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This paper presents a study on the interlaminar shear strength (ILSS) retention of three types of glass fiber–reinforced polymer (GFRP) bars with different surface textures subjected to four types of conditioning environments (alkaline, alkaline, salt, acidic, and water) at two temperature levels (ambient laboratory and high temperature) for 3, 6, and 12 months. The conditioning temperature plays a critical role in reducing the strength of the bars. Scanning electron microscopy revealed the extent of damage to the fibers, resin, interface, and fracture morphologies in the cross sections. The causes of fiber cracking and lower strength upon exposure were validated by point energy-dispersive X-ray spectroscopy analyses, which detected the leaching of silicon from the fiber structure. Prediction models using multiple linear regression (MLR) and artificial neural networks (ANNs) were developed using Matrix Laboratory (MATLAB R2023b) software and compared. The coefficients of determination of the MLR and ANN prediction models were found to be 0.29 and 0.90, respectively, indicating the superiority of machine learning–based models in identifying and accounting for nonlinearities and highlighting their potential application in GFRP bars. Finally, the correlation between the transverse shear strength (TSS) and ILSS of the tested GFRP bars was identified. The ILSS of the bars was found to be approximately 0.26 times the TSS for any given conditioning scenario. [ABSTRACT FROM AUTHOR]

A new set of robust finite elements for the analysis of general anisotropic multilayered composite plates was presented. Recently, the enhanced-refined zigzag theory (en-RZT) has shown its accuracy in predicting the structural response of laminated plates exhibiting a high transverse anisotropy. Moreover, the en-RZT requires only C0 -continuous shape functions to formulate accurate and efficient finite elements. The formulation of three-node triangular (TRIA3) and four-node quadrilateral (QUAD4) flat finite elements based on the en-RZT kinematics was focused. In order to eliminate the shear-locking effect that affects low-order C0 -based elements, the constrained anisoparametric interpolation strategy and an appropriate element shear correction (ESC) factor were implemented at the element level. Then, the variational consistent triangular (enRZT-T3c) and quadrilateral (enRZT-Q4c) element were obtained and numerically assessed. A detailed analysis has been performed to evaluate the convergence behavior of the newly formulated elements for bending and free-vibration problems. The influence of the mesh distortion, load configurations, and boundary conditions were finely addressed. The results provided and comparisons with 3D models demonstrate the accuracy and robustness of enRZT-T3c and enRZT-Q4c elements for a wide variety of problems and laminate configurations, including ultra-thin arbitrarily oriented multilayered plates. [ABSTRACT FROM AUTHOR]

This document deals with the effect of porosity on the buckling of functionally graded sandwich plates under a nonlinear thermal loading using the four-variable refined plate theory. Different types of functionally graded material (FGM) sandwich plates, as well as various boundary conditions were used to highlight the influence of transverse shear, which is composed of two displacement fields, one is related to transverse displacement, and the second is due to the shearing effect. The transverse shear field follows a new warping hyperbolic function. The governing equations were derived from the virtual work principle based on von-Karman nonlinear geometric strains. This study aims to examine a sandwich-type plate, composed of three layers, the core of the plate is entirely made of ceramic material, and the upper and lower faces of the plate are made of functionally graded material. To solve the governing equations, double trigonometric series were used to simplify computations instead of a highly complicated numerical method. While various parameters are considered such as the volume faction index, porosity, and geometrical configurations, the study shows a perfect agreement between the proposed model and those of different works reported in the literature. [ABSTRACT FROM AUTHOR]

The statement and the analytical and numerical methods for solving a geometrically nonlinear problem for a long noncircular cylindrical panel compliant to transverse shear under a normal surface load are described. The basic equations are based on the geometrically nonlinear theory of shallow shells in quadratic approximation, the Timoshenko hypothesis, and Hooke's law for transversally isotropic materials. Analytical expressions for the components of the stress–strain state are obtained for a shell with hinged longitudinal edges, and the limiting values of the generalized geometric parameter are determined. Numerical results are obtained for long open cylindrical shells of elliptical and oval cross-sections under uniform normal pressure. [ABSTRACT FROM AUTHOR]

