the coefficients. In addition, we validate our theoretical findings through numerical tests.
JOURNAL OF THERMAL STRESSES
(2023)
Article
Mathematics, Applied
Xiaoyu Fu, Hualei Zhang, Xianzheng Zhu
Summary: This paper investigates the energy decay for solutions of the weakly coupled dissipative Schrodinger system. It is shown that under certain assumptions about the damping and coupling terms, sufficiently smooth solutions of the system decay logarithmically with mixed boundary conditions.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Houssem Eddine Khochemane
Summary: This article examines a one-dimensional thermoelastic porous system with microtemperatures. Using the energy method, it is demonstrated that in the case of zero thermal conductivity, the dissipation caused by microtemperatures alone is strong enough to result in exponential stability, regardless of the system's wave speeds or coefficients. This new result improves upon previous findings in the literature.
ACTA APPLICANDAE MATHEMATICAE
(2021)
Article
Mathematics, Applied
Afaf Ahmima, Abdelfeteh Fareh
Summary: In this paper, we investigate a porous thermoelastic system with microtemperature and establish well posedness using Hille-Yosida theorem and Galerkin method. Additionally, we demonstrate through the multiplier method that the dissipation caused solely by the gradient of microtemperature can exponentially stabilize the system. Our findings improve upon previous research by Apaara (J Therm Stress 42:265-278, 2019) and Santos et al. (Acta Appl Math 151: 1-26, 2017), and extend the results of Apalara (Q J Mech Appl Math 70: 363-372, 2017) and Santos et al. (J Diff Equ 253: 2715-2733, 2012) to the case of micro-thermal dissipation.
RICERCHE DI MATEMATICA
(2023)
Article
Mathematics, Applied
J. R. Fernandez, R. Quintanilla
Summary: The study investigates the system of equations determining linear thermoelastic deformations of dielectrics within the MGT theory, focusing on the cases of rigid solid, thermoealstic situations, and one-dimensional exponential decay of solutions. It demonstrates the existence and stability of solutions in these scenarios.
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
(2021)
Article
Thermodynamics
Hamza Zougheib, Toufic El Arwadi, Rodrigo L. R. Madureira, Mauro A. A. Rincon
Summary: Researchers have been interested in the stabilization of Timoshenko systems with dissipative features for many years. Numerous studies have been conducted on Timoshenko systems under various damping effects. This study analyzes a one-dimensional thermooelastic Timoshenko type system in the second frequency spectrum, where the assumption of equal wave speed is not required for exponential decay. The study improves previous results by demonstrating exponential stability without assuming equal wave velocities.
JOURNAL OF THERMAL STRESSES
(2023)
Article
Mathematics, Applied
Hualei Zhang
Summary: This paper studies the longtime behavior of the weakly coupled Euler-Bernoulli plate system with one structural damping. The energy decay rate of the system under certain conditions is analyzed.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Antonio Magana, Marc Magana, Ramon Quintanilla
Summary: This study investigates antiplane shear deformations for isotropic and homogeneous strain gradient mixtures of the Kelvin-Voigt type in a cylinder. The aim is to analyze the behavior of solutions with respect to the time variable when a dissipative structural mechanism is considered. Three different cases are studied, and existence and uniqueness of solutions are proven for each case. Exponential decay of solutions is obtained in the hyperviscosity and viscosity cases, and is also expected when dissipation is generated by the relative velocity.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Computer Science, Interdisciplinary Applications
Moncef Aouadi, Maria Ines M. Copetti
Summary: The study focuses on the dynamic behavior of a thermoelastic diffusion beam with rotational inertia and second sound. The system of equations combines a hyperbolic equation with four parabolic equations to address the physical paradox of infinite propagation speeds in classical heat and mass diffusion laws. The exponential stability of solutions and a finite element approximation are proposed to tackle the mathematical and numerical challenges posed by the system.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
A. J. A. Ramos, A. D. S. Campelo, D. S. Almeida Junior, M. M. Freitas, R. C. Barbosa
Summary: In this paper, a system composed of two parallel wave equations and a heat diffusion equation is studied. Theoretical results on the existence and uniqueness of solution are presented, and the exponential stabilization of the associated semigroup is proved. The semi-discrete problem in finite differences is analyzed, and the energy method is introduced for the first time in the literature to prove the exponential stabilization of the corresponding semi-discrete system. Finally, a fully discrete finite difference scheme is proposed, which combines explicit and implicit integration methods, and numerical simulations are conducted to illustrate the theoretical results.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Hamed Abderrahmane Bouraoui, Abdelhak Djebabla, Toufic El Arwadi, Mohamed Haiour
