This study investigated the elastoplastic behavior of thick, axisymmetric, truncated conical shells under uniform internal pressure, utilizing the first-order shear deformation theory. The governing equations are formulated based on the notion of virtual work and resolved using the matched asymptotic method, a subset of the perturbation technique for systems of differential equations with variable coefficients. Assuming the material is homogeneous, its behavior is modeled as elastic-perfectly plastic. The Prandtl–Reuss flow rule and von Mises yield criterion define the evolution of the plastic zone, while a radial return mapping algorithm establishes the elastoplastic stress field. The current model, unlike previous research limited to unidirectional analysis, concurrently monitors plastic zone development in both axial and radial directions above the yield pressure, hence improving the precision of strain accumulation predictions. Under clamped-clamped boundary conditions, analytical solutions for displacements and stresses are derived. Parametric studies are conducted to examine the effects of the cone semi-vertex angle, the location of yield initiation, and the material yield strength on stress and displacement distributions, as well as on the initiation of plastic deformation. The finite element comparison reveals a 4% difference in displacement between the inner and outer layers, attributed to the first-order shear deformation theory.

Free vibration analysis of bi-directional FGM beams based on first-order shear deformation theory

In this study, the free vibration behavior of a multiscale hybrid curved beam reinforced with carbon nanotubes and glass fibers and having a viscoelastic polymer matrix has been numerically investigated. In this modeling, the elastic modulus and Poisson’s ratio of the polymer matrix are considered as exponential functions of time, and the effective modulus is evaluated using the Halpin–Tsai relationship. The governing equations of the beam are derived using the first-order shear deformation theory (FSDT) and solved using the Generalized Differential Quadrature (GDQ) numerical method. The obtained results show that increasing the mass fraction of carbon nanotubes and increasing the radius of curvature increases the effective stiffness and natural frequencies. Also, increasing the relaxation times due to the viscoelastic nature leads to a decrease in the elastic modulus and, consequently, a decrease in the natural frequencies. Furthermore, different boundary conditions have a significant effect on the dynamic response of the beam, where beams with clamped-clamped boundary conditions show the highest and beams with simply supported boundary conditions show the lowest frequency values. These results can be used in the optimal design of curved viscoelastic composite structures.

Functionally graded porous shell structures with multi-component coupling have gained increasing prominence in advanced engineering applications due to their superior performance and tunable dynamic characteristics. This study investigates the vibration behavior of a coupled shell system consisting of a conical shell and cylindrical shell interconnected through multiple annular plates, establishing a comprehensive theoretical framework for vibration analysis. Based on the first-order shear deformation theory, unified kinematic formulations are developed to describe annular plate, cylindrical shell, and conical shell. A modified variational method incorporating interface potential is proposed to rigorously satisfy continuity conditions at multi-component junctions, effectively addressing the interface compatibility challenge in hybrid shell structures. Two types of functional gradient porosity distributions are comparatively analyzed: power law governed and trigonometric function modulated material configurations. The validity of the theoretical model is confirmed through numerical verification and published studies. Parametric investigations demonstrate that porosity distribution design can manipulate the fundamental frequencies of the coupled system, which provide critical insights for the vibration optimization of functionally graded porous shell systems in aerospace and marine engineering applications.

Metallic structures have been extensively replaced with carbon fiber-reinforced polymer (CFRP) composites in many industries due to their technical advantages and design versatility. Despite these advantages, CFRP composites are sensitive to dynamic loads such as low velocity impact, which can compromise structural integrity with internaldamage. This study introduces a computationally efficient analytical model developed in MATLAB to predict impact damage in unidirectional (UD) CFRP composites, providing a faster and more cost-effective alternative to finite element simulations. The model used First Order Shear Deformation Theory (FSDT) and a Two Degrees of Freedom (TDOF) approach, incorporating a nonlinear contact force model to calculate displacements, absorbed energy and impact forces. A key novelty of this research lies in the multi-level experimental validation conducted with an Instron CEAST 9350 impact testing machine with hemispherical impactor tips at energy levels of 5.6 J, 10.3 J and 16.14 J. Results reveal that the model achieves good agreement with experimental data at lower energy levels, accurately captures the elastic behavior with a minimum error of 1%. However, the model's limitations in simulating nonlinear responses and material damage become more evident at higher energy levels, where the extent of damage has a pronounced effect on energy absorption and dissipation. This underscores the need for incorporating advancedmaterial models that account for damage progression and strain-rate effects to enhance accuracy and reliability. Ultimately, this work supports the development of innovative composite solutions, contributing to more efficient and cost-effective engineering practices.

