Search Results (69)

Spherical caps exploit their intrinsic curvature to achieve efficient stress distribution, delivering exceptional strength-to-weight ratios. This advantage renders them indispensable for aerospace systems, pressurized containers, architectural domes, and structures operating in extreme environments, such as deep-sea or nuclear containment. Their superior load-bearing capacity enables diverse applications, including satellite casings and high-pressure vessels. Meticulous optimization of geometric parameters and material selection ensures robustness in demanding scenarios. Given their significance, this study examines the natural frequency and static response of bio-inspired helicoidally laminated carbon fiber–reinforced polymer matrix composite spherical panels surrounded by Winkler elastic foundation support. Utilizing a 3D elasticity approach and the finite element method (FEM), the governing equations of motion are derived via Hamilton’s Principle. The study compares five helicoidal stacking configurations—recursive, exponential, linear, semicircular, and Fibonacci—with traditional laminate designs, including cross-ply, quasi-isotropic, and unidirectional arrangements. Parametric analyses explore the influence of lamination patterns, number of plies, panel thickness, support rigidity, polar angles, and edge constraints on natural frequencies, static deflections, and stress distributions. The analysis reveals that the quasi-isotropic (QI) laminate configuration yields optimal vibrational performance, attaining the highest fundamental frequency. In contrast, the cross-ply (CP) laminate demonstrates marginally best static performance, exhibiting minimal deflection. The unidirectional (UD) laminate consistently shows the poorest performance across both static and dynamic metrics. These investigations reveal stress transfer mechanisms across layers and elucidate vibration and bending behaviors in laminated spherical shells. Crucially, the results underscore the ability of helicoidal arrangements in augmenting mechanical and structural performance in engineering applications. Full article

Excavation of ultra-shallow pilot tunnels triggers surface settlement and endangers surrounding pipelines. The discontinuous settlement curve from traditional stochastic medium theory cannot be directly integrated into the foundation beam model, limiting pipeline deformation prediction accuracy. The key novelty of this study lies in proposing an improved coupled method tailored to ultra-shallow burial conditions: converting the discontinuous settlement solution into a continuous analytical one via polynomial fitting, embedding it into the Winkler elastic foundation beam model, and realizing pipeline settlement prediction by solving the deflection curve differential equation with the initial parameter method and boundary conditions. Four core factors affecting pipeline deformation are identified, with pilot tunnel size as the key. Shallower depth (especially 5.5 m) intensifies stratum disturbance; pipeline parameters (diameter, wall thickness, elastic modulus) significantly impact bending moment, while stratum elastic modulus has little effect on settlement. Verified by the Xueyuannanlu Station project of Beijing Rail Transit Line 13, theoretical and measured settlement trends are highly consistent, with core indicators meeting safety requirements (max theoretical/measured settlement: −10.9 mm/−8.6 mm < 30 mm; max rotation angle: −0.066° < 0.340°). Errors (max 5.1 mm) concentrate at the pipeline edge, and conservative theoretical values satisfy engineering safety evaluation demands. Full article

The integration of silica nanoparticles (NS) into cementitious composites has emerged as a promising strategy to refine the microstructure and enhance concrete performance. Beyond their chemical role in accelerating hydration and promoting additional C–S–H gel formation, silica nanoparticles act as physical fillers, reducing porosity and improving interfacial bonding within the matrix. These dual effects result in a denser and more resilient composite, whose mechanical and dynamic responses differ from those of conventional concrete. However, studies addressing the vibrational and modal behavior of nano-reinforced concretes, particularly under elastic and viscoelastic foundation conditions, remain limited. This study investigates the dynamic response of NS-reinforced concrete slabs using a refined quasi-3D plate deformation theory with five (05) unknowns. Different foundation configurations are considered to represent various soil interactions and assess structural integrity under diverse supports. The effective elastic properties of the nanocomposite are obtained through Eshelby’s homogenization model, while Hamilton’s principle is used to derive the governing equations of motion. Navier’s analytical solutions are applied to simply supported slabs. Quantitative results show that adding 30 wt% NS increases the Young’s modulus of concrete by about 26% with only ~1% change in density; for simply supported slender slabs, this results in geometry-dependent increases of up to 18% in the fundamental natural frequency. While the Winkler and Pasternak foundation parameters reduce this frequency, the damping parameter of the viscoelastic foundation enhances the dynamic response, yielding frequency increases of up to 28%, depending on slab geometry. Full article

