Search Results (8)

This study presents an analytical investigation into the free vibration behavior of perforated nanobeams resting on a Kerr-type elastic foundation within the framework of Eringen’s nonlocal elasticity theory. Specifically, Eringen’s nonlocal elasticity theory is employed to inherently capture small-scale effects, while the three-parameter Kerr model is utilized to provide a mathematically consistent representation of shear continuity and realistic surface interactions. In this context, the governing equations of motion for a perforated Euler–Bernoulli nanobeam are derived using Hamilton’s principle, incorporating both the nonlocal parameter and perforation geometric factors, namely, the filling ratio and the number of holes. The resulting equations are solved analytically via the Navier method for simply supported boundary conditions. The results indicate that the Kerr foundation model exhibits an intermediate behavior between the Winkler and Pasternak models, owing to the stiffness-reducing effect of its upper spring layer connected in series. A key finding is the “masking effect,” where high foundation stiffness significantly suppresses the frequency reduction caused by nonlocal small-scale effects. Furthermore, it is observed that in the absence of foundation support, the vibration behavior is governed by the competition between mass reduction and stiffness loss depending on the number of holes; however, foundation dominance stabilizes the system regardless of perforation geometry. Full article

This study investigates the free vibration behaviors of functionally graded (FGM) plates with a porous structure, resting on a Kerr-type elastic foundation, while accounting for thermal effects and complex material property distributions. Within the framework of higher-order shear deformation theory (HSDT), two novel shape functions are introduced to accurately model transverse shear deformation across the plate thickness without employing shear correction factors. These functions are constructed to satisfy shear stress boundary conditions and capture nonlinear effects induced by material gradation and porosity. A variational formulation is developed to describe the dynamic response of FGM plates in a thermo-mechanical environment, incorporating temperature-dependent material properties and three porosity distributions: uniform, linear, and trigonometric. Numerical solutions are obtained using in-house MATLAB codes, allowing complete control over the formulation and interpretation of the results. The model is validated through detailed comparisons with existing literature, demonstrating high accuracy. The findings reveal that the porosity distribution pattern and gradient intensity significantly influence natural frequencies and mode shapes. The trigonometric porosity distribution exhibits favorable dynamic performance due to preserved stiffness in the surface regions. Additionally, the Kerr-type elastic foundation enables fine tuning of the dynamic response, depending on its specific parameters. The proposed approach provides a reliable and efficient tool for analyzing FGM structures under complex loading conditions and lays the groundwork for future extensions involving nonlinear, time-dependent, and multiphysics analyses. Full article

To investigate the effect of isolation piles on surface subsidence induced by excavation and to explore the influence of isolation pile layout parameters on the subsidence behind the piles, this study employs a combined approach of theoretical calculation and model testing to systematically analyze the control effect of isolation piles on excavation-induced deformation. Based on a three-stage analysis method, the Kerr three-parameter foundation model is first introduced to solve the deflection differential equation and calculate the lateral deformation of the underground continuous wall induced by excavation. The boundary element method is then used to compute the additional stress near the isolation piles caused by the wall displacement, considering the shielding effect of pile groups. The lateral deformation of the isolation piles due to excavation is calculated, and the boundary element method is applied again to determine the additional stress induced by the pile displacement. Finally, the Mindlin solution is employed to compute the surface subsidence behind the isolation piles. Laboratory-scale experiments on subsidence control using isolation piles are conducted, and the results are compared with theoretical calculations to verify the validity of the theory. The results show that, compared to the condition without isolation piles, the presence of isolation piles reduces the surface subsidence by 0.099 mm. Increasing the diameter, elastic modulus, or pile-to-wall distance of the isolation piles, as well as reducing the spacing between isolation piles, helps reduce both the lateral deformation of the isolation piles and the surface subsidence behind the piles. Under the parameters used in this study, the reduction in lateral deformation of the underground continuous wall reaches 0.112 mm, 0.054 mm, 0.147 mm, and 0.172 mm, while the reduction in subsidence reaches 0.07 mm, 0.027 mm, 0.094 mm, and 0.124 mm, demonstrating significant deformation control effects. The conclusions derived from this study can be directly applied to practical foundation pit engineering. They offer valuable insights for optimizing the selection and arrangement of isolation piles, thereby providing effective guidance for controlling ground subsidence induced by excavation activities on site. Full article

