Abstract
This paper presents a novel and efficient First-Order Shear Deformation Theory (FSDT) utilizing only four unknown displacement variables to analyze the mechanical buckling behavior of functionally graded transparent (FGT) doubly curved shells, offering a significant reduction in numerical complexity compared to classical models. The study, which focuses on shells composed of Sapphire and Soda-lime glass, derives governing equations via Hamilton's principle and obtains closed-form Navier-type solutions for simply supported boundaries. Extensive parametric analyses reveal that the dimensionless critical buckling load is highly sensitive to the material gradation index k, with higher k values reducing stiffness and stability. The results demonstrate that spherical geometries provide the greatest buckling resistance due to their balanced double curvature, while biaxial loading and increasing radius-to-side ratios significantly diminish structural stability. This accurate and economical theoretical framework provides crucial insights for the design of lightweight, transparent, and high-performance structural components in modern architectural facades and advanced aerospace applications.
Address
Mohamed Soufiane Ibka: Laboratoire Signaux et Images (LSI), University of Science and Technology of Oran, Mohamed Boudiaf, Bir ELDjir, 31000, Algeria
Djilalli Mokhefi: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000, Mascara, Algeria
Aicha Bessaim: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000, Mascara, Algeria; Département de Génie Civil, Faculté d'Architecture et de G Civil, Université des Sciences et de la Technologie d
Abstract
We provide an analytical approach for antisymmetric and symmetric stability of angle-ply and cross-ply behavior of composite beam structures, exposed to mechanical forces with boundary conditions that are simply supported. A unified, refined hyperbolic model serves as the foundation for the formulation. Shear correction factors are not used; the zero traction boundary conditions are satisfied by the theory on the beam surfaces, and take into consideration the transverse shear stresses' hyperbolic distribution. The principle of minimum total potential energy is based on the governing equations. The analytical (closed-form) solutions are obtained by means of the Navier-type approach, and eigenvalue problems are solved to find critical buckling loads. Comparing some of the current findings with those found in the bibliography helps validate the current theory. In order to determine the stability behaviors of composite beams, it can be determined that the suggested theory is accurate and straightforward.
Address
Mokhtar Bouazza: Department of Civil Engineering, University Tahri Mohammed of Bechar, 08000, Bechar, Algeria; Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, Sidi Bel Abbes 2200, Algeria
Tawfiq Becheri: Department of Civil Engineering, University Tahri Mohammed of Bechar, 08000, Bechar, Algeria
Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia; Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt
Noureddin Benseddiq: Mechanics Laboratory of Lille, CNRS UMR 8107, University of Lille 1, 59655 Villeneuve d'Ascq, France
Abstract
A great number of beam theories have been developed to study the behavior of isotropic and composite beams, which can be categorized into three groups: classical beam theory (CBT), first-order shear deformation beam theory (FSDT), and higher-order shear deformation beam theories (HSDTs). The conventional HSDT displacement field involves three unknown variables. In this work, a new refined parabolic shear deformation theory (RPSDT) is applied to investigate the mechanical behavior of thick simply supported isotropic beams, considering the effects of transverse shear deformation. Anotable feature of this theory is that the number of variables is identical to that of the well-known CBT, owing to the introduction of a simple displacement field involving only two variables. In this theory, the displacement field depends only on two independent variables (w0,o) and incorporates a coefficient (k) that is dependent on the beam's geometry. The transverse shear stresses can be easily calculated from the fundamental relations of elasticity, while satisfying the condition of zero shear stress on the top and bottom surfaces of the beam. The governing differential equations and their corresponding boundary conditions are formulated using Hamilton's principle and solved through the Navier-Type solution method. The proposed computational model is applied to several examples of simply supported beams, and the obtained results are compared with those from existing higher-order shear deformation beammodels, showing good agreement. The numerical results demonstrate that the proposed approach is highly suitable for predicting themechanical behavior of isotropic beams.
