Search Results (62)

Glass fiber-reinforced polymer (GFRP) composites exhibit significant advantages over conventional structural webbing materials, including lightweight and corrosion resistance. This study investigates the localized compression performance of the proposed GFRP grid web–concrete composite beam through experimental and numerical analyses. Three specimen groups with variable shear-span ratios (λ = 1.43, 1.77) and local stiffener specimens were designed to assess their localized compressive behavior. Experimental results reveal that a 19.2% reduction in shear-span ratio enhances ultimate load capacity by 22.93% and improves stiffness by 66.85%, with additional performance gains of 77.53% in strength and 94.29% in stiffness achieved through local stiffener implementation. In addition, finite element (FE) analysis demonstrated a strong correlation with experimental results, showing less than 5% deviation in ultimate load predictions while accurately predicting stress distributions and failure modes. FE parametric analysis showed that increasing the grid thickness and decreasing the grid spacing within a reasonable range can considerably enhance the localized compression performance. The proposed analytical model, based on Winkler elastic foundation theory, predicts ultimate compression capacities within 10% of both the experimental and numerical results. However, the GFRP grid strength adjustment factor β_g should be further refined through additional experiments and numerical analyses to improve reliability. Full article

In long-distance, large-section rectangular pipe jacking operations, machine deviation is an inevitable factor that poses substantial challenges to the accurate prediction of frictional resistance. To address this issue, a novel methodology is proposed to analyze the dynamic interactions at the pipe–soil–slurry interfaces. This approach integrates real-time alignment monitoring with the Winkler elastic foundation theory to enhance predictive accuracy. A comprehensive predictive framework is developed for excavation profiles and pipeline deflection curves under varying thrust distances, enabling the quantification of complex contact states. By applying Newton’s law of friction and the Navier–Stokes fluid mechanics equations, calculation methods for the frictional resistance of pipe–soil contact and pipe–mud contact are systematically derived. Furthermore, a predictive model for the jacking force in long-distance rectangular pipe jacking, accounting for complex contact conditions, is successfully established. The jacking force monitoring data from the 233.6-m utility tunnel pipe jacking project case is utilized to validate the reliability of the proposed theoretical prediction method. Parametric analyses demonstrate that doubling the subgrade reaction coefficient enhances peak resistance by 80%, while deviation amplitude exerts a 70% greater influence on performance compared to cycle parameters. Slurry viscosity emerges as a critical factor governing pipe–slurry interaction resistance, with each doubling of viscosity causing up to a 56% increase in resistance. The developed methodology proves adaptable across five distinct operational phases—machine advancement, initial jacking, stable jacking, deviation accumulation, and final jacking—establishing a robust theoretical framework for the design and precision control of ultra-long pipe jacking projects. Full article

This study numerically investigated free vibration characteristics of functionally graded material (FGM) beams on Winkler–Pasternak three-parameter elastic foundations using the modified generalized differential quadrature (MGDQ) method. To compare the effects of different beam theories on the predicted frequency responses, an nth order generalized beam theory was employed to establish the governing equations of the system’s dynamic model within the Hamilton framework. As a pioneering effort, a MATLAB (version 2021a) computational program implementing the MGDQ method was developed to obtain the free vibration responses of foundation-supported FGM beams. Parametric analyses were conducted through numerical simulations to systematically examine the influences of various factors, including beam theories, damping coefficients, foundation stiffness parameters, boundary conditions, gradient indices, and span-to-thickness ratios, on the natural frequencies and damping ratios of FGM beams. The findings provide an essential theoretical foundation for dynamic characteristic analysis and functional design of foundation-supported FGM beam structures. Full article

To investigate the mechanism of ground hydraulic fracturing technology in preventing mine earthquakes induced by hard–thick roof (HTR) breakage in coal mines, this study established a Timoshenko beam model on a Winkler foundation incorporating the elastoplasticity and strain-softening behavior of coal–rock masses. The following conclusions were drawn: (1) The periodic breaking step distance of a 15.8 m thick HTR on the 61,304 Workface of Tangjiahui coal mine was calculated as 23 m, with an impact load of 15,308 kN on the hydraulic support, differing from measured data by 4.5% and 4.8%, respectively. (2) During periodic breakage, both the bending moment and elastic deformation energy density of the HTR exhibit a unimodal distribution, peaking 1.0–6.5 m ahead of cantilever endpoint O, while their zero points are 40–41 m ahead, defining the breaking position and advanced influence area. (3) The PBSD has a cubic relationship with the peak values of bending moment and elastic deformation energy density, and the exponential relationship with the impact load on the hydraulic support is $F_{ZJ}=5185.2e^{0.00431L_p}$. (4) Theoretical and measured comparisons indicate that reducing PBSD is an effective way to control impact load. The hard–thick roof ground hydraulic fracturing technology (HTRGFT) weakens HTR strength, shortens PBSD, effectively controls impact load, and helps prevent mine earthquakes. Full article