The present study models the deflection of nonlinear waves over a Kirchhoff plate underlying a Pasternak-like elastic foundation. A promising version of the tanh expansion analytical method has been deployed for the construction of regular exact solutions for the model, including the application of certain ansatz functions for validations and yet construction of more solutions. The resulting frequency equation and the modulation instability spectrum have been obtained for the linearized model, including the expressions for the related phase and group velocities. In addition, the study examines the equilibrium status of the resulting dynamical system with the help of the bifurcation analysis. Numerically, nonlinear deflection and dispersion of waves have been simulated through the acquired expressions and equations. Notably, the study notes that increasing both the Pasternak-like nonlinear parameter $\eta$ and time variation (for $x>0$) decreases the nonlinear deflection in the plate, while increasing the stiffness of the Winkler foundation increases deflection in the medium. In addition, the study establishes, concerning the determined frequency equation, that increasing the Winkler foundation stiffness increases the dispersion of nonlinear waves in the medium, while an opposite trend has been noted concerning the imposed Pasternak-like nonlinear foundation. In addition, both phase and group velocities, the gain function for modulation instability, and the resulting dynamical system have been noted to be greatly affected by the variation of the imposed foundational parameters. Lastly, this study has potential applications in various engineering fields while modeling and analysis of mechanical structures supported by additional structures. Full article

The dynamic model and nonlinear forced vibration of a laminated beam with magnetostrictive layers, embedded on a nonlinear elastic Winkler–Pasternak foundation, in the presence of an electromagnetic actuator, mechanical impact, dry friction, a longitudinal magnetic field, and van der Waals force is investigated in the present work. The dynamic equations of this complex system are established based on von Karman theory and Hamilton’s principle. Then, by means of the Galerkin–Bubnov procedure, the partial differential equations are transformed into ordinary differential equations. The Optimal Auxiliary Functions Method (OAFM) is applied to solve the nonlinear differential equation. The results obtained are validated by comparisons with numerical results given by the Runge–Kutta procedure. Local stability in the neighborhood of the primary resonance is examined by means of the homotopy perturbation method, the Jacobian matrix, and the Routh–Hurwitz criteria. Global stability is studied by introducing the control law input function and using the approximate solution obtained by the OAFM in the construction of the Lyapunov function. La Salle’s invariance principle and Potryagin’s principle complete our study. The effects of some parameters are graphically presented. Our paper reveals the immense potential of the OAFM in the study of complex nonlinear dynamical systems. Full article

This paper investigates the mechanical behavior of PBL shear connectors in UHPC during the elastic stage, utilizing push-out experiments and numerical simulation. This study simplifies the mechanical behavior of PBL shear connectors in UHPC under normal service conditions as a plane strain problem for the UHPC dowel and a Winkler’s Elastic foundation beam theory for the transverse reinforcement. The UHPC dowel is a thick-walled cylindrical shell subjected to non-axisymmetric loads inside and outside simultaneously in the plane-strain state. The stress solution is derived by assuming the contact stress distribution function and using the Airy stress function. The displacement solution is subsequently determined from the stresses by differentiating between elastic and rigid body displacements. By modeling the transverse reinforcement as an infinitely long elastic foundation beam, its displacement solution and stress solution are obtained. We obtain the load–slip curve calculation method by superimposing the displacement of UHPC with the transverse reinforcement in the direction of shear action. The proposed analytical solutions for stress and slip, as well as the method for calculating load–slip, are shown to be reliable by comparing them to the numerical simulation analysis results. Full article

The shear-compression failure of key strata leads to stair-step collapse and severe mine pressure, posing significant safety risks in coal mines. Existing theories fail to account for the boundary conditions and breaking sizes of key strata, making accurate description of shear-compression failure difficult. A periodic breakage mechanics model for key strata was developed using Timoshenko Beam and Winkler Foundation Theory, incorporating transverse shear deformation. The deflection, rotation angle, bending moment, and shear force were calculated, and a shear-compression failure criterion function f(x) was derived. The main conclusions include the following: (1) shear-compression failure is influenced by the thickness–span ratio, cohesion, internal friction angle, and elastic modulus of the key strata, but not by the elastic foundation coefficient and shear modulus; (2) shear-compression failure occurs when the thickness–span ratio reaches 0.4; (3) when the internal friction angle is 25°, 30°, 35°, or 40°, shear-compression failure does not occur if cohesion exceeds 8.0, 7.5, 7.0, or 6.5 MPa, respectively, with a larger internal friction angle corresponding to a smaller critical cohesion; (4) when cohesion is 6 MPa, 8 MPa, 10 MPa, or 12 MPa, shear-compression failure does not occur if the internal friction angle exceeds 44°, 32°, 19°, or 8°, respectively, with larger cohesion correlating to a smaller critical internal friction angle; and (5) once cohesion or internal friction angle surpasses a critical value, the failure criterion approaches a constant value, preventing failure; the elastic modulus has a greater effect on shear-compression failure than the shear modulus, with higher elastic modulus increasing the likelihood of failure. Full article

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