Purpose In this study, the vibration analysis of composite plate reinforced with various volume fractions of multi-walled carbon nanotube (MWCNT) nanocomposite has been investigated analytically. Design/methodology/approach The mathematical model for the vibration analysis of the plate was solved to evaluate the plate’s response and natural frequency for different design parameters. The first-order shear deformation theory was employed to formulate the governing differential equation of motion of the plate with simply supported boundary conditions. Findings The plate structure used for the free vibration test comprises multi-layers of Perlon, Carbon, Kevlar and Kenaf, each with dimensions of 0.5 × 0.5 × 0.01 m. The matrix material used is the thermoplastic resin (orthocryl resin); it is widely used in biomaterial and energy applications to hold reinforcing materials such as Kevlar fibers, carbon fibers, or fillers. The material has several properties essential to composite structures, including flexibility, durability, strength and reinforcements. This composite fiber is oriented in two directions (Bidirectional at a 90° angle to each other). This results in a more balanced distribution of strength and stiffness in both directions. Nanoparticles with volume fractions of 0.5%, 1%, 1.5%, 2% and 2.5% were added. The results show that the free vibration characteristics and mechanical properties, including elastic modulus, response and natural frequency increase with the addition of volume fraction of the nanomaterial. Practical implications The research could lead to the development of lighter, more efficient aircraft structures with enhanced vibration resistance and mechanical strength, contributing to better performance, fuel efficiency and safety. The developed reinforced composite could be utilized in aircraft elements where weight reduction and greater durability are crucial. Originality/value The reinforcement of 2.5% MWCNT volume fraction increases the natural frequency of the composite plate by about 13.5% and the modulus of elasticity by 25.3%.

This study investigates the thermal free vibration of cylindrical and hyperboloid sandwich shells featuring a soft isotropic core and two functionally graded (FG) face sheets. The FG face sheets consist of ceramic–metal mixtures with temperature-dependent properties varying continuously through the thickness according to a power-law distribution, whereas the lightweight homogeneous core provides limited shear stiffness. To overcome the shear locking difficulties often encountered in low-order finite elements, the mixed interpolation of tensorial components of four-node quadrilateral element (MITC4) is developed within the framework of an improved first-order shear deformation theory (iFSDT). The governing equations of motion are derived systematically from Hamilton’s principle, and thermal effects are incorporated through temperature-dependent stiffness matrices and initial thermal stresses. Numerical simulations are performed to validate the accuracy and efficiency of the proposed model against available benchmark results, followed by a comprehensive parametric study. The effects of the material gradient index, face-to-core thickness ratio, elastic boundary conditions, and thermal environments on the natural frequencies are systematically investigated. The obtained results demonstrate that a soft core leads to a pronounced reduction in structural stiffness, whereas graded face sheets effectively alleviate thermal degradation and improve vibration resistance. The proposed MITC4-based formulation provides a robust and computationally efficient framework for accurate vibration analysis and design optimization of advanced FGM sandwich shell structures in thermal operating conditions.