This work presents accurate values for the dynamic stiffness matrix coefficients of Levinson beams under axial loading embedded in a Winkler–Pasternak elastic foundation. Levinson’s theory accounts for greater shear deformation than the Euler–Bernoulli or Timoshenko theories. Using the dynamic stiffness approach, an explicit algebraic expression is derived from the homogeneous solution of the governing equations. The dynamic stiffness matrix links forces and displacements at the beam’s ends. The Wittrick–Williams algorithm solves the eigenvalue problem for the free vibration and buckling of uniform cross-section parts. Numerical results are validated against published data, and reliability is confirmed through consistency tests. Parametric studies explore the effects of aspect ratio, boundary conditions, elastic medium parameters, and axial force on beam vibration properties. The relative deviation for the fundamental frequency is almost $6.89\%$ for a cantilever beam embedded in the Pasternak foundation, $5.16\%$ for a fully clamped beam, and $4.79\%$ for a clamped–hinged beam. Therefore, Levinson beam theory can be used for calculations relevant to loads with short durations that generate transient responses, such as impulsive loads from high-speed railways, using the mode superposition method. Full article

The present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect. The expressions of the nonlinear differential equations were obtained for the pinned–pinned boundary conditions with the help of the Galerkin–Bubnov procedure and Hamiltonian approach. The nonlinear differential equations were studied using an original, explicit, and very efficient technique, namely the optimal auxiliary functions method (OAFM). It should be emphasized that our procedure assures a rapid convergence of the approximate analytical solutions after only one iteration, without the presence of a small parameter in the governing equations or boundary conditions. Detailed results are presented on the effects of some parameters, among them being analyzed were the damping, frequency, electromagnetic, and nonlinear elastic foundation coefficients. The local stability of the equilibrium points was performed by introducing two variable expansion method, the homotopy perturbation method, and then applying the Routh–Hurwitz criteria and eigenvalues of the Jacobian matrix. Full article

This paper presents numerical investigations into the free vibration properties of a sandwich composite plate with two fiber-reinforced plastic (FRP) face sheets and a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) core made of functionally graded carbon nanotube-reinforced composite resting on Winkler/Pasternak elastic foundation. The material properties of the FG-CNTRC core are gradient change along the thickness direction with four distinct carbon nanotubes reinforcement distribution patterns. The Hamilton energy concept is used to develop the equations of motion, which are based on the high-order shear deformation theory (HSDT). The Navier method is then used to obtain the free vibration solutions. By contrasting the acquired results with those using finite elements and with the previous literature, the accuracy of the present approach is confirmed. Moreover, the effects of the modulus of elasticity, the carbon nanotube (CNT) volume fractions, the CNT distribution patterns, the gradient index p, the geometric parameters and the dimensionless natural frequencies’ elastic basis characteristics are examined. The results show that the FG-CNTRC sandwich composite plate has higher dimensionless frequencies than the functionally graded material (FGM) plate or sandwich plate. And the volume fraction of carbon nanotubes and other geometric factors significantly affect the dimensionless frequency of the sandwich composite plate. 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

This research represents the first theoretical investigation about the vibration behavior of circular organic solar cells. Therefore, the vibration response of asymmetric circular organic solar cells that represent a perfect renewable energy source is demonstrated. For this purpose, the differential quadrature method (DQM) is employed. The organic solar cell is modeled as a laminated plate consisting of five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. This cell is rested on a Winkler–Pasternak elastic foundation and assumed to be exposed to various types of hygrothermal loadings. There are three different kinds of temperature and moisture variations that are taken into account: uniform, linear, and nonlinear distribution throughout the cell’s thickness. The displacement field is presented based on a new inverse hyperbolic shear deformation theory considering only two unknowns. The motion equations including hygrothermal effect and plate–foundation interaction are established within the framework of Hamilton’s principle. The DQM is utilized to solve these equations. In order to ensure the accuracy of the proposed theory, the present results are compared with those reported by other higher-order theories. A comprehensive parametric illustration is conducted on the impacts of different parameters involving the geometrical configuration, elastic foundation parameters, temperature, and moisture concentration on the deduced eigenfrequency of the circular organic solar cells. Full article