Summary: This study numerically and theoretically investigates a thermoelastic Bresse system with heat conduction based on the theories of Green and Naghdi. The study establishes the existence and uniqueness of solutions as well as exponential stability regardless of the system's parameters. It also presents a finite element approximation and shows the discrete energy decay. Numerical results with an error estimate based on additional regularity of the solution are provided.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Zhuangyi Liu, Ramon Quintanilla, Yang Wang
Summary: This paper considers the mathematical model of a three-phase-lag thermoelastic plate and presents analyticity and exponential stability results for the associated C-0 semigroup under certain conditions. The semigroup retains analyticity even when tau(nu) < K*tau(q), but instability of the solution is proven using the Routh-Hurwitz rule.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Jacobo Baldonedo, Jose R. Fernandez, Antonio Magana, Ramon Quintanilla
Summary: In this work, a boundary-initial value problem for non-simple porous elastic materials is considered numerically. The mechanical problem is formulated as a hyperbolic linear system, and the solution is approximated using the finite element method. The numerical scheme shows linear convergence under adequate regularity conditions, as demonstrated through numerical simulations.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2022)
Article
Mechanics
Jose R. Fernandez, Ramon Quintanilla
Summary: This paper analyzes a problem involving a mixture composed of MGT viscoelastic material and an elastic solid. It provides an existence and uniqueness result by deriving the system of equations governing the deformations of such material. The paper uses the semigroups theory of linear operators and proves the exponential decay of solutions while introducing an extra assumption, and also demonstrates the impossibility of location.
Article
Mathematics, Applied
Aissa Guesmia, Jaime E. Munoz Rivera, Mauricio A. Sepulveda Cortes, Octavio Vera Villagran
Summary: This paper studies the well-posedness and stability of structures with interfacial slip and two infinite memories affecting transverse displacement and rotation angle. A unique solution with regularity properties is proven for a large class of kernels, showing convergence to zero at infinity without restrictions on parameter values. Numerical analysis of theoretical results will also be provided.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Jacobo Baldonedo, Jose R. Fernandez, Ramon Quintanilla
Summary: This paper numerically investigates porosity problems with three different dissipation mechanisms, analyzing the root behavior for each case. Fully discrete approximations are introduced using the finite element method and Newmark-beta scheme, with numerical results showing the energy evolution depending on the viscosity coefficient.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Noelia Bazarra, Jose R. Fernandez, Ramon Quintanilla
Summary: In this work, a numerical analysis is conducted on a problem involving a mixture of MGT viscoelastic solid and an elastic solid. The problem is formulated as a linear system with two coupled hyperbolic equations. Fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. Some one-dimensional numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the solution.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Jacobo Baldonedo, Jose R. Fernandez, Ramon Quintanilla
Summary: In this study, we investigated three different dissipation mechanisms in the Moore-Gibson-Thompson porosity. We proved the existence of a unique solution for all three cases and analyzed the resulting point spectrum. Our findings showed an exponential energy decay for the first case, while only a polynomial decay was observed for the second and third cases. Numerical simulations were presented to illustrate the behavior of the discrete energy for each case.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2022)
Article
Mathematics
Noelia Bazarra, Jose R. Fernandez, Ramon Quintanilla
Summary: In this work, a numerical study was conducted on a dynamic thermoviscoelastic problem involving micropolar materials. The finite element method and implicit Euler scheme were used for fully discrete approximations. Through proving stability properties and error estimates, it was concluded that the linear convergence is achieved under certain regularity conditions.
ELECTRONIC RESEARCH ARCHIVE
(2022)
Article
Mathematics
Leonardo H. Alejandro Aguilar, Jaime E. Munoz Rivera, Pedro Gamboa Romero
Summary: In this work, we investigate the modeling of systems with memory that involve a mixture of n materials. The results indicate that the stability of the corresponding semigroup is determined by the inclusion of the imaginary axis in the resolvent set of the infinitesimal generator. This finding further suggests the absence of polynomial stability for the corresponding semigroup.