This study presents an analytical investigation of the thermomechanical stability of hyperbolic doubly curved shells reinforced with graphene origami auxetic metamaterials (GOAMs) and resting on a Pasternak elastic foundation. The proposed model integrates shell geometry, thermal–mechanical loading, and architected auxetic reinforcement to capture their coupled influence on buckling behavior. Stability equations are derived using the First-Order Shear Deformation Theory (FSDT) and the principle of virtual work, while the effective thermoelastic properties of the GOAM phase are obtained through micromechanical homogenization as functions of folding angle, mass fraction, and spatial distribution. Closed-form eigenvalue solutions are achieved with Navier’s method for simply supported boundaries. The results reveal that GOAM reinforcement enhances the critical buckling load at low folding angles, whereas higher folding induces compliance that diminishes stability. The Pasternak shear layer significantly improves buckling resistance up to about 46% with pronounced effects in asymmetrically graded configurations. Compared with conventional composite shells, the proposed GOAM-reinforced shells exhibit tunable, folding-dependent stability responses. These findings highlight the potential of origami-inspired graphene metamaterials for designing lightweight, thermally stable thin-walled structures in aerospace morphing skins and multifunctional mechanical systems.

Abstract To address the issue of erosion-induced cracks on the rotor blades of turboprop aircraft and helicopters in strong wind-sand environments and their impact on vibration characteristics, this study conducted a full-scale erosion simulation of the blade using Fluent software under pitch angles of 45° and 60° and rotational speeds of 500 rpm and 1000 rpm. The simulation revealed the distribution pattern of erosion damage and identified the leading edge and blade tip regions as the primary erosion zones. Based on the obtained damage distribution, the blade was simplified as a rotating composite laminated beam model. Utilizing the first-order shear deformation theory (FSDT) and Hamilton’s principle, a dynamic model of the rotating composite laminated beam containing single or double cracks was established. The influence of parameters such as crack depth, crack location, rotational speed, and pitch angle on the vibrational characteristics of the blade was systematically investigated through numerical methods. The results indicate that increased crack depth, crack proximity to the blade root, higher rotational speed, and larger pitch angle all significantly alter the vibration behavior of the blade. This study provides a theoretical basis and simulation support for the anti-erosion design and preventive maintenance of propeller blades in harsh wind-sand environments.

This study uses a layerwise theory to present an isogeometric analysis of the free vibration characteristics of pre-twisted composite plates reinforced with curvilinear fibers. Given the widespread use of twisted plates in aerospace and mechanical engineering applications, variable stiffness composite laminates are employed to achieve desirable mechanical properties and facilitate more efficient design. A layerwise theory, incorporating first-order shear deformation theory assumptions for the displacement field, is adopted to improve the accuracy of the solution compared to equivalent single-layer theories while maintaining computational efficiency compared to full 3D elasticity models. The governing equations for free vibration analysis are developed using Hamilton’s principle and the energy method. The geometry is discretized using an isogeometric approach, employing cubic NURBS basis functions, which allow for accurate geometric modeling and simultaneously serve as the approximation functions in the finite element formulation. Numerical results for the eigenvalue problem are obtained, and the influence of various parameters, including pre-twist angle, layup configuration, curvilinear fiber orientation angles, aspect ratios, and edge conditions, on the free vibration of the composite plates, is investigated. The results demonstrate good agreement with those reported in the literature, validating the accuracy and efficiency of the proposed formulation.

This article systematically investigates the vibration characteristics of functional gradient carbon nanotube reinforced composite truncated conical shells under arbitrary boundary conditions. First, a structural dynamic model is developed based on the first-order shear deformation theory. The mid-surface displacement field is constructed using Jacobi polynomials to accurately capture the deformation behavior of the shell under complex boundary constraints. Subsequently, the governing equations for free vibration are derived via the Lagrange energy method, and a solution framework for the forced vibration response under single-point pulse excitation is established using the modal superposition approach. The proposed model is validated through comparison with existing literature and finite element results, confirming its accuracy and effectiveness and providing a solid theoretical basis for subsequent vibration analysis. Finally, the effects of carbon nanotube distribution patterns, weight fractions, and fiber laying angles on the structural vibration response are systematically analyzed, yielding a set of engineering-relevant conclusions with practical significance for structural design and vibration control.

