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AbstractVarious intriguing morphological patterns emerge on the surfaces of growing, developing, or aging tissues, organs, and colonies of microorganisms. Our research draws inspiration from biological growth processes and applies differential growth to film-substrate systems. The strain mismatch induced by this approach leads to distinctive buckling patterns. Through a combination of finite element analysis (FEA) and theoretical analysis, we derive a comprehensive expression for the strain energy in a buckled film-substrate system subjected to differential growth. By solving the energy equations, our study investigates the intricate interplay of material properties, growth functions, and geometric characteristics. This exploration provides valuable insights into the deformations induced by growth in membrane structures and soft materials. Additionally, we establish a phase diagram that characterizes the buckling patterns. It opens avenues for innovative geometric design and 3D self-assembly techniques. Furthermore, our findings have the potential to inspire applications in fields such as soft robotics and flexible electronics. [ABSTRACT FROM AUTHOR]

The aim of the present study is to elucidate the non-linear stability characteristics of randomly distributed carbon nanotube-reinforced fiber composite (RD-CNTRFC) beams subjected to thermo-mechanical loading. Effective material properties of RD-CNTRFC are estimated using the Eshelby-Mori-Tanaka approach and Halpin–Tsai micromechanical techniques. The material properties are considered to be temperature-dependent, and the influence of carbon nanotube (CNT) agglomeration is also incorporated in material properties estimation of hybrid matrix. The strain-displacement relations are assumed by incorporating the higher-order shear deformation theory and geometrical nonlinearity (von Kármán). The governing partial differential equations are obtained by minimizing the total potential energy of the beam. Buckling loads of beam subjected to in-plane compressive loads are estimated using Eigen value approach. Similarly, buckling temperatures are also determined by solving Eigenvalue problem iteratively due to temperature-dependent material properties. The non-linear equilibrium paths under thermal and mechanical loadings are traced through iterative Eigenvalue approach. Numerical results are presented to elucidate the influence of various parameters like CNT agglomeration, ply sequences, span-to-depth ratio, boundary conditions, and mass fraction of CNTs. [ABSTRACT FROM AUTHOR]

In this research, the optimization of the geometric parameters of a 3-layer composite plate with an elliptical cutout in the center was investigated utilizing an artificial neural network and genetic algorithm for the first time to obtain the minimum ratio of linear buckling load to weight and the ratio of the diameters of the ellipse. After completing 294 simulations in Abaqus finite element software and forming an artificial neural network with two hidden layers, the function obtained in the artificial neural network was used as the objective function in the genetic algorithm, and the optimal values for the angle of the ellipse with the horizon axis, the diameter ratio of ellipses as well as the fiber angle of the middle layer of the composite were obtained. using artificial neural networks, three algorithms, Levenberg-Marquardt, Bayesian regularization; and scaled conjugate gradient backpropagation, were compared and the number of neurons in each algorithm was compared. The results showed that Levenberg-Marquardt's algorithm is more accurate compared to other algorithms. In the end, the optimal values for the angle of the ellipse with the horizontal axis; as the fiber angle of the middle layer of the composite and, the ratio of the oval diameters as α = 12.3001 degree , θ = 5.9481 degree and D = 1.5690. [ABSTRACT FROM AUTHOR]

This article aims to investigate the buckling and free vibration behaviors of nanocomposite beams reinforced with functionally graded (FG) agglomerated carbon nanotubes (CNTs) in polymeric beams matrix. In order to estimate the material properties of the FG CNTs reinforced beam, the Eshelby–Mori–Tanaka rule on the basis of equivalent fiber is employed. Moreover, the Lagrange's principle is used to achieve the governing equations under supposition of the refined higher order beam theory without need of any shear correction factor. The differential quadrature finite element method (DQFEM) as a robust and precise numerical procedure is utilized to achieve the natural frequencies and buckling loads with various boundary supports. Then, the assessment of the effects of different factors such as of CNTs agglomeration parameters, different patterns of CNTs distribution, length to thickness quotients, and mixed boundary conditions on the vibrational and buckling responses of agglomerated CNTs reinforced beam are explored. It is concluded that the current numerical solution based DQFEM is efficient and accurate for predicting the mechanical behavior of the nanocomposite structures. Moreover, the stability and vibration responses of the NC beams can be significantly affected by tailoring the agglomeration parameters. [ABSTRACT FROM AUTHOR]

The stiffened plate is one type of representative thin-walled structure consisting of plates reinforced by varying stiffeners to strengthen its resistance to buckling deformation. However, the mechanism by which stiffeners could efficiently improve the buckling resistance of such structures has not been well reported. Therefore, to investigate the mechanism and predict buckling behavior of the structures accurately, a refined Reddy-type global-local stiffened plate model (RGLS) is established firstly, which can fulfill continuous condition of in-plane displacement and transverse shear stress among the adjacent layers between the plate and stiffeners. In conjunction with the established model, a refined triangular element which can accommodate the continuous condition of transverse shear stresses at the interface between the plate and the stiffeners is constructed. Subsequently, on the basis of the unidirectional stiffened sandwich structures, the symmetric grid-stiffened sandwich structures are proposed. The buckling behavior of grid-stiffened structures is further explored by the present element. A full experimental study and a system of numerical examples have been performed to assess the reliability of the established elements. These examples demonstrate that the buckling loads could be captured by the developed element with high computational efficiency and accuracy. However, the models will significantly overrate buckling loads of the stiffened sandwich structures without considering the continuum condition of the transverse stresses at the plate-stiffener interface. [ABSTRACT FROM AUTHOR]