Deep excavations clearly impact adjacent existing properties and threaten their operational safety. Predicting the deformation of existing infrastructure induced by nearby underground construction is the main concern of urban underground development. This paper presents an analytical calculation method for predicting underground pipe gallery deformations induced by adjacent deep excavations. First, the authors assume the existing pipe gallery to be nonexistent in the soil and propose a solution to calculate the excavation-induced vertical movements of the soil at the position of the existing pipe gallery. Thereafter, the authors simplify the existing pipe gallery as an elastic beam on a Winkler foundation to calculate its deformation. Finally, the method is verified by the good agreement found between the calculated result and the field measurement of the construction of the Shanghai Hongqiao CBD project. The proposed analytical method of this work can provide accurate evaluation results for similar engineering projects. Full article

The Winkler foundation modulus is key to evaluating the response of underground structures using the elastic foundation beam model. In this paper, an improved formula of the Winkler foundation modulus for a beam embedded in a full space is proposed to overcome the limitation of inconsistent assumptions in previous studies. To achieve this goal, the bending responses of the beam are obtained using the elastic foundation beam model and three-dimensional elastic continuum model, respectively, wherein a consistent assumption is proposed that tangential interactions at the beam–ground interface are ignored in the two models. In addition, as deformation of the site is an important source of the underground structure response, the beam is applied to standard soil displacement of the free field on the Winkler foundation to improve the accuracy of the Winkler modulus obtained by fitting solutions based on the concentrated force on the beam. The formula for the Winkler foundation is obtained by equating the first zero of the bending moment in the two models. The Winkler foundation modulus is verified by comparing the results with numerical solutions and previous studies. Full article

Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) and non-uniform (uneven). The elastic foundation is defined by two parameters (Winkler and Pasternak). To obtain the mathematical model of the problem, the first-order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction are modeled by means of a power law. Variational Ritz’s method joined with the R-functions theory is used for obtaining a semi-analytical solution of the problem. The approach is applied to a number of case studies and validated by means of comparative analyses carried out on rectangular plates with a traditional finite element approach. The proof of the efficiency of the approach and its capability to handle actual engineering problems is fulfilled for FGM plates having complex shapes and various boundary conditions. The effect of different parameters, such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions, on the vibrations is studied. Full article

This research delves into the complexities of backflow phenomena in finite-length and flat-walled fractures with elastic walls, specifically focusing on power-law fluids, whose shear-thinning behavior distinguishes them from Newtonian fluids. We model the backflow process under the lubrication approximation and by incorporating the linear Navier slip law. We numerically examine the influence of parameters such as slip length, fluid rheology, and external pressure on the backflow propagation of the carrier fluid. Our findings underscore the significant role played by the rheological index in determining the fracture closure rate. Additionally, our investigations highlight the marked effect of external pressure variations on pressure distribution within the fracture. Notably, the friction coefficient at the fracture walls, as denoted by a dimensionless slip number, exhibits limited influence on the fundamental dynamics of the problem. These insights advance our understanding of power-law fluid backflow and have wide-ranging applications across various engineering disciplines. Full article

This article derives approximate formulations for Rayleigh waves on a coated orthorhombic elastic half-space with a prescribed vertical load acting as an elastic Winkler foundation. In addition, perfect continuity conditions are imposed between the coating layer and the substrate, while suitable decaying conditions are slated along the infinite depth of the half-space. The effect of the thin layer is modeled using appropriate effective boundary conditions within the long-wave limit. By applying the Radon transform and using the perturbation method, the derived model successfully captures the physical characteristics of elastic surface waves in coated half-spaces. The model consists of a pesudo-static elliptic equation decaying over the interior of the half-space and a singularly perturbed hyperbolic equation with a pseudo-differential operator. The pseudo-differential equation gives the approximate dispersion of surface waves on the coated half-space structure and is analyzed numerically at the end. Full article

Semiconductor chips on a substrate have a wide range of applications in electronic devices. However, environmental temperature changes may cause mechanical buckling of the chips, resulting in an urgent demand to develop analytical models to study this issue with high efficiency and accuracy such that safety designs can be sought. In this paper, the thermal buckling of chips on a substrate is considered as that of plates on a Winkler elastic foundation and is studied by the symplectic superposition method (SSM) within the symplectic space-based Hamiltonian system. The solution procedure starts by converting the original problem into two subproblems, which are solved by using the separation of variables and the symplectic eigenvector expansion. Through the equivalence between the original problem and the superposition of subproblems, the final analytical thermal buckling solutions are obtained. The SSM does not require any assumptions of solution forms, which is a distinctive advantage compared with traditional analytical methods. Comprehensive numerical results by the SSM for both buckling temperatures and mode shapes are presented and are well validated through comparison with those using the finite element method. With the solutions obtained, the effects of the moduli of elastic foundations and geometric parameters on critical buckling temperatures and buckling mode shapes are investigated. Full article