Critical velocities of a two-layer composite tube subjected to a uniform internal pressure moving at a constant velocity are analytically derived by using a first-order shear deformation shell theory incorporating the transverse shear, rotary inertia and material anisotropy. The composite tube consists of two perfectly bonded axisymmetric circular cylindrical layers of dissimilar materials, which can be orthotropic, transversely isotropic, cubic or isotropic. Closed-form expressions for four critical velocities are first derived for the general case by including the effects of transverse shear, rotary inertia, material orthotropy and radial stress. The formulas for composite tubes without the transverse shear, rotary inertia or radial stress effect and with simpler anisotropy are then obtained as special cases. In addition, it is shown that the model for a single-layer, homogeneous tube is included in the current model as a special case. To illustrate the newly derived closed-form formulas, a composite tube with an isotropic inner layer and an orthotropic outer layer is analyzed as an example. The numerical values of the lowest critical velocity of the two-layer composite tube predicted by the new formulas compare well with existing data. [ABSTRACT FROM AUTHOR]

Introduction: In this paper, based on the properties of unit functions, we present accurate solutions to beam bending under various transverse loads and edge restraint conditions, using equations based on Bernoulli’s hypothesis and the hypothesis taking into account transverse shears. By comparing the analytical solutions obtained for a rectangular beam, we determined beam length-to height (L/h) ratios for cases when the difference in deflections is less than the permitted value. Thus, criteria for Bernoulli’s hypothesis application were obtained. The results of beam bending analysis can be applied when studying rod systems using the force and displacement methods. In this case, Bernoulli’s hypothesis is used. All the ratios obtained are simple and clear. However, this hypothesis is applicable for the analysis of thin-walled structures. Meanwhile, the hypothesis taking into account transverse shears can be used for structures of medium cross-section height. To ensure accurate results when studying building structures (beams, plates, shells, rod systems), the criterion of Bernoulli’s hypothesis (hypothesis of the straight normal) applicability was needed. Purpose of the study: We aimed to build a mathematical deformation model and develop a method for the analysis of bending in elastic Timoshenko beams with account for transverse shears. Methods: By applying generalized functions and direct integration of the differential equation for the bending line, we obtained analytical expressions for the deflection function under various boundary conditions. Results: Based on the proposed method, we performed beam analysis under various transverse loads and edge restraint conditions. We also evaluated the scope of Bernoulli’s hypothesis application for the main types of beams used in the analysis of rod systems by the displacement method.

In this paper, a displacement based shear deformation theory formulated on the cubic in-plane displacement field equation of Reddy and Liu is presented for the static bending analysis of isotropic circular cylindrical shells. The adopted displacement field accounts for a quadratic (parabolic) distribution of the transverse shear through the shell thickness as well as satisfies the need for a stress free upper and lower boundary surfaces of the shell. The equations of static equilibrium are obtained on application of the principle of virtual work. Numerical results of the bending analysis for the displacements and stresses are presented for the simply supported shell. A comparison made to those of the Kirchhoff-Love theory for varying shell length to mean – radius of curvature ratios, shows good agreement for thin shells irrespective of the shell length to radius of curvature ratio ( l / a ). The transverse sharing effect is found to be noticeable in the deformation of thick shells, however, this effect diminishes with a continuous increase in l / a ratios.

This paper presents closed-form expressions for the energy release rate and mode partitioning of face/core debonds in sandwich composites with orthotropic faces and core, by use of an elastic foundation analysis. The elastic foundation analysis used here is comprehensive and includes the deformation of the substrate part (core and the bottom face) and is done for generally asymmetric sandwich construction. To capture the transverse shear effects, the Timoshenko beam theory is used, which introduces an additional degree of freedom. A finite length sandwich is treated as having a debonded section, where the debonded top face and the substrate are free, and a bonded section, where an elastic foundation is used between the face and the substrate. The interaction between the face and the substrate in the bonded section is modeled using both normal and shear spring distributions. A double-cantilever beam specimen with applied external moments and shearing forces is chosen to demonstrate the procedure. The energy release rate is obtained by use of the J-integral. A mode partitioning measure in terms of the crack flank opening and shearing displacements is used. The results are compared with finite element results and show very good agreement. [ABSTRACT FROM AUTHOR]