A novel 3D centrosymmetric lattice that exhibits a large twist angle during compression is proposed by tailoring the twist buckling mode of a body-centered cubic lattice and a simple cubic truss to the first. The imperfections of offset and multimaterial systems are introduced to control the twist direction. Effects of geometrical parameters and material properties on twist behavior are studied. Results suggest that the buckling-driven lattice configuration can twist at an angle of 100° and an average angle per unit axial strain of 6.7°/%. The novel configurations can be used as force switches, safety devices, and temperature-controlled transmission devices. [ABSTRACT FROM AUTHOR]

AbstractThe primary aim of this study is to analyze the buckling behavior of carbon-nanotubes (CNT) reinforced plates using a closed-form dynamic stiffness formulation. The dynamic stiffness method (DSM), typically employed for analyzing plate vibrations, is adapted here for the buckling analysis of various configurations of CNT-reinforced composite plates with internal line support and subjected to uniaxial and biaxial in-plane loads. The displacement field is based on the first-order shear deformation theory, and the analytical expressions for governing differential equations and natural boundary conditions are derived via Hamilton’s principle. The dynamic stiffness matrix is developed for individual plate elements, considering Levy-type boundary conditions. These matrices are then combined to form a global dynamic stiffness matrix, which is solved using the Wittrick–Williams (W–W) algorithm to obtain the critical buckling load. A comprehensive comparative analysis is undertaken to ascertain the accuracy and computational efficacy of the present DSM with alternative numerical methodologies, alongside detailed parametric studies to explore plate buckling characteristics. It should be noted that the DSM is known to provide accurate results as it is based on the exact governing differential equation. Therefore, the reported buckling results can serve as a benchmark for future research in this field. [ABSTRACT FROM AUTHOR]

This study aims to develop semi-empirical formulas for foretelling the buckling loads of clamped and simply supported rectangular isotropic panels with central circular perforation exposed to different ratios of biaxial load conditions. The empirical formulas were developed and evaluated using Gene Expression Programming (GEP), Artificial Neural Network (ANN), and Finite Element Method (FEM). A total of 714 data set, generated using the FEM, is used to establish and validate the empirical formulas. This study investigates the effect of perforation sizes, plate aspect ratios, and biaxial load ratios on the buckling strength of perforated panels. The proposed formulas will allow a quick and easy estimation of buckling loads for perforated rectangular panels with acceptable accuracy without the need for sophisticated calculations. The results of the empirical formulas were comparable reasonably well with the results of the finite element analysis (FE) and available literature findings. [ABSTRACT FROM AUTHOR]

AbstractThis present work investigates the buckling load optimization of the laminated composite plates with the elliptical hole under different non-uniform edge loads. The design objective is the maximization of the critical buckling load by determining the optimum fiber orientations in the layers. The stability equations are derived based on the first-order shear deformation theory (FSDT) of the laminated plates. The critical buckling loads are calculated using the finite element method with the nine noded rectangular element having five degrees of freedom per node. The bonobo optimizer (BO) algorithm is employed to optimize the laminated composite plates with the elliptical hole. The computer programming is developed in the MATLAB environment. Besides, the parametric studies are conducted for different types of the non-uniform edge loads, boundary conditions, cutout radius ratio and aspect ratios and the obtained numerical results are compared. Finally, the optimum results show that these factors play an imperative role in the optimum pattern and stacking sequence of the laminated composite plates with hole. The new significant findings can aid the designers in the structural design, and other industrial applications. [ABSTRACT FROM AUTHOR]

AbstractTubular structural composites are widely used in applications where high stiffness and low weight are required. This work proposes the study and evaluation of the influence of damage on the structural responses of thin-walled structures made of composite materials, as well as the development of a buckling prediction model using artificial intelligence. The methodology is approached on a few main fronts, namely: i) numerical modeling of the direct problem of the structure in finite elements, ii) modeling and parameterization of delamination in the elliptical shell model; iii) obtaining a database through finite element updating and iv) formulation and construction of the regression and prediction model using artificial neural networks. The numerical results showed that, as expected, the presence of delamination has a significant impact on the occurrence of buckling. The study also showed that it is possible to predict buckling values, with extremely satisfactory results - an error of around 1%, provided that more complex regression methods are used, such as regression by artificial neural networks, since the relationship between damage and buckling values is not trivial. [ABSTRACT FROM AUTHOR]

The present study is focused on the numerical and experimental investigation of the non-linear buckling behavior and ply-failure analysis of a hybrid composite shell under uniform hydrostatic pressure exposed on its outer surface. Laminated composite shells made of glass fiber reinforced polymer (GFRP) composites with and without multi-walled carbon nanotubes (MWCNT) reinforcement are considered for the investigation. The critical buckling pressure is numerically determined by performing a buckling analysis on a hybrid composite shell with consideration of various non-linearities such as material non-linearity, geometric non-linearity, and geometric imperfection using the commercially available software ANSYS®. The governing non-linear differential equations of composite shell structures are solved using the arc-length approach and non-linear finite element analysis. The nanotubes dispersion, distribution, structural integrity, aspect ratio, functional group, and purity level of CNT reinforcement with epoxy matrix materials are quantified using field emission scanning electron microscopy (FE-SEM). The elastic and plastic properties of the GFRP lamina with and without MWCNT reinforcement are experimentally determined based on ASTM D3039. The critical buckling pressure obtained through experiments on a GFRP composite shell with and without MWCNT reinforcement is compared with the results obtained from the numerical analysis to validate the effectiveness of the present numerical model. Parametric studies are undertaken to investigate the first ply failure analysis, the effect CNT reinforcement, aspect ratio of MWCNT, and different lamination sequences on the critical buckling pressure of the composite shell. It was observed that the Von-Misses stresses developed on the composite structures with ply angles of either all layers as 0° or combination of ply angles with 0° and 90° is always less than those of the structures having ply-angles such as 45° and 60°, irrespective of CNTs reinforcement. Furthermore, the highest critical buckling pressure was obtained with reinforcement of 1.5 wt% MWCNT in the composite shell with ply orientation of [90°]4s. [ABSTRACT FROM AUTHOR]