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
(2022)
Article
Mathematics, Applied
Noelia Bazarra, Jose R. Fernandez, Ramon Quintanilla
Summary: This paper investigates the energy decay of problems involving domains with radial symmetry in three different settings: strong porous dissipation and heat conduction, weak porous dissipation and heat conduction, and poro-thermoelasticity with microtemperatures. Exponential energy decay is shown in all three problems. Furthermore, finite element simulations are used to numerically demonstrate this behavior for each problem.
ACTA APPLICANDAE MATHEMATICAE
(2022)
Article
Mathematics, Applied
N. Bazarra, J. R. Fernandez, R. Quintanilla
Summary: In this paper, a numerical study is conducted on a thermoelastic problem in the Moore-Gibson-Thompson theory, with dielectric effects included. The results show that by adding a viscous term and using the finite element method and implicit Euler scheme, discrete stability properties and a priori error estimates can be obtained.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Jose R. Fernandez, Ramon Quintanilla
Summary: In this work, the spatial decay for high-order parabolic (and combined with a hyperbolic) equation in a semi-infinite cylinder is considered. A Phragmen-Lindelof alternative function is proven, and by applying appropriate inequalities, it is shown that the decay follows a square distance decay to the bounded end face of the cylinder. The thermoelastic case is also studied, where heat conduction is modeled using a high-order parabolic equation. New relevant results are obtained by considering appropriate functions that have not been considered before.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Bruna T. S. Sozzo, Jaime E. M. Rivera
Summary: In this article, the vibrations of a beam composed of a thermoelastic material and a simply elastic material are studied using the Euler-Bernoulli model. The main result shows that the associated semigroup is differentiable and possesses important properties such as being of Gevrey class 12, exponentially stable, and having a regularizing effect on the initial data.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
L. Liverani, Y. Mammeri, V. Pata, R. Quintanilla
Summary: This article discusses the well-posedness of the Whitham-Broer-Kaup system on bounded domains. It provides conditions for the existence and uniqueness of solutions, depending on the sign of the parameter x = alpha - beta(2). An explicit representation of solutions is given when x > 0, while uniqueness in the class of strong solutions is guaranteed for x <= 0, with sufficient conditions for exponential instability.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
(2023)
Article
Mathematics, Applied
Marco Campo, Maria I. M. Copetti, Jose R. Fernandez, Ramon Quintanilla
Summary: In this work, a thermoelastic problem in the dual-phase-lag theory with two temperatures is studied from both variational and numerical perspectives. Existence and uniqueness results are proved, and numerical analysis leads to the conclusion of linear convergence of the algorithm.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mechanics
Zhiqiang Meng, Xu Gao, Hujie Yan, Mingchao Liu, Huijie Cao, Tie Mei, Chang Qing Chen
Summary: This paper presents a cage-shaped, self-folding mechanical metamaterial that exhibits multiple deformation modes and has tunable mechanical properties, providing multifunctional applications in various fields.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Hasan Murat Oztemiz, Semsettin Temiz
Summary: Sandwich panel composites have various applications and their mechanical behavior and performance depend on material properties and geometry. The load-carrying capacity of S-core composite sandwich panels increases with the increase of the core wall thickness, but decreases with the increase of the core height.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Yang Sun, Wei Zhang, Weipeng Hu, Mabao Liu
Summary: The study presents a novel computational framework to investigate the effect of graphene percolation network on the strength-ductility of graphene/metal composites. It utilizes the Cauchy's probabilistic model, the field fluctuation method, and the irreversible thermodynamics principle.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Elaheh Kazemi-Khasragh, Juan P. Fernandez Blazquez, David Garoz Gomez, Carlos Gonzalez, Maciej Haranczyk
Summary: This study explores group interaction modelling (GIM) and machine learning (ML) approaches for predicting thermal and mechanical properties of polymers. ML approach offers more reliable predictions compared to GIM, which is highly dependent on the accuracy of input parameters.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Yafei Yin, Shaotong Dong, Dong Wu, Min Li, Yuhang Li
Summary: This paper investigates a bending-induced instability in sandwiched composite structures, and establishes a phase diagram to predict its characteristics. The results are of great significance in understanding the physical mechanisms of bending instability and providing design guidelines for practical applications.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Dhairya R. Vyas, Sharen J. Cummins, Gary W. Delaney, Murray Rudman, Devang V. Khakhar
