Abstract
The recently developed mode-based posteriori error estimation (Jung et al. 2022) exhibits excellent predictive capability as an error estimator. However, since its implementation requires trained network through deep learning, we focus on a simple mode-based error estimator for general use, without the network. In this paper, we propose a new posteriori error estimation using the simplified mode-based finite element formulation for the analysis of plane stress and plane strain problems. The proposed posteriori error estimation simply predicts an error calculated by the difference between the direct and recovered solutions of finite element analysis (FEA). To simply calculate the accurate recovered solution, geometry dependent bending modes and volumetric locking treatment are adopted. We demonstrate the predictive performance of the proposed error estimator through various numerical examples with 4-node finite elements.
Key Words
4-node finite element; bending mode; finite element analysis; mode-based formulation; plane stress and plane strain problems; posteriori error estimation
Address
Seunghwan Park: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
Jaeho Jung: School of Mechanical Engineering, Chungbuk National University, 1 Chungdae-ro, Seowon-Gu, Chungbuk 28644, Republic of Korea
Abstract
Magneto-electro-elastic (MEE) materials, renowned for their multi-field coupling effects and exceptional energy interconversion capabilities, have become pivotal in advanced technologies such as aerospace, geological exploration, and biomedical engineering. Despite their broad applications, the nonlinear dynamic behavior of geometrically imperfect MEE cylindrical shells subjected to simultaneous axial motion and low-velocity impacts remains unexplored. To address this gap, this study establishes a comprehensive theoretical framework. First, the displacement field is formulated using Love's thin-shell theory, explicitly incorporating initial geometric imperfections. Next, Maxwell's equations are integrated into the constitutive relations, yielding a coupled magneto-electro-elastic model that accounts for material imperfections. The governing equations are then derived via Hamilton's variational principle and solved numerically through the Galerkin method combined with the fourth-order Runge-Kutta algorithm. Furthermore, rigorous comparative analysis and convergence verification in this study ensure the reliability of the results. Eventually, parametric studies are conducted to elucidate the effects of shell geometry, impactor characteristics, and environmental factors on the dynamic response, specifically focusing on the evolution of contact force and profiles of central deflection. Although this study provides new theoretical insights into low-velocity impact issues in aerospace and related fields, its applicability to high-velocity impact scenarios remains to be verified.
Key Words
axial motion; cylindrical shell; low-velocity impact; magnetoelectric-elastic materials
Address
Yi-Li Dong and Gui-Lin She: College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044, China
Abstract
In this study, nonlinear bending, buckling, free- and forced vibrations of thin penta-graphene plates resting on elastic foundations were investigated in deterministic and stochastic environments. The thin plates undergo small strain conditions described by the classical plate theory and extended Hamilton principles. The Bubnov-Galerkin method and fourth-order Runge-Kutta methods were applied for explicit closed-form solutions of nonlinear static and dynamic behaviors of penta-graphene plates considering geometry imperfection. Effects of elastic foundations, geometry imperfection, and excitation amplitudes and frequencies on deterministic bending, buckling, and vibration of penta-graphene plates were examined. For analyzing the plate in stochastic environments, randomness of material properties, geometry, and elastic bases were sampled using Monte Carlo simulations. Stochastic bending, buckling, and vibration analysis of penta-graphene plates were performed using theoretical solutions and statistical methods. Geometry ratios of penta-graphene plates have strong effects on their stochastic bending behaviors, elastic foundations have strong effects on stochastic buckling behaviors, while both geometry ratios and vibration
amplitudes show strong effects on the backbone and forced-response curves of penta-graphene plates.
Key Words
bending and buckling; dynamics; free vibration; penta-graphene plates; stochastic analysis
Address
Minh-Chien Trinh: Department of Mechanical System Engineering, Jeonbuk National University, 567, Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do, 54896, Republic of Korea; Department of Civil and Environmental Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, 05006, Republic of Korea
Hyungmin Jun: Department of Mechanical System Engineering, Jeonbuk National University, 567, Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do, 54896, Republic of Korea; Graduate School of Mechanical-Aerospace-Electric Convergence Engineering, Jeonbuk National University, 567, Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do, 54896, Republic of Korea
Nguyen Dinh Duc: Faculty of Civil Engineering, VNU Hanoi, University of Engineering and Technology, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam
Seung-Eock Kim: Department of Civil and Environmental Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, 05006, Republic of Korea
Duc-Kien Thai: Department of Civil and Environmental Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, 05006, Republic of Korea
Abstract
This study is concerned with the dynamic behavior of an axially translating Bernoulli-Euler beam interacting with a stationary in-span harmonic oscillator. The governing equations for the transverse vibrations of the beam and oscillator are introduced. Approximate solutions are obtained using the Galerkin's method. Numerical results demonstrate the influence of translational velocity on the system's natural frequencies and mode shapes. The effect of the mass and stiffness parameters of the harmonic oscillator on the dynamics of the axially translating beam is extensively studied. Comparisons of the numerical results with those in existing literature show consistent overall trends. Since the studied model is not directly available in the literature, the numerical results are validated through simulations using the finite element method. This study provides a modest guide for real engineering applications by revealing the vibration characteristics of the combined system consisting of an axially translating Bernoulli-Euler beam and a harmonic oscillator.