This study presents the quasi-three-dimensional, higher-order shear-deformation theory for the stress and displacement analysis of sandwich plate subjected to concentrated force. Using expansion of thickness coordinate in the displacement field, the effects of both transverse shear and normal deformations are included. The theory satisfies the zero shear stress conditions on the top and bottom surfaces of sandwich plate. Hence, the shear correction factor is not required, generally associated with the First order shear deformation theory (FSDT). The boundary-value problem of the theory is derived using the principle of virtual work. Transverse shear and normal stresses are recovered from the stress-equilibrium equations of the theory of elasticity, and the continuity condition is satisfied at the interface between layers and stress boundary condition at the external surfaces. In addition, this study provides the effects of transverse normal strain on flexural response of sandwich plate. Closed-form solutions for simply supported sandwich plate subjected to concentrated force are obtained for various side-to-thickness ratios. The results of the present theory are compared with third-order shear and normal deformation theory, first-order shear-deformation theory, and the classical plate theory. The inclusion of the effect of transverse normal strain in the theory showed significant deviations in displacements and stresses. [ABSTRACT FROM AUTHOR]

This article presents a new higher-order beam model. The present beam model is governed by differential equations that are similar to those present in some existing higher-order beam models; however, the present beam model makes use of a novel method of calculating the transverse shear stiffness, which facilitates the calculation of a shear-warping stiffness without the need for an assumed warping displacement field, and without introducing any additional kinematic variables. The present beam model also facilitates the recovery of the distributions of longitudinal normal stresses and transverse shear stresses. The authors postulate that the bending and shear terms in first-order shear deformation theory represent the first two terms in an infinite series that would constitute an ideal one-dimensional beam model, and it is suggested that the present beam model constitutes the first four terms in this hypothetical infinite series. The present beam model is solved for several example beams, and the results are compared with those of existing classical and higher-order beam models, as well as computational results from finite element analyses. It is shown that the present beam model is able to accurately represent deformed shapes and stress distributions pertaining to beams that exhibit non-trivial shear compliance as well as non-trivial shear-warping stiffness. In the case of laminated composite beams comprising a large number of laminae, the present beam model offers a level of analytical fidelity that is comparable to that of existing zigzag beam models; however, unlike zigzag beam models, the present beam model is equally well suited for the analyses of beams comprising any number of laminae. [ABSTRACT FROM AUTHOR]

In the article, constructions made of orthotropic multilayer composite material, in particular, layered orthotropic plates are considered. Numerical modeling and analysis of the stress-strain state for the plates are carried out on the basis of one version for the refined theory of layered plates. The bending problems for plates of medium thickness and thin multilayer plates of symmetric and asymmetric structures are investigated. All studies are conducted taking into account the properties of orthotropy and multilayering for the composite material from which the plates are made. The general algorithm for the numerical calculation of the stress-strain state for layered plates with orthotropic layers is developed on the basis of the finite difference method. This algorithm is implemented on a PC by a software package. [ABSTRACT FROM AUTHOR]

A geometrically nonlinear problem for a long cylindrical shell compliant to transverse shear and subject to a local static load is formulated and exactly solved. The basic equations are derived using the geometrically nonlinear theory of shallow shells of the second order, Timoshenko's hypothesis, and Hooke's law. The results are obtained using generalized functions for a shell hinged at the longitudinal edges under piecewise-uniform pressure. [ABSTRACT FROM AUTHOR]

The abrupt change in the properties of composite materials across the interface between different materials can cause strong inter-laminar stresses leading to delineation, cracking and other damage mechanisms. To remedy these defects, functional gradient materials (FGM), in which the properties of materials vary constantly, have been proposed. The purpose of this paper is to analyze the thermomechanical bending behavior of ceramic / metal thick plates (FGM). This work presents a model employing a new transverse shear function. The numerical results obtained by the present analysis are presented and compared with those available in the literature. It can be concluded that this theory is effective and simple for static analysis of FGM plates in thermal environments.

In this paper, we derive the meso-scale equations of motion for particle reinforced Timoshenko beam from corresponding micro-scale equations by letting the scale parameter denoting the ratio of the particle radius and beam thickness decrease to zero. The beam is cantilevered at one end and is subject to a normal pressure of constant magnitude at the other end. The displacement field and the stress-strain state of the beam are determined for a decreasing sequence of values of the scale parameter to establish the convergence of solutions numerically using the finite element analysis. [ABSTRACT FROM AUTHOR]

In this work, expressions for estimating the modal density, speed of the bending wave, critical frequency and coincidence frequency of panels are derived considering orthotropic properties of the face sheets, transverse shear deformation and the rotary inertia. Presence of rotary inertia results in an increase in the modal density and a reduction in the speed of the bending waves. The influence is significant at higher frequencies. The critical and coincidence frequencies increase due to rotary inertia. Results for a typical equipment panel of spacecraft are presented and they show the need for incorporating rotary inertia while determining these parameters. [ABSTRACT FROM AUTHOR]

Thick composite disks are utilized in fast-rotating machines, including turbine disks and flywheels. Dynamic equations of motion for a rotating composite disk have been formulated in a polar coordinate system using Hamilton's principle, and numerical analysis has been performed by finite element interpolation. The natural frequencies of isotropic and laminated composite disks have been obtained when the rotational speed changes. The effects of transverse shear and rotary inertia on the vibration characteristics of rotating disks have also been investigated. [ABSTRACT FROM AUTHOR]

In this work, the formulation of a new triangular finite element is presented for static and free vibration of plate bending. The developed element which contains the three essential external degrees of freedom at each of the three corner nodes is based on the Reissner/Mindlin theory and the strain-based approach. This element is based on the linear variation of the three bending strains and constant transverse shear strains. The present element performances are evaluated through several tests related to moderated thick and thin plates with various shapes where it is found to be numerically more efficient than the bilinear element. [ABSTRACT FROM AUTHOR]

The dynamic stability problem of a Timoshenko beam supported by a generalized Pasternak-type viscoelastic foundation subjected to compressive axial loading, where rotary inertia is neglected, is investigated. Each axial force consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic stability of a beam as a function of viscous damping coefficient, variance of the stochastic force, shear correction factor, parameters of Pasternak foundation, and intensity of the deterministic component of axial loading are obtained. With the aim of justifying the use of the direct Liapunov method analytical results are firstly compared with numerically obtained results using Monte Carlo simulation method. Numerical calculations are further performed for the Gaussian process with a zero mean as well as a harmonic process with random phase. The main purpose of the paper is to point at significance damping parameter of foundation on dynamic stability of the structure. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174011]

We develop a basic element of the procedure of construction of the near-threshold part of the diagram of fatigue fracture for metallic materials under the conditions of transverse shear. It is proposed to use a square sample with edge cut and a force scheme of its cyclic loading. We determine the strain-stress state of a square plate with edge crack (regarded as a prototype of the proposed specimen) under the conditions of transverse shear by two independent methods (finite-element method and the method of singular integral equations). The stress intensity factor KII is determined for a broad interval of relative crack lengths with regard for the smooth contact of the crack faces and the presence of friction between the faces. [ABSTRACT FROM AUTHOR]

Abstract This study reports the formulation of a realistic aircraft wing model based on thin-walled composite beam theory. In this model, NACA 4-digit-series airfoils were selected for the wing-section. The circumferentially asymmetric stiffness lay-up was implemented and two different sets of coupling systems corresponding to the proposed model were utilized. The eigenvalue problem was solved by the extended Galerkin method and the natural frequencies were computed as a function of the ply angle. The results of the free vibration analysis along with the governing system of the proposed model contributes to the theory of anisotropic thin-walled beams, emphasizing the importance of thin-walled structures in the design of advanced aeronautical structures. Highlights • The formulation of a realistic aircraft wing model based on the thin-walled composite beam theory is presented by employing NACA 4-digit-series airfoils as the wing-section. • The free vibration analysis of this wing model is performed for two different sets of coupling systems, which feature Extension-Horizontal Bending-Horizontal Transverse Shear (E-HB-HTS) and Vertical Bending-Twist-Vertical Transverse Shear (VB-T-VTS). • The first four natural frequencies of E-HB-HTS and VB-T-VTS coupling systems are computed as a function of ply angle. • Various non-classical effects as well as the effects of a number of geometrical aspects on the natural frequencies are examined and discussed. • The transverse shear is found to have a significant effect on the natural frequencies of the E-HB-HTS coupling system than the ones of VB-T-VTS coupling system. [ABSTRACT FROM AUTHOR]

Highlights • Effect of transverse shear on plastic response due to localised blast is studied. • Theoretical solutions for displacement field are derived using plasticity theory. • Analytical results are validated against numerical ones. • Numerical models include pure Lagrangian and Coupled Eulerian–Lagrangian methods. • Pulse-shape-independent solutions are obtained based on effective parameters. Abstract Localised blast loads due to proximal charges are encountered in a variety of circumstances. This paper proposes an analytical solution for the dynamic plastic response of a rigid-perfectly plastic thick square plate subject to a localised explosion. The proposed model is an extension of the analytical model proposed by Micallef et al [1] to study circular plates which is adopted and modified in order to study impulsively loaded square plates where the effect of shear deformation is included. A piecewise continuous blast load function was assumed with axisymmetric spatial distribution of constant pressure in the central zone and exponentially decaying beyond it. Using the constitutive framework of limit analysis and incorporating the interactions between bending moment and transverse shear forces in the analyses, transverse displacement and response duration were examined on three classes of plates, classified according to the length to thickness ratio parameter ν. The results were furnished in terms of the impulsive velocity, which is a function of the localised blast load parameters. A theoretical solution for plates with ν > 2 was sought for the non-impulsive blast loads. Parametric studies were performed to elucidate the effect of loading parameters and plate thickness on the permanent deformation. The theoretical solutions have been found generic and can predict, by the correct choice of the load parameters, the dynamic response of most blast load scenarios brought about by proximal or distal charges. It was found that, for proximal impulsive blasts, the effect of transverse shear becomes irrelevant for even moderate values of ν , which effect is inconsequential on both central and endpoint displacements at discontinuous interface in the range of ν > 5. Since the short duration pulse is of concern, localised pressure loads affect only a small area of the plated structures. Thus, whilst the theoretical treatments also examine the fully clamped plates, the boundary conditions in such loads do not influence the overall response of the structure compared to the static or global blast loads. [ABSTRACT FROM AUTHOR]

Binder-stabilised preforms are being used increasingly in the production of large composite structures, such as wind turbine blades, to increase the throughput. The transverse shear behaviour of the preform is one of the driving factors in the development of wrinkling during manufacturing but has not previously been characterised in the literature. In this paper, the combined intra- and inter-ply deformations during transverse shearing of a binder-stabilised preforms for wind turbine blade manufacturing are characterised by a new test methodology. The results from two experimental campaigns are presented. In the first campaign, preform specimens are subjected to monotonic loading to a nominal transverse shear angle of 18.0° with three different deformation rates. The results show an increase in maximum load levels with greater deformation rates. In the second campaign, preform specimens are subjected to deformation-controlled cyclic loading with two different deformation amplitudes corresponding to a nominal transverse shear angle of 1.5° and 12.2°, respectively. During cyclic loading, permanent deformation is observed in all preform specimens and the maximum load at the 19th cycle is reduced to 48% of the maximum load at the first cycle for the tests with deformation amplitudes of 12.2°. The data generated in this study is freely available at https://doi.org/10.17632/9m78sg3zwn.1. [ABSTRACT FROM AUTHOR]