This paper explores the plane stress problem for a cantilever beam under shear loading that causes bending, specifically focusing on functionally graded materials (FGMs). These materials exhibit a gradual change in mechanical properties, promoting enhanced performance over traditional homogeneous materials. The authors introduce a new formulation for the elastic modulus of FGM, incorporating two graduation parameters: one for material composition variation along the beam and another for the longitudinal elastic modulus ratio, which characterizes stiffness variation. The study formulates the static equilibrium equations that relate external forces, stresses, and internal deformations. Analytical expressions derived from these equations predict stress and displacement distributions within the beam, particularly under a tangential load at the free end, which induces shear and bending deformations. The analysis reveals how the gradation parameters influence the beam's structural response, demonstrating the effect of elastic modulus variation on stress distribution and deflection behavior. The study culminates in an analytical framework for assessing FGM cantilever beams under shear loading, enhancing understanding of material gradation impacts on structural behavior and aiding in the design and optimization of advanced engineering structures utilizing FGMs.
This paper investigates the plane stress behavior of a cantilever beam made of functionally graded material (FGM) subjected to combined shear and bending loading. A new formulation of the elastic modulus of FGM materials is proposed, incorporating two graduation parameters: the first representing the material gradation and the second the ratio of the longitudinal elastic modulus. Three models of the mechanical property distribution through the beam thickness are considered: the classical variation, the new model-1, and the new model-2. The mathematical formulation, based on the static equilibrium equations, is developed to predict the distribution of stresses and displacements in the beam subjected to a tangential force applied at its free end. The influence of the graduation parameters k1, k2 and the length-to-thickness ratio L/h on the stress and displacement response is also analyzed.
A complete laboratory-based seismic testing is the ideal standard qualification method to determine the amplified response accelerations of the electric power utility equipment. As an alternative to the complete experimental procedures, an analytical methodology with partial experimentation is proposed to assess the structural performance prior to the seismic qualification experiments in the present analogy. The proposed approach is based on the free vibration tests conducted at manufacturing unit, an analytical study of acceleration transmissibility and phase shifts of individual modes of the structure. This method also focuses on understanding the state of the system at post resonance. Different types of substation equipment are analyzed for the dynamic response and a case study of 36 kV circuit breaker is presented in this work. Harmonic vibrations of 0.2 g ground accelerations applied to index the modal parameter i.e., damping ratios at corresponding natural frequencies. Force transmission and phase lag at individual modes of the system opposing random ground accelerations are computed. The plots of frequency response curves of majority of the tested substation equipment showed the response acceleration is low at higher frequency ratios. Also, the response acceleration is not influenced by damping of the structure in the region of high frequency ratios. The presented methodology reduces the experimental complexities in the laboratories and the final qualification can be done in single attempt.
In this article, the mechanical and thermal buckling analysis of simply-supported functionally graded plates resting on an elastic foundation is conducted using an innovative higher shear deformation theory (HSDT) in conjunction with the Airy stress function method. The key novelty of this work lies in the exact resolution of the equilibrium equations through the Airy stress function, eliminating the need for shear correction factors, and in the introduction of a new transverse shear function that ensures a parabolic variation of transverse shear stresses across the thickness while naturally satisfying the stress-free boundary conditions at the surfaces. Three types of thermal loads are considered: uniform, linear, and nonlinear distributions through the thickness. The material properties of the plate vary according to a power-law distribution based on the volume fraction of its constituents. Numerical results are presented to assess the effects of the power-law index the foundation stiffness and geometric ratios on the critical buckling load and the critical buckling temperature, highlighting the accuracy and efficiency of the proposed methodology.
This research presents Structural Health Monitoring (SHM) techniques that employ static, modal, harmonic, and transient analyses of functionally graded material (FGM) cracked plates, modeled using First-Order Shear Deformation Theory (FSDT). Crack effects are represented using an equivalent stiffness-reduction method, enabling efficient damage modeling without introducing geometric discontinuities. The study analytically investigates static deflection under concentrated loading, free vibration, harmonic response at resonance, and transient response to impulsive excitation. The primary objective is to predict plate behavior and assess damage history using SHM methodologies, validated by monitoring changes in natural frequencies and dynamic responses of damaged thin plates. Finite element models are developed for cracked steel plates with varying crack lengths and orientations. Results indicate that stress increases with crack length but decreases as the crack orientation aligns more closely with the plate axis (y-axis). Both crack length and orientation significantly influence static compliance, natural frequencies, resonance amplitudes, and transient decay, highlighting the sensitivity of dynamic response parameters to damage severity. The combined use of static and dynamic indicators provides a comprehensive framework for SHM of functionally graded material plates, supporting effective damage detection and integrity assessment. Analytical results exhibit strong agreement with ANSYS simulations, with discrepancies remaining below 1% at a/c=0.01 for all crack angles considered. These findings establish a quantitative relationship between crack parameters and frequency reduction, confirming the model's applicability for vibration-based structural health monitoring of porous FGM plates.