The current article presents the modeling and investigation of thermo-mechanical buckling behavior for the porous functionally graded (FG) plates of rectangular and skew geometry. In this article, the modified rule of mixture and power law distribution is incorporated in the Third order Shear Deformation Theory (TSDT) to establish the governing equations using principle of minimum potential energy (PMPE). Finite element meshing is introduced using four node rectangular elements to discretize the FG plate for stability analysis. The constituents of the FG plate are continuous and vary over the thickness in accordance with modified power-law. Porosity is associated as locally distributed density and estimated using modified power law. To ascertain the effective boundary restraints skewness to the FG plate is imposed via transformation matrix. The computation of the critical non-dimensional buckling load for the structures subjected to uni-axial compressive and different thermal loads is executed via Gauss numerical integration. The assessment of the present formulation is performed against the buckling parameter available in the reference literature. Stability characteristics is evaluated under three different temperature distributions. The impact of material compositions, different thermal load, porosity distributions and various other parameters on the stability characteristics of porous FG structures are thoroughly investigated. [ABSTRACT FROM AUTHOR]

The effect of thermo-mechanical load coupling and porosity distributions on vibration and buckling characteristics of Functionally Graded Sandwich Plates (FGSPs) with cutouts is investigated by Finite Element (FE) formulation. Two sandwich configurations are considered and physical neutral surface is incorporated due to material asymmetry. Novel dynamic approach is proposed to evaluate buckling loads. Results obtained are compared with experimental, numerical solutions in literature and revealed that the FGSP buckling capacity under thermomechanical loads improves on using ceramic with lower thermal expansion coefficient. Also, at higher temperature rises, buckling capacity increases due to increasing porosity content, whereas capacity reduces at lower temperature rises. [ABSTRACT FROM AUTHOR]

In the current work, the dynamic and buckling properties of hybrid fiber-reinforced polymer composite beams are investigated. The hybrid composite beam is made of polyester matrix, carbon fiber, and jute fiber. The mechanical characteristics of carbon/jute/polyester composites were examined using ASTM standards. Experimental dynamic analysis was performed on jute, carbon, and hybrid carbon/jute composite beams. The validity of a finite element (FE) model based on higher-order theory was examined, and it exhibits outstanding agreement for composite beams when compared to experiments and literature. The hybrid composite beams have a considerable impact on structural stiffness when compared to neat jute/polyester composite beams. In this work, the effects of end conditions, taper angles, and composite layers are also investigated in relation to the dynamic and buckling properties of uniform and tapered hybrid carbon/jute/polyester composite beams. The findings imply that hybrid composites can be a superior substitute material for automotive applications. [ABSTRACT FROM AUTHOR]

Integral forms of Eringen's nonlocal theory are employed to model nanoscale constitutive relations without possible potential paradoxes. The Timoshenko beam theory as well as the element-free Galerkin method are accepted to model rotating nanobeams and develop numerical solutions of critical rotating angular velocities for nanobeams. Optional setting angles as natural defects are taken into account in buckling analyses. Important design parameters, including length-to-height ratios, ratios of hub radii to lengths, setting angles, and additional supports are carefully assessed between local and nonlocal beams. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) exhibit a unique buckling behavior due to their slender tubular geometry and thin-walled circular cross section. This study aims to analyze effect of nonlinear cross-sectional deformation on buckling of CNTs. To accomplish this, CNTs are modeled as beam structures, and the analysis is conducted using the Variational Asymptotic Method (VAM) and a geometrically exact beam theory, as well as nonlinear finite element analysis (FEA). The study considers various loading cases, including pure axial compression and combined loading scenarios, such as bending-axial compression and torsion-axial compression. The results of the study indicate that inclusion of cross-sectional deformation-induced nonlinearity reduces the critical buckling load of CNTs. The reduction is 2–5% for pure axial compression and 10–40% for combined loading cases. The results are validated against existing literature and commercial finite element software, ABAQUS®. Additionally, parametric studies with different slenderness and radius-to-thickness ratios were carried out to further understand the impact of these parameters on buckling of CNTs. Finally, the study presents 3D deformed shapes of CNTs during buckling by combining the results of the 1D analysis and the 2D cross section analysis. The findings show that nonlinearity associated with radius-to-thickness ratio has a significant impact on the cross-sectional ovalisation of CNTs and is critical in evaluating their buckling behavior. This aspect of nonlinearity is often overlooked in continuum modeling methods of CNTs, making this study an important contribution to the field. [ABSTRACT FROM AUTHOR]

AbstractThis paper investigates the vibration and buckling analysis of porous metal foam thin-walled box beams. These beams exhibit a unique structural configuration with symmetrical and asymmetrical porosity distributions along their wall thickness, thereby altering the effective mechanical properties. The first-order shear deformable beam theory is employed and the governing equations are derived using the Hamilton’s principle. Numerical results are presented for porous metal foam thin-walled box beams under simply-supported, clamped–clamped and clamped-free boundary conditions. The effects of various porosity parameters, length-to-side and side-to-wall-thickness ratios on the beams’ performance are also examined. A comprehensive comparison between the porous metal foam thin-walled box beams and their counterparts in the form of equivalent homogeneous are presented. [ABSTRACT FROM AUTHOR]

This paper focuses on the buckling of nontypical ellipsoidal domes under uniform external pressure. According to the strength and stiffness optimisation theory, the structure of the ellipsoidal dome was optimised respectively, and two meridional profiling curves of the ellipsoidal dome were obtained. Two mass-equivalent ellipsoidal domes with variable wall thickness and one mass-equivalent ellipsoidal dome with constant wall thickness were fabricated using CNC machining, with a nominal long-axis and short-axis radius of 100 and 75 mm, respectively. The geometry, wall thickness, and buckling load of each ellipsoidal dome were measured. The agreement between numerical predictions and experimental results is good. The results indicate that the ellipsoidal dome with variable wall thickness has a relatively large load-carrying capacity. [ABSTRACT FROM AUTHOR]