Polyurethane (PU) foam combined with Graphene Nanoplatelets (GNPs) and Multi-Walled Carbon Nanotubes (MWCNTs) offers a promising solution for providing improved mechanical properties such as higher stiffness, improved energy absorption, and enhanced damping. In this study, to homogenize the mechanical and physical properties of hybrid nanocomposite, the generalized Halpin–Tsai (GHT) scheme along with Biot’s theory is extended. In addition, three different porosity distribution functions are employed to consider the effect of porosity in the homogenized hybrid nanocomposite. This research aims to illuminate the circumferential vibrational behavior of Annular Hemispherical Shells (AHSs) made from these nanocomposites, particularly under different Boundary Conditions (BCs). The dynamic behavior of AHSs using Donnell’s shell theory and First-order Shear Deformation Theory (FSDT) is examined. Furthermore, the elastic foundation is modeled using the two-parameter Winkler-Pasternak theory, which considers both the normal and shear interactions between the shell and the supporting medium. The governing equations are derived through Hamilton’s principle and discretized using the Generalized Differential Quadrature Method (GDQM) to achieve high accuracy in capturing the dynamic features of these composite structures. A key novelty of this research lies in the dynamic analysis of AHSs made from GNP/MWCNT-reinforced porous PU foam, subjected to arbitrary boundary conditions and modeled using an advanced homogenization framework and the GDQM. The study also looks into how Skempton’s coefficient, porosity, nanocomposite combination ratio, elastic medium stiffness, BCs and Circumferential Wave Number (CWN) affect the vibrational response.

Abstract This study presents an analytical formulation for evaluating the nonlinear equilibrium equations and axial buckling behavior of functionally graded (FG) auxetic cylinders subjected to combined axial and radial loading. The FG auxetic cylinder includes two inner and outer FG layers and one re-entrant honeycomb core layer. The mechanical properties of the FG layers vary through the thickness, and the presented formulation applies to any FG layers with power-law volume fractions. The governing equations are derived using the first-order shear deformation theory (FSDT) and von Kármán nonlinear relations. Nonlinear equilibrium equations are solved using the perturbation technique, while a closed-form solution is obtained for the stability equations with variable coefficients. A detailed parametric study explores the effects of FG layer properties, geometric features, and re-entrant honeycomb core parameters on both deformation and buckling performance. Results show that FG layers significantly impact the structural response. Radial displacement is highly sensitive to radial loading, and positive radial pressure improves buckling resistance. The influence of honeycomb geometry is limited. These insights offer valuable guidance for the optimal design of FG auxetic cylinders in structural and multifunctional applications.

This paper presents an analytical investigation of the free vibration behavior of fiber metal laminate (FML) beams with three types of boundary conditions, considering the temperature-dependent properties and the interfacial slip. In the proposed model, the non-uniform temperature field is derived based on one-dimensional heat conduction theory using a transfer formulation. Subsequently, based on the two-dimensional elasticity theory, the governing equations are established. Compared with shear deformation theories, the present solution does not rely on a shear deformation assumption, enabling more accurate capture of interlaminar shear effects and higher-order vibration modes. The relationship of stresses and displacements is determined by the differential quadrature method, the state-space method and the transfer matrix method. Since the corresponding matrix is singular due to the absence of external loads, the natural frequencies are determined using the bisection method. The comparison study indicates that the present solutions are consistent with experimental results, and the errors of finite element simulation and the solution based on the first-order shear deformation theory reach 3.81% and 3.96%, respectively. At last, the effects of temperature, the effects of temperature degree, interface bonding and boundary conditions on the vibration performance of the FML beams are investigated in detail. The research results provide support for the design and analysis of FML beams under high-temperature and vibration environments in practical engineering.

In this paper, a full-domain stochastic response analysis is performed based on the meshless method to reveal the time–frequency dynamic characteristics, including the power spectral density (PSD) responses in the frequency domain and the evolving PSD distribution in the time domain for a sandwich trapezoidal plate–shell coupled system. The general governing equations are derived based on the first-order shear deformation theory (FSDT), linear piston theory and Hamilton’s principle, and the stochastic excitation is integrated into the meshless framework based on the pseudo-excitation method (PEM). By constructing the meshless shape function covering the entire structural domain from Chebyshev polynomials and discretizing the continuous domain into a series of nodes within a square definition domain, the points are assembled according to the sequence number and the equilibrium relationship on the coupling edge to obtain the overall vibration equations. The validity is demonstrated by matching the mode shapes, PSD responses, time history displacement and critical flutter boundaries with FEM simulation and reported data. Finally, the time–frequency characteristics of each substructure under global and single stochastic excitation, and the effect of aerodynamic pressure on full-domain stochastic vibration, are revealed.