Efficient labor forecasting remains a critical yet underexplored challenge in industrialized construction, particularly in Pre-Engineered Building (PEB) fabrication environments characterized by repetitive workflows, tradespecific labor dynamics, and cost-sensitive schedules. This study proposes a classification-enhanced machine learning framework that integrates Random Forest regression with real-time biometric labor data to predict workforce requirements. Projects are systematically classified using fixed thresholds for labor intensity and variability, yielding behaviorally distinct groups that improve model specialization and reduce forecast variance. Dedicated Random Forest models are trained for each classification group, leveraging structured biometric attendance logs to ensure input data fidelity. Model performance is assessed using RMSE and MSE metrics, while a profitability-based evaluation quantifies financial outcomes associated with prediction deviations. Experimental results show that over 88% of forecasts fall within an acceptable +/- 5% tolerance range, and over 91% of cases result in profit-positive deployment decisions. The framework demonstrates superior accuracy for stable labor types and high adaptability across varying project complexities. By unifying behavioral classification, biometric integration, and financial assessment, this study delivers a robust, scalable forecasting approach for data-driven workforce planning in modular construction systems.
This paper presents a novel approach to mitigate shear interface stress in steel beams reinforced with composite materials. The proposed solution is distinctive as it integrates shear strains from both the beam and the reinforcing plate, leading to improved accuracy in predicting critical interface stresses and the composite structure's overall behavior. The analysis is based on a parabolic shear stress distribution assumption across the thickness of both the steel beam and the bonded plate. A parametric analysis is conducted to explore various factors impacting the stability of the composite plate, acknowledging that interface stresses depend on the material and geometric properties of the reinforcement. The results show that parameter variations have a significant effect on maximum shear stresses within the composite material. Numerical findings substantiate the new solution's efficacy and elucidate key aspects of interfacial stress distributions. This research deepens the comprehension of mechanical interactions at the interface and supports the design process for composite-steel hybrid structures.
This research deals with deformation of a two-dimensional homogeneous transversely isotropic thermoelastic-diffusive solid under chemical potential and thermal loads within the framework of Moore-Gibson-Thompson (MGT) thermoelasticity with two temperatures. Fourier transformation is used to solve the problem and then numerical inversion technique is applied to obtain the solution in physical domain. The application of a time harmonic concentrated and distributed loads are considered to show the utility of the obtained solution. Graphical representation of variation in the stress components, conductive temperature and chemical potential with distance is depicted by taking the effect of frequency.
This article proposes a new type of aluminum-wood composite beam that reduces material weight and enhances lightweight construction. The beam is reinforced by composite material plates, providing additional rigidity. The beam has three cross-sections: I-shape, U-shape, and rectangular tube, with adhesive connection for both interfaces. The interfacial stresses in aluminum-wood composite beams reinforced by composite laminates are analyzed using nonlinear elastic theory and strain compatibility approach. The model considers shear deformations of the interface and is intended to be applied to all types of bonded materials. Theoretical predictions are compared with existing solutions, contributing to understanding the mechanical behavior of the interface and designing aluminum-wood structures reinforced by composite materials.
In the present manuscript, we focus our investigation on the intralaminar hybrid composite plates, where the bending behavior is addressed employing a reliable and efficient refined high-order theory. The present refined theory successfully simulates the plate's real behavior by considering the shear effect in deformations, counting only four variables in the mathematical formulation and ensuring the parabolic distribution of these shear strains and stresses. Also, the nullity of shear stresses at the plate's top and bottom faces is guaranteed by the present refined theory. Unlike conventional composites, hybrid composite materials offer compelling features like the opportunity to create new and advantageous structures by varying the fiber combinations and proportions. This variation leads to diverse kinds of hybrid composites, each of which is intended for specific applications, depending on the characteristics expected by manufacturers. The present theory's numerical and graphical results are validated against other literature-issued high-order theories. This validation is followed by a parametric study to highlight the effect of various parameters on the behavior of hybrid composites. Based on this research, we can conclude that the suggested refined theory is reliable, precise and efficient for investigating the bending behavior of intralaminar hybrid composite plates.