AbstractSandwich structures are susceptible to wrinkling when subject to in-plane compressive loads, which threatens structural safety. To accurately investigate the failure behavior, the following work is to be required. Firstly, the wrinkling behavior of sandwich plates is a typical three-dimensional (3D) issue. To consider a 3D effect, an enhanced higher-order finite element formulation including transverse normal strain has been proposed for the first time. Utilizing the proposed finite element formulation, a refined quadrilateral element model has been constructed. Secondly, the buckling and wrinkling behaviors of square sandwich plates have been investigated. The performance of the proposed model has been evaluated by comparing it with the quasi-3D solutions, the results obtained from the 3D finite element method (3D-FEM), and other models. The differences between the buckling and wrinkling failure behaviors have been carefully explained. Thirdly, the effects of boundary conditions on buckling and wrinkling deformation have been explored in detail. By utilizing the proposed model, the translation mechanism between the buckling and wrinkling deformations of sandwich plates under different boundary conditions has been revealed, which can help other investigators to well understand the buckling and wrinkling behaviors of sandwich plates. It can be shown that the wrinkling behaviors of thick sandwich plates occur earlier than the buckling behaviors when the thickness ratio of core to face panel is more than 35. Besides, it also can be shown that the buckling and wrinkling loads decrease gradually with the relaxation of the boundary restriction. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the stability and vibration characteristics of variable stiffness laminated composite (VSLC) beams subjected to thermo-mechanical loadings. A semi-analytical model is developed to determine the buckling and vibration characteristics of variable stiffness composite beams. The model employs a displacement-based Ritz approach to derive the matrix representation of the governing equations. Modified constitutive relations are derived to account for the Poisson effects that arise due to the development of zero-stress conditions in the width direction of beams. The material properties and temperature variations are assumed to be constant across the thickness of the beam. Moreover, finite element calculations are carried out using commercial software ABAQUS in conjunction with a MATLAB-generated input file, which is utilized to capture fiber angle variations within the beam. Numerical results are obtained to elucidate the effect of slenderness ratio, modulus of elasticity ratio, boundary conditions, number of layers, and ply-sequence on the free vibration and instability characteristics of VSLC beams subjected to mechanical loadings and thermal environments. This study underscores the crucial importance of taking these factors into account for precise and dependable design and analysis of such composite beams in engineering applications. [ABSTRACT FROM AUTHOR]

AbstractIn this article, a simple refined shear deformation theory that eliminates the use of a shear correction factor was presented for buckling analysis of in-plane bi-directional functionally graded (IBFG) porous plates under various boundary conditions. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. Material properties of IBFG are assumed to vary continuously along with two different directions simultaneously, that is, the longitudinal and transversal ones, respectively. Governing equations and boundary conditions are derived. Analytical solutions were obtained for buckling analysis of (IBFG) porous plates. Several numerical examples are presented to demonstrate the performance and effectiveness of the proposed theory. The effects of material gradations, aspect ratios, and porosity on IBFG plate responses are examined in detail as well. [ABSTRACT FROM AUTHOR]

The buckling behavior of moderately thick and thick stiffened composite plates with different stiffener layouts is formulated based on the higher-order shear deformation theory. This investigation is performed under axial compression using the Finite Strip Method and experiment. The effects of dimensions, orientation, eccentricity, torsional stiffness, position and geometric configuration of stiffeners on the buckling load coefficient are achieved by employing the principle of minimum potential energy. Six grid-stiffened composite plate specimens with ortho-grid, angle-grid, and orthotropic-grid stiffeners are tested. The results of the presented method show good outcomes with those of experimental tests and the finite element ANSYS code. [ABSTRACT FROM AUTHOR]

The main goal of this article is to extend the Carrera unified formulation (CUF) in polar coordinates to analyze the mechanical and thermal buckling of functionally graded (FG) circular plates with axisymmetry. The governing equations are derived using CUF in polar coordinates for FEM. The fundamental nuclei, and accordingly, the elemental matrices for a 3-node line axisymmetric element are proposed. Mechanical and thermal buckling under uniform, nonlinear temperature rise with and without the effect of convection has been investigated. The results have been verified with several plate theories and the finite element method using the second-order axisymmetric 2D elements. [ABSTRACT FROM AUTHOR]

The contribution provided in this article is to examine free vibration and stability response of bidirectional graded material beams (BDFB) considering different boundary conditions. The stretch effect by means of a normal deformation in conjunction with the shear deformation influence are integrated for accurate results. The beam materials features are expected to depend on gradation pattern over the length and transverse directions via power law form. Lagrange's principle is employed in order to extract the governing equations of motion. A novel approach namely differential quadrature-based Galerkin method (DQGM) is used as an effective and accurate semi-analytical tool to compute the critical stability loads and natural frequencies of (BD-FG) beam for the first time. The approach takes features from simplicity and reduced computational cost of the DQ in combination with the efficacy of the Galerkin method for its analytical aspect and easy dealing with mixed boundary conditions resulting in more accurate results. The correctness of the results obtained from the present approach for two-directional functionally graded materials (FGMs) beams have been verified. Finally, the impacts of design parameters such as material grading exponent distributions, length to thickness ratios, porosity amount, and end support types on the natural frequencies and maximum of stability loads related to the present 2D-FGM beams are examined. [ABSTRACT FROM AUTHOR]