Address
Nadjet Berrekheroukh: University Mustapha Stambouli of Mascara, B.P. 305, 29000, Mascara, Algeria
Kada Draiche: Department of Civil Engineering, University of Tiaret, BP 78 Zaaroura, 14000, Tiaret, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Emrah Madenci: Department of Civil Engineering, Necmettin Erbakan University, 42090, Konya, Turkey
Yasin Onuralp Özkiliç: Department of Civil Engineering, Necmettin Erbakan University, 42090, Konya, Turkey; World Class Research Center, Advanced Digital Technologies, State Marine Technical University, Saint Petersburg, Russia
Essam Althaqafi: Civil Engineering Department, College of Engineering, King Khalid University, Abha, 61421, Saudi Arabia
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
Abstract
This study evaluates the structural performance and long-term capacity of viaduct piers designed using different codes and modeling approaches, including calculations obtained from the original design documentation PTP-5, a 3D extended model of the structure with the utilization of SOFiSTiK software (PTP-5-3D), and finally a 3D model based on the Eurocode-prescribed loads (Eurocode). A comparative analysis of bending moments, axial forces, shear, and torsion reveals that Eurocode predicts higher design forces due to conservative load combinations. 3D models provide a more comprehensive representation compared to the 2D original design, as they take into account the bridge's curvature. Assessment of pier capacities after 42 years shows that mid-span piers (S3 and S4) are most critical, with reduced residual strength, whereas other piers retain sufficient capacity. Nonlinear pushover analysis of pier S4 indicates greater vulnerability in the longitudinal direction under seismic loading. Performance levels IO, LS, and CP are applied to classify potential damage and guide safety measures. The results emphasize the importance of accurate 3D modeling, long-term aging effects, and conservative seismic load considerations in ensuring the safety and durability of viaduct piers. Targeted monitoring, maintenance, or retrofitting of critical piers is recommended to maintain structural integrity and serviceability over time.
Address
Naida Ademović: University of Sarajevo-Faculty of Civil Engineering, Patriotske lige 30, 71 000 Sarajevo, Bosnia and Herzegovina
Haris Murati: "DADI Gradnja" Bulevar Veljka Vlahovića bb, 81000 Podgorica, Montenegro
Abstract
Recently, mixed HO-WN (i.e., High order-Wavenumber) method was introduced for dynamic analysis of concrete gravity dam-reservoir systems. This is formulated by FE-(FE-TE) approach (i.e., Finite Element-(Finite Element-Truncation Element)). In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the mixed HO-WN (i.e., High order-Wavenumber) condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It should be emphasized that three alternatives are discussed for this approach. The first two alternatives result in one additional degree of freedom at each node in comparison with usual modeling in practice which employs Sommerfeld truncation condition. While, the third alternative leads to two additional degrees of freedom. The method in each case is generally derived by combining the High-order and Wavenumber approaches. The present study expands the above-mentioned formulation for dam-reservoir systems to include the effect of foundation rock. Thereafter, the response of Pine Flat dam-water-foundation rock system is studied due to horizontal and vertical ground motions for two types of reservoir bottom conditions of full reflective and absorptive. The initial part of study is focused on the time harmonic analysis. In this part, it is possible to compare the transfer functions against corresponding responses obtained by FE-(FE-HE)-FE approach (referred to as exact method which employs a rigorous fluid hyper-element). Subsequently, the transient analysis is carried out. In that part, the results in each case are compared against the corresponding results obtained by the high order H-W condition applied on the truncation boundary. It is worthwhile to emphasize that results for high order H-W condition (e.g., O5-5) are not sensitive to L/H value. Therefore, they can be envisaged as exact results (in numerical sense) in time domain.
Key Words
absorbing boundary conditions; dam-water-foundation rock; high-order condition; Pine Flat dam; truncation boundary; wavenumber approach
Address
Vahid Lotfi, Solmaz Dehghanmarvasty: Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran
