ABSTRACT This study investigates the feasibility of using strain response as a diagnostic indicator for detecting transient hydraulic events in pipeline. Circumferential strain was measured on a reducer pipe using both strain gauges and a non-contact method based on digital image correlation (DIC). Theoretical strain values are calculated from internal pressure using shell theory and compared with experimental results. A frequency domain analysis is conducted to identify the dominant components associated with water hammer, and a low-pass filter is applied to isolate transient-induced fluctuations. Cross-correlation analysis is used to evaluate the agreement between theoretical values, strain gauge data, and DIC data. The results show that the optical system successfully captures the key dynamic features of water hammer-induced strain responses, achieving high correlation with both theoretical values and strain gauge measurements. These findings demonstrate the feasibility of using optical techniques as a non-contact alternative for pipeline monitoring and suggest their potential for independent application under conditions where physical access is limited. The proposed approach contributes to the development of diagnostic strategies for pipeline integrity assessment and offers a practical method for capturing transient hydraulic events without relying on invasive sensor deployment.

Abstract The aim of this research was to determine the optimal dimensions of a tapered, bisymmetric, thin-walled, I-shaped cantilever for which, at a constant mass, the critical load causing the buckling of the beam reaches the maximum value. Optimal solutions were sought in a discrete set of admissible values of the taper coefficients of the I-bar’s web and/or flanges. A model of a thin-walled bar with an open cross-section, whose mathematical description was derived on the basis of the momentless theory of shells, was used to analyse the considered problem described by a system of four coupled differential equations with variable coefficients. The equations were solved using Chebyshev series of the first kind to approximate the generalized displacement functions, and the recurrence algorithm presented in earlier publications by the author(s). A tapered cantilever with a bisymmetric cross-section, subjected to the action of a uniformly distributed load, was analysed. The load can be applied to the I-bar’s upper flange or to its lower flange, or it can act in the centre of the web. The obtained critical load values were compared with those obtained using the finite element method and the commercial Sofistik software. In the set of linearly tapered cantilevers with a bisymmetric double-tee cross section, the cantilevers with the highest taper coefficients of the web and the flanges (the free end having the smallest possible dimensions) were found to be optimal (in their case, at a constant mass, the critical buckling load reaches its maximum value).

Abstract The influence of structural defects on the amplitude‐frequency characteristics of three‐layer cylindrical shells with a discretely symmetric lightweight, rib‐reinforced filler under internal impulse loading under different boundary conditions was theoretically analyzed. Circular ruptures in the reinforcing ribs of the structures were modeled as structural defects. The model of the theory of Tymoshenko shells and rods was used to analyze the elements of the elastic structure under independent static and kinematic hypotheses for each layer. The equations of motion were obtained by the Hamilton–Ostrogradsky variational principle. A corresponding finite element model of a cylindrical shell was created, which reflects the relationship between the potential energy of deformations in the shell and the potential of applied forces. The results of amplitude deformations and von Mises stresses obtained by the finite element method for shells with ruptures under different boundary conditions were compared with the corresponding values for three‐layer cylindrical shells without ruptures. The influence of lightweight aggregate on dynamic processes that can lead to an accident was investigated. Similar studies were conducted on the frequency characteristics of three‐layer cylindrical shells with structural defects.

A geometrically nonlinear shell theory for thin-walled tubes and beams subjected to large displacements and cross-section deformation

Asymptotically accurate and geometric locking-free finite element implementation of a refined shell theory

ABSTRACT An accurate analysis of bending properties is essential for understanding the damage behavior of multi‐layered composite pipes. Currently, two‐dimensional (2D) theoretical models based on the Lekhnitskii stress function or complex expressions with unknowns are primarily used to analyze the bending characteristics of composite pipes. These approaches cannot accurately predict the stress distribution of every layer and initial damage in composite pipes under bending conditions. In accordance with nonlinear cylindrical shell theory, this study parameterizes the ellipticity deformation in each layer and establishes the constitutive equation of pipes while considering material nonlinearity and the stiffness degradation model. The virtual work principle and failure criterion are applied to develop a 3D mechanical analysis model to assess the bending properties of pipes. A four‐point bending test and numerical simulation are carried out to validate this theoretical model. On this basis, the stress distribution, stiffness degradation mechanism, and damage failure characteristics of pipes under bending conditions are analyzed. The research findings show that axial stress, radial stress, and shearing stress are largely controlled by bending deformation, while hoop stress is primarily affected by elliptical cross‐section deformation. The initial failure mode is mainly matrix tensile failure in the outermost reinforced layer. When the winding angle is less than or equal to 45°, fiber/matrix shear failure occurs first. When the winding angle exceeds 45°, matrix tensile failure becomes the primary failure mode. This study enhances the understanding of multi‐layered wound composite pipes' behavior under bending conditions and provides insights for improving design and reliability in offshore applications.

Here the problem of formulating a representative model problem of shell theory is considered. We study two ways to obtain a constant-coefficient expression for the strain energy density function of a linearly elastic shell. The first formulation has already been given in the context of the analysis of boundary layers in thin shells, while the other is introduced here. It appears that the essential difference between the formulations is that the constant-coefficient expressions for the strains given here depend on four geometric parameters instead of the two parameters of curvature needed by the earlier derivation. The source of this discrepancy is investigated and shown to be related to the properties of the metric tensors that are attainable by means of different parametrizations of a given surface.

A new analytical solution is successfully developed for nonlinear pressured buckling analysis of complexly curved toroidal shell segments made from functionally graded graphene-reinforced metal matrix composite (FG-GRMMC) stiffened by spiral FG-GRMMC stiffeners and integrated with electric effects of piezoelectric layers is presented in this research. The analysis is based on Donnell’s shell theory combined with the large deflection nonlinearities, and parabolic and sinusoid shapes are considered in the longitudinal direction of shells. Additionally, an improved technique is proposed to approximate the stress function of shells in a nonlinear form. The Ritz energy method is employed to solve the governing equation system, while the smeared stiffener technique, improved to accommodate the behavior of FG-GRMMC stiffeners, is used to model the contribution of spiral stiffeners. Numerical simulations demonstrate the effects of complex curvature, material parameters, spiral stiffener distribution, and piezoelectric actuation on the buckling and postbuckling responses.

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.

A method for reconstructing radial excitation forces on a cylindrical shell using only radial displacement measurements is presented. Based on Flügge’s thin shell theory, the established relationships between radial excitation forces and the resulting circumferential, tangential, and radial displacements on a cylindrical shell are given. An inverse problem model is then formulated to reconstruct the radial excitation forces in the absence of circumferential and tangential displacement data. The radial excitation forces are estimated using Iterative Reweighted Tikhonov regularization (IRTR) and Sparse Bayesian Learning (SBL) integration. Validation through modal superposition and finite element methods demonstrates the robustness and accuracy of the proposed approach across a broad frequency range and under varying signal-to-noise ratios. Additionally, the study investigates the influence of measurement intervals on the cylindrical shell surface, showing that smaller intervals enhance accuracy while larger intervals provide more stable results. The results highlight significant improvements over traditional methods such as the Force Analysis Technique (FAT).

A qualitative analysis of the localised wave on a thin isotropic elastic shell is carried out, in which the kinematics of the semi-infinite shell is governed by the Kirchhoff–Love assumptions of the Donnell–Mushtari thin shell theory. Non-homogeneity in the material properties of the shell is considered and characterised by a continuously varying grading function along the transverse coordinate of the shell. The model incorporates the Gurtin and Murdoch surface elasticity theory to ascertain the influence of surface mechanical parameters on the properties of the bending wave at the free edge of a cylindrical shell. The implementation of the asymptotic integration technique on the equations of motion and free edge boundary conditions of a circular cylindrical shell enables the extraction of the dispersion of bending wave within a small range of the half-thickness-to-curvature ratio. The effects of grading index and elastic parameters of the shell on the propagating frequency are established through the asymptotic dispersion relation, equivalent to a plate dispersion equation within the framework of the Kirchhoff–Love thin plate theory.