This paper presents a simple refined plate theory (S-RPT) which contains only three unknown variables in the displacement field for bending and buckling analysis and only one unknown variable in the displacement field for free vibration analysis. Unlike other simplified plate theories, S-RPT in its simplification (1) takes into account the Poisson's ratio variation along the thickness direction (2) takes into account the full coupling of in-plane and transverse displacements. These features make S-RPT applicable to the analysis of bending, buckling, and free vibration of functionally graded porous plates reinforced with graphene platelets (FGP–GPLs). Some simplified plate theories already available in the literature can be regarded as special cases of S-RPT. The S-RPT is first used in isotropic and metal–ceramic functionally graded plates to verify its accuracy. Then, the effect of pore distribution, GPLs distribution, porosity coefficient, aspect ratio, thickness ratio, and GPLs weight fraction on the bending, buckling, and free vibration behaviors are investigated based on S-RPT. [ABSTRACT FROM AUTHOR]

AbstractThis paper investigates the effects of multiple materials configurations on the buckling performance, total mass, and manufacturing cost of an existing omega stiffened composite panel. The buckling response of omega stiffened composite panel is predicted and verified using available data in literatures. The multiple materials are introduced into the omega stiffened composite panel. The material distribution, stacking sequences of panel skin, T sub-stiffeners and omega sub-stiffeners are optimized to improve the critical buckling load with reducing the total mass and manufacturing cost. During the optimization process, three classical loading conditions of the stiffened panel are considered, while ensuring compliance with the constraints imposed by ply manufacturing. A generalized optimization design framework for stiffened panels is employed, and NSGA-II algorithm is utilized to achieve the optimum design of stiffened panels. Results demonstrate that the introduction of multiple materials to the omega stiffened composite panel can lead to improved buckling performance, along with reduced manufacturing cost and total mass. Additionally, the proposed multiple-material optimization design framework can be further applied to the structural design of other types of stiffened composite panels in the future. [ABSTRACT FROM AUTHOR]

This article considers a bidirectional functionally graded (BDFG) beam with various distributions of volume fraction. The impact of these distributions on the buckling and bending response of BDFG beam with general boundary conditions is investigated via a quasi-3D solution. It is assumed that the beam is exposed to a set of in-plane varying compressive loads and there mechanical characteristics change in both directions. Also, the BDFG beam is considered to be exposed different external mechanical loads. Hamilton's principle is employed to derive the governing equations, which are then solved using analytical solution to obtain buckling and bending characteristics. The precision of the current formulation is investigated via a comparison with available data in literature. Some numerical results are presented and discussed to assess the effect of different parameters such type of volume fraction, boundary condition, varying load, and beam geometry on the buckling and bending of BDFG beam. [ABSTRACT FROM AUTHOR]

Stochastic vibration and buckling analysis of functionally graded sandwich thin-walled beams with I-section based on the first-order shear deformation theory is for the first time proposed in this paper. The material properties of beams in both web and two flanges are assumed to be continuously varied in its thickness. Additionally, the constituent material properties are randomly changed according to the lognormal distributions. These stochastic variabilities are then propagated to the stochastic responses of the thin-walled beam through a beam solver with hybrid series-type approximation functions. To achieve efficient evaluations for stochastic responses including natural frequencies and critical buckling loads, polynomial chaos expansion (PCE) based surrogate model is developed. The efficiency and accuracy of PCE's results are assessed by comparing with those of crude Monte Carlo simulation. Sensitivity analysis is carried out to compare the importance of the uncertainty in material properties to stochastic responses. New results reported in this paper can be interesting benchmarks for scientific and engineering community in the future. [ABSTRACT FROM AUTHOR]

In this study, a new mixed-field zigzag shell model is proposed in terms of Reissner's Mixed Variational Theorem (RMVT) for the composite laminates with curvature. In this model, refined zigzag theory (RZT) is employed to improve the accuracy and efficiency by introducing through-the-thickness piecewise linear warping functions. Moreover, the shear correction factors are eliminated. It is also different from the published models for composite laminated shells, the continuity conditions of interlaminar transverse shear stresses (TSSs) are satisfied a priori based on RMVT. The equilibrium equations and related boundary conditions are also derived from RMVT. Subsequently, the static performance, natural frequencies, and critical loads of composite laminates with curvature are verified by comparing them with the 3D elastic solutions and other existing ones. It is observed that the present model accounts for not only the efficiency of the low-order models but also the accuracy of the high-order models. Finally, it is shown that the ply stacking, side-to-thickness ratios, and side-to-radius ratios play an important role in percentage errors between the present model and the previous ones. [ABSTRACT FROM AUTHOR]

There is an critical need in kinetic envelope design to propose sustainable solutions that can adjust to changing outdoor conditions. Bistable composite laminates are compliant systems appealing for kinetic building envelopes because they present two stable equilibrium states and transition between them with little input energy. This study characterizes the behavior of bistable laminates for kinetic screens by developing an FEA model and conducting experimental testing to validate the model and compare both data sets. The FEA model predicts the laminates' cured states, snap-through movement, and required actuation force. The FEA model can accurately predict the cured states of the laminates. Regarding the movement of the laminate and actuation force, the simulation results mostly correlate quantitatively with the experimental data and differ qualitatively. However, the FEA model can accurately predict the critical force required to snap through the laminates, which ranges between 2.5 and 4 N. [ABSTRACT FROM AUTHOR]

Existing conventional materials are usually difficult to achieve multiple tunable stress plateau characteristics, which hinders their multifunctional applications. This study proposes a multiple stable stress plateau metamaterial. A theoretical model for predicting stress plateaus was established, and its accuracy was verified by experimental and numerical methods. The proposed material exhibits a three-stage deformation mode owing to sequential snap-through and Euler buckling at the microscopic unit cell level under compression. The effect of geometric parameters on the stress plateau was studied. The results indicated that the first plateau stress can be tuned independently by altering the angle between the inclined thin and thick beams, whereas the third plateau stress can be tuned independently by changing the thickness of the vertical thick beams. The first and second plateau stresses can be tuned by varying the thickness ratio of the inclined and vertical thin beams. Moreover, the total number of stress plateaus and the range of each stress plateau could also be tuned by changing the thickness ratio of the inclined and vertical thin beams and the vertical thick beams. Using the energy efficiency method, we obtained the experimental and numerical plateau stresses for each specimen. Notably, the experimental, numerical, and theoretical results were in good agreement. This study is expected to provide guidance for the design of multifunctional metamaterials with multiple tunable stress plateaus. [ABSTRACT FROM AUTHOR]