To establish digital twin model of the vehicle-bridge interaction system under random track irregularity excitation, it is necessary to compute the system response in real time. Traditional methods are time-intensive and lack real-time capability, whereas surrogate model-based approaches can rapidly and accurately predict dynamic response. This study proposes a surrogate model that employs the Sparrow Search Algorithm to optimize Long Short-Term Memory neural networks for predicting the dynamic response of vehicle-bridge interaction system under random excitation. Initially, a physical model of the vehicle-bridge interaction system is established, incorporating track irregularities to calculate the dynamic response and generate training samples. Subsequently, an SSA-LSTM surrogate model is developed and trained. Finally, the surrogate model is utilized to predict the dynamic response of the vehicle-bridge interaction system under arbitrary track irregularity excitations. To validate the robustness of the proposed algorithm, the prediction results of various surrogate models are compared. The results indicate that the proposed surrogate model achieves higher computational efficiency compared to classical mechanical models of the vehicle-bridge interaction system. Moreover, the SSA-LSTM surrogate model outperforms traditional LSTM and Backpropagation surrogate models in terms of prediction accuracy for the dynamic response of the vehicle-bridge interaction system.
A novel refined shear deformation theory with three variables is proposed to investigate the buckling behavior of two-directional coated functionally graded nanobeams. The displacement field is formulated based on the principles of Euler-Bernoulli beam theory. This study examines two distinct categories of coated functionally graded nanobeams: Hardcore and Softcore nanobeams. Three material distribution patterns are considered: a bidirectional configuration, a unidirectional transverse distribution, and a unidirectional axial arrangement. The strain gradient nonlocal elasticity theory is implemented to account for small-scale effects. The equilibrium equations governing nanobeams are derived using the total potential energy principle. A refined solution approach, leveraging Galerkin's method, addresses various boundary conditions efficiently. The functionally graded beam is modelled on an elastic foundation described by the Winkler, Pasternak, and Kerr models. The obtained results show that the buckling behavior of the coated nanobeams is significantly influenced by the coating layer's thickness, material properties, boundary conditions, and gradient distribution. We find that the two-directional coating configuration can improve buckling resistance and reduce sensitivity to loading direction compared to traditional one-directional coatings. The findings of this study have important implications for the design and optimisation of nanoscale structures and devices, particularly in applications where mechanical stability and reliability are critical, such as in nanoelectromechanical systems (HEMS) and nanoscale sensors.
A problem of deformation of a double porous thermoelastic half space medium with fractional order heat transfer having Three-Phase-Lag (TPL) has been considered and discussed, due to the application of a thermo-mechanical force. A transformed procedure is taken to obtain the transformed form of result of the formulated problem. Inverse transformation of the solution is performed through a computer program for a specific model. The numerical solutions are drawn graphically for different cases. The effect of Three-Phase-Lag on Dual-Phase-Lag and the effect of fractional order and depth parameters on deformation is observed.
Despite significant interest in the mechanics of nanostructures, the propagation behavior of guided waves in porous functionally graded (FG) doubly-curved nanoshells remains unexplored, particularly concerning the influence of different boundary constraints. The present study is therefore dedicated to addressing this void by developing a comprehensive analytical model for this problem. Based on the nonlocal strain gradient theory (NSGT) framework and incorporating the effect of moment of inertia, the governing equations of motion for porous functionally graded doubly curved shells are derived. The Galerkin technique is employed to eliminate the spatial variables from the partial differential equation system, thereby converting it into an ordinary differential equation with respect to time. By applying the boundary conditions and solving the characteristic equation, the dispersion characteristics of porous functionally graded strain gradient doubly curved shells with different boundary conditions are determined. The results indicate that the phase velocity of the hyperbolic curved plate is the smallest, followed by the cylindrical curved plate, then the ellipsoidal curved plate, with the spherical shell exhibiting the maximum phase velocity. Clearly, the spherical shell has the highest stiffness, naturally resulting in the maximum phase velocity. Additionally, at low wave numbers, the effects of nonlocal and strain gradient parameters on the dispersion relation are negligible.
This paper examines the free vibration of a cracked nano-beam with non-ideal support, considering thermo-piezoelectric effects through Euler-Bernoulli beam theory and nonlocal strain gradient theory (NSGT). A new approach models crack propagation in nano-beams using torsion springs within the NSGT framework, incorporating thermo-piezoelectric effects. The governing equations, incorporating non-ideal boundary conditions and related effects, are derived using Hamilton's method. The nano-beam is divided into two segments linked by a massless spring, accounting for additional strain energy and the deflection slope discontinuity induced by the crack. This study examines the effects of non-ideal supports, crack position, piezoelectricity, temperature variations, normal stress and strain, and the nonlocal parameter on the system's dynamic behavior. Comparisons with vibrational existing studies reveal strong agreement, emphasizing the significant impact of these parameters on characteristics.