This article uses refined higher-order shell theories to generate higher-order closed-form solutions for the static and vibration analysis of laminated sandwich hyperbolic and elliptical paraboloids, which are scarcely addressed in existing literature. A generalized theory is employed to formulate several equivalent single-layer shell models. Most refined and classical shell theories can be theoretically unified because a theory is independent of the selection of the shearing stress function. The theory generates an appropriate distribution of transverse shear stresses through the thickness of the shell and does not require a problem-dependent shear correction factor. The governing equations of motion and associated boundary conditions are derived using Hamilton’s principle. Higher-order Navier-type closed-form solutions are obtained for simply supported boundary conditions. For laminated composite and sandwich paraboloids, nondimensional results are presented in tabular and graphical forms. The study emphasizes the impact of shell curvature, thickness ratio, and layups on the deflection, stresses, and natural frequencies of laminated and sandwich paraboloids. A comparison is made between the results of several refined shell theories and, if available, with results from previous publications. A major highlight of the present research is the first-time presentation of numerical results for laminated and sandwich paraboloids, establishing new benchmarks.

ABSTRACTAccurate modeling and examination of nonlinear vibration behavior of multilayer structural elements consisting of nanocomposite (NC) materials before use is of great importance in terms of structural safety and operational security. Considering the complex mechanical properties of such structures, detailed analyses will not only ensure safety but also prevent serious economic losses caused by possible failures. In this study, modeling of mechanical properties of multilayer cylindrical shell structures consisting of homogeneous NC and functionally graded nanocomposite (FG‐NC) layers and solution of nonlinear vibration problem are discussed. The shear deformation theory (SDT), originally developed for homogeneous cylindrical shells, has been extended to multilayer structures incorporating FG‐NC layers. Within this framework, the dynamic equations and related expressions for cylindrical shells composed of FG‐NC layers are derived based on the von Kármán‐type nonlinear shell theory. The resulting nonlinear partial differential equations (NL‐PDEs) are solved using the Galerkin method and a modified version of the Poincaré–Lindstedt method (P‐LM). In the final part of the study, the effects of shear stresses, carbon nanotubes (CNT) distribution patterns, symmetric and antisymmetric layer configurations, and the number of layers on the dimensionless nonlinear natural frequencies (DNLFP) of cylindrical shells with various geometric and structural characteristics are examined in detail and evaluated through numerical analyses. The findings reveal the multifaceted influence of stacking sequence and pattern selection on the DNLFP, particularly highlighting the necessity of considering those effects in the design process under high‐temperature and low‐stiffness conditions.

The article presents the results of numerical studies of natural vibrations of truncated straight conical shells of revolution completely filled with an ideal compressible fluid. The shell thickness is not constant along the generatrix and changes according to various laws. The behavior of the elastic structure and liquid medium is described in the framework of the classical shell theory, which is based on the Kirchhoff–Love hypotheses and the Euler equations. The equations of shell motion together with the corresponding geometric and physical relations are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation written with respect to the hydrodynamic pressure is transformed to a system of differential equations using the method of generalized differential quadrature. The solution of the formulated boundary value problem is developed by the Godunov orthogonal sweep method and is reduced to the calculation of natural vibrational frequencies. To this end, a step-by step computational procedure is applied in combination with the subsequent refinement of the found values in the obtained range by the Muller method. The validity of the results obtained is verified by comparison with the known numerical solutions. For shells with different cone angles and combinations of boundary conditions (free support, rigid clamping and cantilevered support), the dependence of the lowest vibration frequencies obtained with a power (linear and quadratic, having symmetric and asymmetric forms) and harmonic (with positive and negative curvature) thickness change were investigated. The influence of boundary conditions on the possibility of the existence of configurations (cone angle, law of thickness variation, ratio of maximum or minimum cross-section thickness) that ensured an increase in the fundamental frequency compared to shells of constant thickness with restrictions on the weight of the structure was estimated.