Address
Metin Gürgöze: Faculty of Mechanical Engineering, Technical University of Istanbul, Istanbul, Türkiye
Serkan Zeren: Department of Mechatronics Engineering, Kocaeli University, Kocaeli, Türkiye
Abstract
This study examines the hygro-thermo-mechanical bending of FG nanoplates supported by varying elastic foundations. It is expected that the thickness of the materials will change, and the formulation will take into account the effects of numerous power law distributions. To minimize the number of unknowns and account for the effects of stretching, the analyses employ a quasi-3D theory. By merging Eringen's theory for nonlocal integral elasticity with a quasi-3D high-order plate theory, the equilibrium equations are obtained while accounting for the nano-size effect. Two variable factors, each represented by multiple functions, are used to model the elastic basis on which the nanoplates rest. Navier's technique is used to solve the equations for the problem of a simply supported nanoplate, and the results are obtained. The FG nano-plate's bending response is thoroughly examined in relation to the volume fraction index k, geometric attributes, elastic foundation nano size coefficient, and various temperature rise profiles. The results are compared to those reported in the academic literature.
Key Words
bending; Eringen's theory; FG nanoplates; hygro-thermo-mechanical loads; nonlinear foundation
Address
Madiha Boussalem: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Laboratoire d'Ingénierie et Sciences des Matériaux Avancés, Abbes Laghrour University, Khenchela, Algeria
Abdelhakim Bouhadra: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Abderrahmane Menasria: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Belgacem Mamen: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Salah Refrafi: Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria
S.R. Mahmoud: GRC Department, Applied College, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Abstract
In this research the bending behavior and free vibration characteristics of imperfect functionally graded (IFG) beams are examined. The investigation incorporates cases where these beams are resting on both elastic and viscoelastic foundations. It is assumed that the IFG beam's material properties change continuously with thickness in accordance with the volume percentage of its constituent parts. The study employs a refined three-variable first-order shear deformation theory to consider kinematic relations. Hamilton's principle is employed to derive equations of motion. The development of the present theory is similar to the first-order simple shear deformation theory. With the assumption that the IFG beam is simply supported, this research presents the analytical solution. In order to showcase the precision of the developed theory, comparisons are conducted between the results derived from existing theories and present results of the proposed theory. Finally, a comprehensive discussion on the effects of span-to-depth ratio, porosity volume percentage, and viscoelastic foundations is provided.
Key Words
bending; functionally graded material; porosity; vibration; viscoelastic foundation
Address
Mamia Benchohra: Département de Technologies, Institut des Sciences, Centre Universitaire Nour Bachir Bachir El-Bayadh, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Imene Laoufi: Department of Civil Engineering and Publics Works, Innovative Materials Laboratory and Renewable Energies, University of Relizane, Algeria
Amina Attia: Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, Civil Engineering Department, University of Ain Temouchent, Algeria
Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria
Abdeldjebbar Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Mechanical Engineering Department, Faculty of Science and Technology, University of Rélizane, Algeria
Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
Murat Yaylaci: Department of Civil Engineering, Recep Tayyip Erdogan University, 53100, Rize, Turkey; Turgut Kiran Maritime Faculty, Recep Tayyip Erdogan University, 53900, Rize, Turkey; Murat Yaylaci-Luzeri R&D Engineering Company, 53100, Rize, Turkey
Ayed Eid Alluqmani: Department of Civil Engineering, Faculty of Engineering, Islamic University of Madinah, Madinah, Saudi Arabia
S.R. Mahmoud: GRC Department, Applied College, King Abdulaziz University. Jeddah 21589, Saudi Arabia