In this study, the stiffener geometry was optimized using curvilinear 3D printing to enhance the buckling resistance. A bio-inspired skin/stiffener composite that mimicked spider-web structures was generated. A dataset was formulated for the regression analysis, covering buckling stresses under distinct feature values. The regression equations, crafted using a deep neural network trained on the dataset, were evaluated. The derived regression equation was subjected to sequential quadratic programming, a mathematical optimization, to determine the optimal value of the explanatory variable. This was aimed at maximizing the buckling stress-to-stiffener volume ratio, which is the objective variable. The optimized arrangement exhibited significantly improved buckling resistance, with approximately 163% higher buckling stress than conventionally designed structures with straight stiffeners of similar weight. [ABSTRACT FROM AUTHOR]

In the following research, the buckling of multilayered CNT/GPL/Fibre/Polymer hybrid composite Levy-type nanoplates resting on Winkler–Pasternak support is investigated using modified nonlocal first-order plate theory. The different layers of the plate are assumed to be reinforced with functionally graded carbon nanotube composite or functionally graded graphene platelets composite. Modified nonlocal first-order plate theory is used to capture the molecular effects at nanoscale and extract the buckling equations. The along-thickness variation of reinforcing nanocomposites may be uniform or functionally graded, and functionality can be linear or nonlinear based on specific functions presented by scientists. Using a closed-form analytical solution, these partial differential governing equations are changed to a set of coupled ordinary differential equations that may be solved for the Levy-type boundary conditions (i.e., two opposite edges with simply supported and two other with edges arbitrary). The obtained results may be used as a useful benchmark for validation of other works developed in the future. [ABSTRACT FROM AUTHOR]

AbstractThis work presents an efficient analysis of buckling for functionally graded carbon nanotube reinforced composite (FG-CNTRC) joined conical–cylindrical laminated shells with lateral pressure and axial compressive load considering thermal effect. The governing equilibrium equation of the joined conical–cylindrical shell (CO-CYL) is determined using the first-order shear deformation theory (FSDT), Donnell kinematic assumptions, von-Kármán geometrical nonlinearity, and considering thermal effect. A semi-analytical solution, generalized differential quadrature (GDQ) method, and artificial springs are applied during the solution procedure. The comparison studies have demonstrated a remarkable 97% reduction in running time compared to the finite element method (FEM). [ABSTRACT FROM AUTHOR]

AbstractAdopting an effective layup sequence in laminated composite structures has always compelled scientists to investigate the behavior of laminated composite constructions. The present article presents the buckling analysis of double- and cross-helicoidal laminated composite plates using recently proposed HOZT. The Buckling behavior of helicoidal plates is compared to that of quasi-isotropic and cross-ply laminated composite plates. Higher buckling loads are seen for helicoidal plates, particularly those with free edges. The influence of skew angle, aspect ratio, thickness ratio, and plate end conditions on the helicoidal plate’s buckling behavior are also investigated. [ABSTRACT FROM AUTHOR]

The nanoplates have been used extensively in electronic devices, during the working process they can be affected by external forces. To enhance the working performance of mechanical systems, flexoelectric effects are usually added, therefore, it is necessary to study the mechanical behavior of these material structures under the effect of these effects. This is the first research to examine the vibration response and static buckling of variable flexoelectric nanoplates using the FEM and novel shear deformation theory type hyperbolic sine functions, where the thickness is adjusted by linear and nonlinear rules. This is a simple theory, which does not need any shear correction factors, while the mechanical responses of the structures are still described exactly. The numerical results of this work are compared with those of the analytical approach and other methods. Then, the influences of geometrical and material parameters on the free vibration and static bucking of the structure are explored. The data shows that the flexoelectric effect has a strong effect on the free vibration and static bucking behavior as well as the vibration mode shapes of the nanoplates. The working performance is increased when taking into account the effect of flexoelectricity. This work also shows that for each changing rule of plate thickness, the flexoelectric effect also significantly changes the mechanical response of the plate. This is an important suggestion in the design and use of plate structures in engineering practice. [ABSTRACT FROM AUTHOR]

Curved panels are structural elements that form the skin of wings, fuselages and tail booms in aircraft. Buckling of these structures would adversely affect aircraft performance. Due to this, the problem of buckling has been extensively researched in the past. Most of the research has been restricted to the analysis of flat composite panels and analysis of curved panels through simplifications involving geometry, material properties and boundary conditions. The present study aims to develop an analytical solution that can predict the critical buckling load for a wider range of problems. An analytical solution was developed in order to obtain the critical buckling load for a doubly-curved composite laminate under compression, shear, moment or any combination of the three loads. The assumptions of the classical laminate plate theory were used in order to obtain the displacement fields as well as strains of the laminate. The energy method was employed in order to obtain the critical buckling load for various load cases. The values obtained through the analytical solution are compared to the critical buckling loads obtained through finite element analysis (FEA). The highest deviation of critical buckling load from FEA was calculated to be 16.55%. Variation of the critical buckling load with respect to the radius of curvature, boundary conditions and stacking sequence was analyzed. The developed solution was also found to be valid for cases when radii of curvatures are unequal as well as when the length and breadth of laminate are unequal. [ABSTRACT FROM AUTHOR]