This article presents a novel methodology for constructing shell theories with fully customizable kinematic fields specifically designed for multi-layered composite shells. The proposed framework introduces the independent expansion functions for each displacement component, enabling component-specific theory refinement. This approach significantly extends the capabilities of existing shell theory formulations while maintaining computational efficiency. The present work employs an enhanced version of the Carrera unified formulation (CUF) to characterize through-thickness kinematics. The proposed framework utilizes a combination of Taylor and Lagrange polynomial expansions to construct structurally efficient shell theories. The formulation employs the finite element method for mid-surface discretization using Lagrange-type elements. To mitigate locking phenomena, the framework incorporates the mixed interpolation of tensorial components (MITC) technique. Plates and cylindrical shells are studied here. The current numerical results are validated against established reference solutions from the literature. Comprehensive accuracy assessments are performed for both displacement fields and stress distributions. These analyses reveal a strong dependence of optimal model selection on key problem parameters.

This study delves into the vibration characteristics of a piezoelectric cylindrical shell situated on an elastic foundation under various physical fields and boundary conditions. The investigation stems from the necessity to comprehend the behavior of nanobuilding blocks on foundations in the realm of nanoelectromechanical systems, which cater to applications in intricate environments. Employing a semi-analytical approach, we combine wave-based methods with Kirchhoff–Love shell theory and nonlocal theory. By applying the Hamilton principle, we derive kinematic relationships and governing equations for the cylindrical shell. Our methodology adopts a wave function approach to establish displacement solutions, integrating scaling parameters to formulate control equations for the piezoelectric shell’s vibration model. This model enables the extraction of natural characteristics and determination of steady-state responses to diverse external loads. The accuracy of our model is verified through numerical examples, comparative analyses, and experimental results. Furthermore, a parametric study is conducted to evaluate the influence of non-local parameters, elastic support stiffness, and external physical fields on the characteristics and response of the cylindrical shell. Ultimately, a prediction model for the piezoelectric cylindrical shell under multi-field conditions is developed, offering a theoretical foundation and references for the advancement of nanoelectromechanical systems.

In this work, a non-partial derivative perturbation approach is developed with second-order statistical moments for vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical panels. To address uncertainties, the modified perturbation stochastic method (MPSM) is applied. The analysis is grounded in the first-order shear deformation shell theory (FSDT) and employs the shape functions of kernel particles from mesh-free methods to model the displacement field of the panels. The Young’s moduli of carbon nanotubes (CNTs) and the matrix are modeled as one-dimensional and two-dimensional random fields, respectively, and are discretized using the Karhunen-Loève (K-L) expansion. These random fields are mapped from rectangular to cylindrical regions to create a random field model for the cylindrical panels, and the first six eigenvalues and eigenfunctions are calculated. The MPSM and reproducing kernel particle method (RKPM) are then used to estimate the second-order moments of the structural random dimensionless natural frequencies. This method significantly reduces computational costs while maintaining high accuracy. The sensitivity of the natural frequencies to the random fields is also analyzed, considering the influence of multiple random variables, the panel’s aspect ratio, and the span angle, with stochastic bands plotted accordingly. The findings show that the natural frequencies are predominantly affected by the random fields E 11 CNT and E m , while the distribution of CNTs, the aspect ratio, and the span angle of the panel play a significant role in the sensitivity of the natural frequencies.

