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УДК 539.3
Исследование термомеханического изгиба многослойных функционально-градиентных пластин с использованием комбинированной 2D-модели интегральной пластины
H. Belarbi1, B. Boucham1, F. Bourada1, A. Kaci1,2, M. Bourada1, A. Tounsi1,3,4
1 Университет Сиди-Бель-Аббеса, Сиди-Бель-Аббес, 22000, Алжир 2 Университет Саиды им. доктора Тахара Мулая, Саида, 20000, Алжир 3 Университет нефти и полезных ископаемых им. короля Фахда, Дахран, 31261, Саудовская Аравия 4 Ливано-Американский университет, Библ, Ливан
В работе исследовано изгибное поведение многослойной функционально-градиентной пластины Ti-6A1-4V/ZrO2 при термомеханическом нагружении в рамках интегральной теории сдвиговой деформации. Используемая формулировка обеспечивает параболическое распределение напряжений поперечного сдвига без необходимости введения дополнительных коэффициентов. Рассмотрены различные модели многослойных пластин с различной толщиной слоев из разных типов материалов. Предполагается непрерывное и плавное изменение свойств функционально-градиентных слоев, которое описывается экспоненциальной и степенной функциями. Основные дифференциальные уравнения системы получены с помощью принципа виртуальной работы и подхода Навье. Для проверки точности предлагаемой модели проведены сравнения. Представлены различные параметрические примеры, иллюстрирующие влияние геометрии, размеров, типа многослойной пластины, а также неоднородности материала на статическое изгибное поведение исследуемой структуры.
Ключевые слова: многослойная функционально-градиентная пластина, неоднородность, четырехпа-раметрическая модель интегральной пластины, термомеханический изгиб, прогиб и напряжения, принцип виртуальной работы, подход Навье
DOI 10.55652/1683-805X_2024_27_3_178-182
Investigation on thermomechanical bending of functionally graded sandwich plates using a novel combined 2D integral plate model
H. Belarbi1, B. Boucham1, F. Bourada1, A. Kaci1,2, M. Bourada1, A. Tounsi1,3,4,5
1 Faculty of Technology, University of Sidi Bel Abbes, Algeria 2 Faculty of Technology, Dr. Tahar Moulay University of Saida, Saida, 20000, Algeria
3 Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals,
Dhahran, 31261, Saudi Arabia
4 Department of Civil and Environmental Engineering, Lebanese American University, Byblos, Lebanon
5 Interdisciplinary Research Center for Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia
This study presents the flexural analysis of Ti-6A1-4V/ZrO2 functionally graded (FG) sandwich plates under combined thermal and mechanical loading via exponential-cubic-sinusoidal integral shear deformation theory. The current formulation used in the modeling provides a parabolic distribution of transverse shear stresses without requiring additional factors in the formulation. Various sandwich plate models with different layer thicknesses and material types are considered. The FG layers vary continuously and smoothly according to exponential and power-law functions. The governing differential equations of the system are derived and solved analytically using the virtual work principle and Navier's approach. Benchmark comparisons are performed to validate and show the accuracy of the proposed model. Various parametric examples are presented to illustrate the effect of the geometry, dimensions, FG sandwich type and material gradient on the static flexural response of the studied structure.
Keywords: FG sandwich plate, gradient, four-variable integral plate model, thermomechanical bending, deflection and stresses, virtual work principle, Navier's approach
© Belarbi H., Boucham B., Bourada F., Kaci A., Bourada M., Tounsi A., 2024
1. Introduction
Sandwich structures occupy an important place in the manufacture of composite parts. They are present in practically all fields of application. These structures are fabricated by gluing or welding two thin skins on a lighter-weight core with weaker mechanical characteristics, which maintains spacing between the skins and transfers mechanical loads by shear from one skin to the other. Such a structure has very high strength/mass and stiffness/mass ratios in bending. There are various models of sandwich structures. The most recognized and widely used one is a sandwich structure with three homogeneous layers (core and face sheets). A growing trend is the introduction of advanced composite materials in the manufacture of sandwich plates. The incorporation of FG and sandwich structures in the construction sectors has increased considerably to overcome the problem of conventional structures and materials related to their low resistance to high temperatures [1-3]. We find in the literature sandwich plates with faces made of functionally graded material (FGM) and an isotropic core [4-6] or with homogeneous face sheets and an FG core [6-9].
Numerous studies of sandwich panels with FGM face sheets have been made with regard to their use in the design of engineered structures. Analysis of the thermal buckling response of sandwich plates with two FGM faces and a homogeneous central core was presented in [5] using the theory of sinusoidal shear strain. Natarajan and Ganapathi [10] analyzed the static bending and vibrational response of two types of FGM sandwich plates composed of homogeneous face sheets with an FGM core and FGM face sheets with a homogeneous hard core. The analysis was performed using a model of higher-order shear deformation theory (HSDT) and a QUAD-8 shear flexible element. A higher-order theory of shear deformation by thickness stretching was applied by Neves et al. [11] to analyze various behaviors of two FG sandwich models. An analytical model for the response analysis of FG sandwich structures with an isotropic middle layer was proposed by Thai et al. [12] with taking into account the boundary conditions. The dynamic and static behaviors of 2D FG and isotropic sandwich structures were studied by Nguyen et al. [13] for fully FG plates and two sandwich models, one with an FG core and the other with FGM skins. Akavci [14] presented a new theory of quasi-3D shear and normal deformation of plates with a hyperbolic warping function for various responses (stabil-
ity, static, dynamic) using FG sandwich plates with an FG core or FG face sheets.