Summary: In this study, multiple collisions of granules on a substrate are analyzed using Collisional Smooth Particle Hydrodynamics (CSPH) to understand the influence of impact-induced deformation on subsequent collision dynamics. It is found that the collision dynamics are dependent on the impact location and the deformation caused by preceding impacts. The accuracy of three theoretical models is also evaluated by comparing their predictions with CSPH results, and it is discovered that these models are only useful for predicting collisions at the same location repeatedly.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Sneha B. Cheryala, Chandra S. Yerramalli
Summary: The effect of hybridization on the growth of interface crack along the fiber is predicted. The study shows an enhancement in the compressive splitting strength with hybridization due to the lateral confinement effect on the interfacial crack.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Xiang-Nan Li, Xiao-Bao Zuo, Liang Li, Jing-Han Liu
Summary: A multiscale mechanical model is proposed to quantitatively describe the macro-mechanical behavior of fiber reinforced concrete (FRC) based on its multiscale material compositions. The model establishes the stiffness and strength equations for each scale of FRC and demonstrates the influence of steel fiber parameters on the mechanical properties of FRC.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Vicente Ramirez-Luis, Hilario Hernandez-Moreno, Orlando Susarrey-Huerta
Summary: In this paper, a Multicell Thin-walled Method is developed for studying the stress distributions in multimaterial beams. This method accurately obtains complex stress fields while reducing the solution time and computational cost. Validation with the finite element method confirms the accuracy of the proposed method.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Yanfeng Zheng, Siyuan Li, Jingyao Zhang, Yaozhi Luo
Summary: This study proposes an enhanced simplified model based on finite particle method (FPM) to consider the link cross-sectional size and contact in Bennett linkages. The model introduces virtual beams and contact forces to accurately simulate the real-world behavior of Bennett linkages. The proposed method is effective for dynamic analysis of large-scale deployable Bennett linkages and shows great potential.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Viktoriya Pasternak, Heorhiy Sulym, Iaroslav M. Pasternak
Summary: This paper investigates anisotropic elastic, magnetoelectroelastic, and quasicrystal solids and presents their equations of time-harmonic motion and constitutive relations in a compact and unified form. A matrix approach is proposed to derive the 3D time-harmonic Green's functions for these materials. The effects of phason field dynamics on the phonon oscillations in quasicrystals are studied in detail. The paper provides a strict proof that the eigenvalues of the time-harmonic magnetoelectroelaticity problem are all positive. It also demonstrates the application of the obtained time-harmonic Green's functions in solving boundary value problems for these materials using the derived boundary integral equations.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Jan Tomec, Gordan Jelenic
Summary: This paper investigates the relationship between different formulations and contact-force models in beam-to-beam contact mechanics. It specifically addresses the recently developed mortar method and develops its variant based on the penalty method. The developed elements are tested using the same examples to provide an objective comparison in terms of robustness and computational cost.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Paulo Teixeira Goncalves, Albertino Arteiro, Nuno Rocha, Fermin Otero
Summary: This work presents a novel formulation of a 3D smeared crack model for unidirectional fiber-reinforced polymer composites based on a stress invariant approach for transverse yielding and failure initiation. The performance of the model is evaluated using monotonic and non-monotonic damage evolution, verified with single element tests and compared with experimental results.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Hanbin Yin, Yinji Ma, Xue Feng
Summary: This paper investigates the peeling behavior of a viscoelastic film bonded to a rigid substrate and establishes a theoretical peeling model. The study reveals three typical relationships between the peeling force and peeling velocity, which depend on the viscous dissipation within the film and the rate-dependent adhesion at the interface. Additionally, factors such as film thickness, interfacial toughness, and interfacial strength are identified as influencing the steady-state peeling force.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
Article
Mechanics
Peter Noe Poulsen, John Forbes Olesen
Summary: Finite Element Limit Analysis (FELA) is increasingly used to calculate the ultimate bearing capacity of structures made of ductile materials. This study presents a consistent and general weak formulation based on virtual work for both the lower and upper bound problem, ensuring uniqueness of the optimal solution. A plane element with linear stress variation and quadratic displacement field is introduced, showing good results for load level, stress distribution, and collapse mechanism even for coarse meshes in verification and reinforced concrete examples.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2024)