This article presents the first theoretical analysis of the bending behavior of circular organic solar cells (COSCs). The solar cell under investigation is built on a flexible Kerr foundation and has five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. The cell is exposed to hygrothermal conditions. The related Kerr foundation lessens displacements and supports the cell. The principle of virtual work is used to generate the basic partial differential equations, which are then solved using the differential quadrature method (DQM). The results of the present theory are validated by comparing them with published ones. The effects of the temperature, humidity, elastic foundation factors, and geometric configuration characteristics on the deflection and stresses of the COSC are examined. Full article

Based on the three-dimensional elasticity theory, the free vibration of functionally graded porous (FGP) sandwich rectangular plates is studied, and a unified solution for free vibration of the plates is proposed in this study. The arbitrary boundary conditions of FGP sandwich rectangular plates are simulated by using the Rayleigh–Ritz method combined with artificial spring theory. The calculation performances of the unified solution for FGP sandwich rectangular plates such as convergence speed and computational efficiency are compared extensively under different displacement functions. In addition, three kinds of elastic foundation (Winkler/Pasternak/Kerr foundations) and three porosity distributions are considered. Some benchmark results and accurate values for the free vibration of FGP sandwich rectangular plates resting on elastic foundations are given. Finally, the effects of diverse structural parameters, elastic foundations with different parameters, and boundary conditions on the free vibration of the FGP sandwich rectangular plates are analyzed. Full article

To calculate the horizontal displacement of the diaphragm wall and surface settlement caused by foundation pit excavation, the three-parameter Kerr foundation model was applied to a diaphragm wall and derived the flexural differential equations of the diaphragm wall and calculated the horizontal displacement of the diaphragm wall using the finite difference calculation method. The boundary element method combined with the Mindlin displacement solution was then used to invert the additional horizontal stress near the diaphragm wall. Lastly, the Mindlin solution was used to calculate the surface settlement. The effectiveness of the proposed calculation method was verified by comparing the horizontal displacement of the diaphragm wall and the surface settlement between the theoretical calculation and the actual project. The theory proves that there is a certain connection between the horizontal displacement of the diaphragm wall and the surface settlement, and the horizontal displacement of the diaphragm wall is larger than the surface settlement. Using this theory to further analyze the foundation pit construction parameters, the greater the thickness and elasticity modulus of the diaphragm wall, and the greater the diameter and number of internal supports, the smaller the horizontal displacement of the diaphragm wall and the surface settlement. The theory can accurately predict the horizontal displacement of the diaphragm wall and surface settlement and provides guidance for the construction of foundation pit projects. Full article

The aim of this research is to study the lateral deformation characteristics of the pile foundation in front of a shield construction and accurately predict its displacement in the shield tunneling direction. The impact of deep-shield construction on the pile foundations was analyzed using the Mindlin elastic solution to determine the lateral displacement. The Kerr foundation model and other factors, like additional shield thrust and uneven shell friction, were considered. The study assessed the impact of the incision distance, shield outer diameter, and additional thrust on pile displacement. The theoretical and numerical solutions of lateral displacement at various shield construction stages were compared to determine the variation law. The results indicate that the theoretical method is reliable, considering its good agreement with the numerical solutions. The buried depth of the shield means that the upper part of the pile is less affected by the additional thrust, leading to less deformation at the top. We recommend using a smaller shield thrust and outer diameter to control the pile’s end and top displacement. Full article

Given their considerable specific surface area and amorphous characteristics, nanoparticles exhibit excellent pozzolanic activity, and when undergoing a reaction with calcium hydroxide, this leads to the generation of a denser matrix by promoting the formation of a greater amount of C-S-H gel, thereby enhancing the strength and durability of the concrete and fortifying the overall structure. Indeed, the present study investigates a comparative study of the buckling and free vibration analyses of concrete beams reinforced with various types of nanoparticles. For its simplicity and accuracy, a higher-order shear deformation theory will be used to analytically model the reinforced concrete beam. Furthermore, the powerful Eshelby’s model is used to derive the equivalent nanocomposite properties. The soil medium is simulated with Pasternak elastic foundation, including a shear layer, and Winkler’s spring, interlinked with a Kerr foundation. The motion equations are derived using Hamilton’s principle. Moreover, based on Navier’s analytical methods, the closed-form solutions of simply supported beams have been obtained. Different parameters, such as type and volume percent of nanoparticles, geometrical parameters, choice of theory and soil medium, on the buckling and dynamic behavior of the beam, are exercised and shown. The major findings of this work indicate that the use of nanoparticles in concretes increases better mechanical resistance and amplifies the natural frequencies. In addition, the elastic foundation has a significant impact on the buckling and vibration performances of concrete beams. Full article