In this work, the buckling analysis of functionally graded materials (FGMs) plates exposed to different load conditions is investigated using an efficient and simple refined plate theory. Uniaxial and biaxial compression loads along with simply supported boundary conditions on rectangular FGM plates are investigated. The effective material properties are computed using the simple power law equation of the volume fraction of the plate constituents. The governing equations are obtained from the principle of virtual works. The accuracy of present analytical solution is confirmed by comparing the present results with those available in existing literature. It can be concluded that the present theory is not only accurate, but also simply in predicting the buckling analysis of functionally graded plates. [ABSTRACT FROM AUTHOR]

In this paper, the mechanics of shear deformable micro beams is investigated via finite element analysis, and a machine learning technique (Deep Learning Neural Network (DLNN)). DLNN is provided for the first time to accurately model and predict this behavior. Using the Finite Element Method (FEM), the obtained coupled equations of motion for shear deformable micro-scale beams are solved using a combination of Timoshenko beam theory and the modified couple stress theory (MCST). The results are compared with literature for each analysis to show the accuracy and the proposed finite element model. After presenting the mechanical model, by using Finite Element Analysis (FEA), a deep learning neural network model is developed for small-scale structures and the capability of this model in predicting different mechanical behavior under thermo-mechanical loading is investigated. It is shown that the presented model has great accuracy in predicting both static and dynamic behavior of small-scale structures with a significant reduction in the computational cost. The application of DLNN for modeling the machines of small- scale structures is a step forward for predicting the behavior of Nano/Micro Electro Mechanical Systems (NEMS/MEMS). [ABSTRACT FROM AUTHOR]

We comment on the paper published by Sakata et al., in J. Adv. Compos. Mater., 2018, 27, 35–51, which was in continuation of the previous work by Sakata and Ben in J. Adv. Compos. Mater., 2012, 21, 445–457. Although the experimental section in both works were identical, the reported numerical values of the linear buckling loads differed. In addition, all the specimens were manufactured using an identical process by employing silicone rubber mold and filament winding technique, and outer skin layers and stiffeners consisted of a fixed number of plies. Nonetheless, different shell thicknesses and stiffeners cross-sectional areas were reported for the specimens. Since the buckling behavior of cylindrical shells is highly sensitive to their thickness, the difference in the reported numerical linear buckling loads of the mentioned studies could be due to different thickness values used as inputs for their numerical analyses. In order to address this subject, the present study aimed to provide complete and comprehensive data on the buckling behavior of unstiffened and grid-stiffened cylindrical shells with the same material properties and geometrical dimensions but various thicknesses. The presented results can be used as a benchmark for future studies. [ABSTRACT FROM AUTHOR]

Abstract In this work, the applicability of nonlinear piezoelectric energy harvesters is demonstrated for high and low-frequency applications. An axially loaded piezoelectric patched beam model is derived considering in-plane stretching. The harvester setup is developed in the laboratory, and the energy-based numerical model is validated with experimental results. Optimum dimensions of the harvester are obtained. The broadband nature of the harvester is explored, considering nonlinear effects and axial loads on the harvester’s performance. The applicability of the proposed harvester is demonstrated meaningfully by exploiting bifurcation between hardening and softening types of non-linearity by adjusting axial loads with the help of a simple tunable harvester setup. [ABSTRACT FROM AUTHOR]

Abstract In this paper, static bending and buckling behavior of the simply supported truncated sandwich conical shell with variable thickness core are examined. The stiffness of the system changes as a result of changes in the porous core’s thickness, which varies along the generator direction. Additionally, there are five various styles of porosity distribution schemes for the porous foam core that are taken into consideration. Hamilton’s principle, FSDT and Galerkin method are utilized to obtain a set of matrix equations for calculating the deflections and critical buckling loads of the system under thermal environment. The static properties and mode are investigated. [ABSTRACT FROM AUTHOR]

This article presents a numerical method for analyzing the compressive buckling of porous power-law functionally graded (PPFG) plates placed on Pasternak foundations, which is based on a novel refined quasi-3-dimensional hyperbolic shear deformation theory (RQHSDT) combined with the Navier solution technique. The RQHSDT employs a novel hyperbolic distribution of in-plane displacements through the plate thickness to account for non-linear variations in transverse shear stresses, satisfies the traction free boundary conditions on the top and bottom surfaces, and accounts for shear deformation and thickness stretching effects of the plates without the use of any shear correction factors. Unlike classical shear and normal deformation theories, the RQHSDT has only four variables in its displacement field, as opposed to five or more variables in other quasi-3D shear deformation theories, which reduces the number of unknown variables and governing equations in plate analyses and simplifies calculations. The governing equations of the buckling problem are derived using the virtual work principle. In problem solving, the Navier solution technique is used to obtain the exact solutions for the rectangular PPFG plates with simply supported edges subjected to in-plane loading. The accuracy of the proposed approach is confirmed by comparing the obtained results to those of previously published quasi-3D shear deformation theories. Using comprehensive parametric studies, the effects of gradient index, porosity fraction index, porosity distribution type, geometric parameters, two-direction compression ratio, and stiffness of foundation parameters on buckling of PPFG plates are investigated. [ABSTRACT FROM AUTHOR]

This article investigates the influence of porosity and localized edge loads on the vibration and buckling characteristics of functionally graded material (FGM) plates using the finite element (FE) method. The analysis is carried out by choosing a single-layer FGM and two different types of FGM sandwich plates in such a way that there is no material discontinuity along the thickness direction. The porosity imperfections are accounted for in this study as criteria of stiffness reduction and are incorporated using modified power law distribution. The vibration and buckling responses are studied by considering four types of localized edge loads on plates with different porosity distributions. The application of different types of localized edge loads on the plate leads to the development of nonuniform in-plane stresses. Hence, they are computed first by using a dynamic approach before obtaining the buckling loads. The accuracy of the FE formulation is first validated for FGM plates by comparing the natural frequencies and the critical buckling loads obtained in the present investigation with the solutions already available in the literature. After validating the accuracy, detailed parametric studies have been performed on plates with varying volume fraction exponent, porosity distribution, porosity index, side-to-thickness ratio, load width ratio, aspect ratio, and support condition, and the results are presented with appropriate conclusions. A probabilistic sensitivity analysis is carried out to identify the significant parameter affecting the buckling load and natural frequency of porous FGM plates subjected to localized edge loads, which considerably aids in the design of the FGM plates. [ABSTRACT FROM AUTHOR]