In today's world, there is an accumulation of glass waste and red brick waste due to several factors. These materials have a significant impact on environmental protection. Among the proposed solutions, incorporating a certain percentage of these wastes into concrete offers an interesting alternative. In this paper, the study focuses on the mechanical and thermal buckling behavior of concrete incorporating declared waste for panel applications. The study aims to develop a program to obtain the thermo-mechanical properties of a biphasic concrete mixture incorporating waste. The adopted model is the Mori-Tanaka model. The same program will then be used to determine the critical buckling load and the variation in the critical buckling temperature based on the first-order shear deformation theory (FSDT) with a correction factor of 5/6. It is clearly demonstrated that the inclusion of waste improves mechanical properties, but negatively affects thermal properties. Similarly, the critical buckling efforts are influenced by this waste incorporation. It is observed that brick waste yields better results compared to glass waste in terms of thermal buckling.

This paper examines the flutter analysis of a nanocomposite cylindrical shell with an adhesive joint under supersonic fluid flow. As the adherents, two outer and inner parts of the shell are fabricated from a polymeric matrix, which is reinforced with graphene nanoplatelets (GNPs) and connected with an elastic homogeneous adhesive. The distribution patterns and mass fractions of the nanofillers in the GNP-reinforced adherents are not necessarily the same. The effective material properties are calculated utilizing the rule of mixture and the Halpin–Tsai model, and the aerodynamic pressure of the external supersonic fluid flow is estimated by using the piston theory. The modeling of the shell is conducted according to the first-order shear deformation theory (FSDT) and Hamilton’s principle is utilized to derive the governing equations along with compatibility and boundary conditions. The governing equations are solved analytically in the circumferential direction utilizing harmonic trigonometric functions and numerically in the axial direction via the differential quadrature method (DQM). The influences of the thickness and type of the adhesive, the lap joint length, the boundary conditions, and the mass fraction and distribution pattern of the GNPs on the flutter boundaries are studied.

In this work, a thorough investigation into buckling and vibratory response of externally nonuniform, internally uniform, green and steel-reinforced concrete functionally graded materials cylindrical beams with external radius changes along their length with linear, convex, and concave configurations, which cause geometric non-uniformities by impacting structural stability to a very large extent, are provided. The work integrates Hamilton’s principle with nonlocal strain gradient theory and first-order shear deformation theory to offer a combined numerical formulation capable of modeling size-dependent phenomena with material hardening and softening simultaneously. The external radius of beam changes along its longitudinal axis with linear, convex, and concave configurations, invoking geometric non-uniformities, impacting structural stability to a very large extent. The finite element solution is employed to solve the governing equations, from which a physics-informed neural network capable of conducting rapid and accurate predictions with a wide design window input is trained. Systematic studies are carried into boundary conditions, material grading, geometrical shapes, and nonlocal coefficients on critical buckling loads and natural frequencies. The work serves to establish a demonstration into how geometry and material grading play a crucial role into tailoring mechanically the characteristics of environmentally friendly, functionally graded structural structures.

Mechanical buckling analysis of porous circular plates with radially graded porosity using first-order shear deformation theory

This study presents an optimization framework to enhance the thermal buckling temperature of a variable angle tow (VAT) laminated composite plate. A finite element model is formulated using first-order shear deformation theory and eight-nodes iso-parametric elements. The developed model is validated by comparing the results of the present model with the existing benchmark solution. A genetic algorithm is employed to optimize the fibre’s path using MATLAB. The effect of geometric and material characteristics, such fiber orientation, aspect ratio, boundary conditions, material anisotropy, and thermal expansion coefficients is extensively examined. The results show that finite element-based optimization can improve the critical buckling temperature by up to 111.76%. These insights are valuable for the efficient structural design of variable-angle tows composite plates, offering potential benefits for various engineering applications.