Thermomechanical behavior is due to the combination of mechanical and thermal loads simultaneously. This type of loading is common in structures used in the aircraft, ship building, marine industries, automotive and civil engineering, and it is necessary to examine their responses under such loading conditions. There are few works that study the bending behavior of graded sandwich structures under various types of load (mechanical/thermal). Zenkour and Al-ghamdi [15] investigated the flexural behavior of 2D graded sandwich structures with a ceramic core and FG skins subjected to thermomechanical loads. Wang and Shen [16] studied the nonlinear behavior (buckling, vibration, bending) of an FG sandwich subjected to thermal environment and resting on an elastic foundation.
Some authors are also interested in crack and fracture problems in the structures. For example, Hiran-naiah et al. [17] investigated the thermomechanical dynamic response and stability of imperfect FG sandwich plates with geometric discontinuity and physical neutral surface. Kanu et al. [18] discussed the effect of fracture on the mechanical behavior of FG structures and materials. Based on the finite element method, Abbas and Razavi [19] examined the ther-moelastic response of a fiber-reinforced anisotropic material by considering a crack problem. Petrova and Schmauder [20] modeled and studied the thermome-chanical fracture of an FG structure taking into account multiple crack interaction. Abouelregal et al. [21] proposed a generalized heat equation for a temperature-dependent nonsimple thermoelastic cylinder with including the Caputo-Fabrizio fractional derivative. Based on an extension of the Fourier approach, the Atangana-Baleanu operator, and a novel nonlocal single core, Atta [22] investigated a thermoelastic medium with a spherical cavity within the framework of partial elastic thermal diffusion theory. Based on the Hermite-Ritz method and classical beam theory, Jena et al. [23] studied the effect of the presence of an elastic substrate on the vibrational characteristics of an imperfect FG beam, taking into account the small scale effect via bi-Helmholtz nonlocal elasticity. Many studies are devoted to the investigation of the thermal and thermomechanical response [24, 25].
The development of different theories to predict the behavior of FG structures has increased because of their wide use in the field of engineering structures. There are several plate theories developed to analyze FG materials. The classical model (classical
plate theory (CPT)) is an extension of the Kirchhoff-Love hypothesis for slender and thin isotropic structures [26-28]. However, it cannot be applied for short and thick FG structures as it takes no account of the shear effect. The second model proposed by Reiss-ner-Mindlin is called the first-order shear deformation theory (FSDT). The accuracy of its solutions depends heavily on the prediction of the best estimates for the shear correction factors to correct uniform shear stresses across the entire thickness of the structure [29-32]. The CPT and FSDT theories were shown to be inadequate for computing accurate solutions of FG plates. Another option is the refined higher-order shear deformation theory (HSDT) [3340]. This model does not need any correction factors and can more accurately predict the behavior of moderate and thick FG plates. However, a larger number of unknown variables in the displacement field in HSDT leads to higher computational costs.
Here we develop a combined four-variable integral model with the aim to reduce the number of unknown variables and computational cost, to obtain accurate results, and to process several types of FG sandwich plates. The thermomechanical bending response of 2D FG sandwich structures is investigated analytically using the model.
The proposed combined exponential-cubic-sinusoidal integral shear deformation theory contains only four variable functions, and therefore its governing equations are reduced compared to other similar solutions. The model takes into account the transverse shear deformation effect in a parabolic manner along the thickness direction and satisfies the stress-free boundary conditions on nonplate surfaces without any requirement for shear correction factors. The equations of stability are derived from the virtual work principle. Navier's technique is applied to obtain the closed form. The numerical values of displacements and stresses obtained with the current theory are verified and compared with various existing solutions. Finally, the effects of certain parameters, such as the load type (transversal and thermal), volume fraction, thermal load, layer-to-thickness ratio and other dimensions, on the sandwich structure response are studied.
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Received 21.11.2023, revised 31.12.2023, accepted 10.01.2024
This is an excerpt of the article "Investigation on Thermomechanical Bending of Functionally Graded Sandwich Plates Using a Novel Combined 2D Integral Plate Model". Full text of the paper is published in Physical Mesomechanics Journal. DOI: 10.1134/S1029959924040118
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Сведения об авторах
Hachemi Belarbi, Dr., University of Sidi Bel Abbes, Algeria, Belarbi22Hachemi@yahoo.com Belhadj Boucham, Prof., University of Sidi Bel Abbes, Algeria, Belhadj-BC@gmail.com Fouad Bourada, Prof., University of Sidi Bel Abbes, Algeria, bouradafouad@yahoo.fr
Abdelhakim Kaci, Prof., University of Sidi Bel Abbes; Université Dr. Tahar Moulay, Algeria, Kaci-univ20@yahoo.fr Mohamed Bourada, Prof., University of Sidi Bel Abbes, Algeria, med_bourada@yahoo.fr
Abdelouahed Tounsi, Prof., University of Sidi Bel Abbes, Algeria; King Fahd University of Petroleum and Minerals, Saudi Arabia; Lebanese American University, Lebanon, tou_abdel@yahoo.com