In the design of in-plane stressed thin plates, the load condition where the distributed edge shear is locally applied along the plate boundaries is often encountered and has thus far not been well investigated. This load configuration can induce buckling instability. The problem of shear buckling instability in such applications has so far received very little attention from researchers owing to the additional analytical difficulties involved in obtaining rigorous solutions to the buckling of plates when subjected to partial loadings, and the present research aims to address the problem and present a rigorous solution. It focuses on investigating the problem of linear and nonlinear buckling of simply supported thin plates subjected to local in-plane shearing using the finite element method. The critical shear buckling stress is determined for different load cases applied to a judiciously designed plate specimen. Compressive, shear and von Mises stress analyses are conducted. The results achieved are summarized as tables, graphs and iso-stress contours. It is shown that the stability effect of the load ratio on the specimen is reached when the load extent covers 55% of the plate sides. The plate buckling in the length direction is justified by significant compressive stresses recorded in this direction. It has been found that, at buckling, a compressive diagonal field action occurs. Finally, the von Mises analysis shows that plasticization occurs at the plate length loading stop points. [ABSTRACT FROM AUTHOR]

Abstract A two-node beam element based on enhanced Timoshenko beam theory with three unknowns is developed for static and buckling behaviors of functionally graded beams. The model considers a quadratic variation of shear strain through the depth, and satisfies zero-shear strain at the top and bottom surfaces of the beam. The concept of a physical neutral axis is introduced to avoid stretching-bending phenomenon. The elementary matrices are derived utilizing the minimum potential energy. The accuracy and performance of the present model are verified through a series of examples. Furthermore, the effect of different parameters on behaviors of beams is discussed. [ABSTRACT FROM AUTHOR]

Porosity defects can emerge during the manufacturing process of Functionally Graded Sandwich Plates (FGSPs). In practice, FGSPs have geometric discontinuities/cutouts and are exposed to Nonuniform In-plane Edge Loads (NIELs). The presence of porosity, cutout and NIELs causes a significant reduction in the stiffness of the plate affecting its vibration and buckling behavior. Therefore, in this paper vibration and buckling results obtained using the Finite Element (FE) method hitherto not reported in the literature are presented for porous FGSPs with cutouts and subjected to NIELs. Four types of porosity distribution models are explored, and the porosity imperfections are modeled as the criteria of stiffness reduction. Porosity-dependent material properties of FGSPs are evaluated using modified power law and sigmoid function. The current study incorporates two distinct kinds of sandwich configuration in such a way that there is no material mismatch along the thickness direction. The application of different cases of NIELs on the plate with cutouts leads to the development of nonuniform stresses. Hence a novel dynamic approach has been proposed to evaluate buckling loads by implementing two sets of boundary conditions. The first set of boundary conditions calculates pre-buckling stress, while second set calculates critical buckling loads. The generated results from the current FE formulation are compared with existing results in the literature to ensure accuracy. Finally, the effect of porosity distribution, NIELs, cutout ratio and its positions, support conditions, volume fraction exponents and geometric parameters on the vibration and buckling response are studied and discussed to arrive at appropriate conclusion. [ABSTRACT FROM AUTHOR]

Based on doublet mechanics theory and various beam theories, this paper presents free vibration of axially loaded zigzag and armchair nanobeams. A two-noded higher order beam element is used to solve the problems of nanobeams with various boundary conditions. The verification studies in terms of fundamental frequencies and buckling loads are performed by comparing the results by the present model with Molecular Dynamic Simulations, Doublet Mechanics, and Eringen's nonlocal theory. The effects of material length scale parameter, slenderness ratio, nanotube model and boundary conditions on the fundamental frequencies of axially loaded nanobeams are investigated in details. Softening material behavior is detected for zigzag and armchair nanobeams. Having stiffer boundary conditions lead to the effect of material length scale parameter to be observed more prominently. [ABSTRACT FROM AUTHOR]

The ultimate strength of spherical shells under external pressure has been an attractive topic in the field of marine structures. However, recent studies have revealed that the current theoretical approaches are hardly compatible with the actual hulls, which indicates that the ultimate strength models still need to be reevaluated and unified. To address this challenge, a comparative study has been conducted in this paper. Various analytical approaches and codified rules are compared through screened experiment data that have realistic imperfections and different shape parameters in the range generally applied for marine structures. The model evaluation criteria have been established by implementing statistical model uncertainty factors in terms of bias and coefficient of variation. A comparison of the results has been made from three different aspects including shell shape, R/t and geometrical parameters to evaluate their performance. Based on the calculation outcome, analysis has been made to study the theory behind those models and determine their limitations and recommended application range. [ABSTRACT FROM AUTHOR]

Abstract The present work intends to use higher-order zigzag theory to analyze double- and cross-helicoidal laminated sandwich plates under buckling conditions. Geometry and boundary effects on buckling and mode shapes are examined. The behavior of helicoidal sandwich plates is compared with the cross-ply and quasi-isotropic lamination schemes. In the case of plates with free edges, the bio-inspired laminated sandwich plates outperform the more traditional cross-ply and quasi-isotropic laminated schemes. Numerous more findings are provided as well, all of which may be used as a standard by which to measure the success of comparable future research efforts. [ABSTRACT FROM AUTHOR]