The structural performance of load-carrying composite structures is significantly influenced by uncertainties in material properties, necessitating reliability quantification and design-for-reliability approaches. Traditional structural reliability evaluation methods, however, often involve high computational costs, limiting their practical use. To overcome this challenge, the present work presents a novel methodology that integrates Support Vector Machine Regression (SVMR), Monte Carlo Simulation (MCS), and the Finite Element Method (FEM) to efficiently assess the structural reliability of tapered composite tubes under axial loading, explicitly accounting for uncertainties in material properties and ply thickness. An approximate-analytical solution based on the Donnell-Mushtari-Vlasov shell theory is developed to predict axial deformation and is used to validate the finite element model. Additionally, the finite element model and approximation-analytical solution are validated against a closed-form analytical solution and experimental results available in the literature, ensuring the accuracy and reliability of the approach. The proposed structural reliability evaluation methodology demonstrates accuracy and computational efficiency I reliability evaluation through comparisons with the direct Monte Carlo Simulation method. Reliability analysis quantifies the influence of random variables on structural response, revealing that designs based solely on mean material properties result in approximately 50% reliability, indicating a 50% probability of failure. Moreover, the taper angle exerts a negligible influence on structural reliability indices, highlighting a key design consideration. This integrated framework provides a computationally efficient and validated tool for the design-for-reliability of tapered composite tubes, enabling broader applications in composite structural engineering.

This study examined the bending behavior of functionally graded (FG) material shells with single-layer-double curvature (spherical, cylindrical, hyperbolic, and elliptical), under the action of both linear and non-linear hygrothermomechanical loads. A simply supported boundary conditions of the shell are used. The elastic properties, thermal expansion coefficient, and moisture expansion coefficients are assumed to vary along the direction of thickness following a power-law distribution of material gradation. The traction-free boundary conditions of shear stresses are satisfied at the top and bottom surfaces of the shell, resulting in a cosine distribution of transverse shear stresses. The principle of virtual work is used to obtain the governing differential equation, which is then solved using the Navier solution technique. The effect of transverse displacement is divided into thickness stretching, bending, and shear effect, which facilitates in predicting the behavior of FGM shells under hygrothermomechanical loading more accurately. The theory considers both the effects of transverse shear and normal strains, which is strongly recommended in the well-established literature. The main objective of this research is to explore how transverse normal strain (with and without), shear deformation, radii of curvature, and volume fraction distribution affect FGM shell bending response under hygrothermomechanical loading. All obtained results are presented in a non-dimensional form and validated by developing higher-order trigonometric shell theory, parabolic shell theory, and first-order shell theory. Many results are presented for the first time in this article and can be used as benchmark for future research studies.

Objective. The paper presents general equations of the moment theory of thin shallow shells with a relatively small rise above the plane of their projection taking into account creep deformation. The problem of the stress-strain state of the shell with boundary conditions is considered. At the edges, the shell is connected to diaphragms that are absolutely rigid in their plane and flexible from it. Resolving equations are obtained for calculating shallow isotropic and orthotropic shells taking into account creep deformations. The problem is reduced to a system of two fourth-order differential equations with respect to deflection and stress function. Method. The solution is given by the numerical-analytical method in the MATLAB software package. The nonlinear Maxwell-Gurevich equation is used as the equation of state between creep deformations and stresses. To determine creep deformations, a linear approximation of the first derivative with respect to time (Runge-Kutta method) was used. To verify the solution to the problem, a shell made of secondary PVC was calculated using the grid method. The method has been tested by comparing the solution with the calculations of other well-known researchers. Result. A program has been developed for calculation in the MATLAB package with the ability to vary the initial data and output a graph of the dependence of displacements and stresses on time. It has been established that stresses and internal forces in an orthotropic shell of the same shape as for an isotropic one are subject to stress redistribution: normal stresses increase, and tangential stresses decrease. Longitudinal and shear forces remain almost constant; stress changes occur mainly due to the redistribution of bending and torque moments. Conclusion. The proposed approach can be applied to the analysis of the stress-strain state and bearing capacity of a reinforced concrete shell as well. There are no restrictions on boundary conditions and types of loading, and the beam material can be not only polymers and composites for construction purposes, but also concrete.