This study pioneers the analysis of low-velocity impact behavior in spinning functionally graded porous circular plates reinforced with graphene platelets (GPLs), employing first-order shear deformation theory. The governing equations are derived via Hamilton's principle, while the plate-impactor interaction is modeled using a modified Hertzian contact law. Numerical solutions are validated against existing literature showing excellent agreement. Parametric studies investigate the effects of:(1) Spinning speed (revealing that higher speeds increase contact force but reduce impact displacement), (2) Porosity characteristics (distribution patterns and coefficients), (3) GPL reinforcement configurations, and (4) Nanofiller weight fractions on the dynamic response. Results highlight that porosity distribution has the most pronounced influence on both contact force evolution and transient center-point deflection, outweighing other variables.
This study investigates the flexural reinforcement of composite box girder bridge decks through combined analytical and numerical approaches using ABAQUS software. The research focuses on deflection, interface stresses, and interfacial slip, while also examining the role of reinforcement type, adhesive properties, and the presence of deck openings. A comprehensive parametric study highlights that material selection, reinforcement configuration, and adhesive characteristics significantly affect structural performance. Moreover, deck openings are shown to increase interfacial stresses and slip due to stress concentration and redistribution.
This paper presents a novel parabolic shear deformation plate theory incorporating the stretching effect for bending analysis of simply supported advanced functionally graded plates resting on a Winkler-Pasternak elastic foundation. The theory considers a parabolic distribution of transverse shear strains and satisfies zero traction boundary conditions on the plate surfaces without requiring shear correction factors. This theory involves only five unknowns, fewer than those in other shear and normal deformation theories. The originality of the present work lies in the introduction of a new displacement field based on undetermined integral variables that simultaneously incorporates both shear and stretching effects, providing a more accurate yet simple formulation compared to existing theories. Material properties are assumed to vary through the thickness direction following a simple power law distribution based on the volume fractions of the constituents. The accuracy of the proposed theory is validated by comparing its results with those available in the literature. The effects of the volume fraction index of the functionally graded material, the side-to-thickness ratio, and the Winkler-Pasternak elastic foundation on the bending responses of functionally graded plates are investigated. The study concludes that the proposed theory is both accurate and straightforward in predicting the bending responses of functionally graded plates, considering the stretching effect on an elastic foundation.
The analysis of fluid-structure interaction (FSI) in storage tanks is a fundamental aspect of structural design, particularly in spherical tanks used for water storage. Numerical methods implemented in finite element software are commonly employed to address this phenomenon. These methods are typically based on complex formulations that integrate fluid dynamics, providing detailed and accurate results. However, in structural design, engineers often prefer simplified models that adequately capture the essence of the problem without requiring complex simulations. This research aims to validate the modeling approach of FSI in spherical storage tanks using a mechanical-equivalent mass-spring model (MEMSM). The impulsive and convective components of the fluid were represented as lumped masses and springs whose stiffness is associated with the oscillation of the convective component. A perfectly fixed base was assumed, neglecting effects of soil-structure interaction (SSI), to remain consistent with experimental conditions used for validation. The model was validated by comparing the natural vibration frequencies, and the results indicate that the MEMSM model predicts these frequencies with a difference of 1.3% for the impulsive component and a maximum difference of 6.7% for the convective component. This result validates the proposed approach and underscores its main contribution: providing an alternative, efficient, and easily implementable tool for the dynamic analysis of spherical tanks, suitable for early stages of structural design without compromising accuracy.
This study develops a Stochastic Finite Element Analysis approach integrating a numerical integration method and a perturbation method to analyze the buckling response of columns subjected to three-dimensional (3D) stochastic material variations. The proposed method discretizes the 3D random field of Young's modulus into fundamental random variables. The method is further enhanced with perturbation techniques, supporting the estimation of important statistical descriptors, including the expected value, coefficient of variation (COV), and standard deviation of the critical buckling load. The accuracy of the Stochastic Finite Element Analysis is validated via Monte Carlo simulations (MCs) implemented with the conventional Finite Element Method (FEM), while spectral expansion techniques are employed to create random instances for the 3D stochastic field model. The results demonstrate that for small spatial correlation lengths, local material fluctuations are effectively averaged due to stochastic homogenization, leading to lower variability in the critical buckling load. Conversely, an expansion of the correlation length results in heightened variability in the critical load, reflecting the impact of stochastic variability of material properties. Among the spatial directions, the characteristic correlation distance along the column's longitudinal axis has the most significant influence on the uncertainty of the critical buckling load, as axial stiffness directly governs the global stability of the structure. Furthermore, the study reveals an approximately linear correlation between the COV of the critical buckling load and that of the elastic modulus, suggesting that material randomness can serve as a predictor of structural stability variability.
