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The quest for safe lower bounds to the elastic buckling of axially loaded circular cylindrical shells has exercised researchers for the past 100 years. Recent work bringing together the capabilities of nonlinear numerical simulation, interpreted within the context of extended linear classical theory, has come close to achieving this goal of defining safe lower bounds. This paper briefly summarizes some of the important predictions emerging from previous work and presents new simulation results that confirm these earlier predictions. In particular, we show that for a specified maximum amplitude of the most sensitive, eigenmode-based geometric imperfections, normalized with respect to the shell thickness, lower bounds to the buckling loads remain constant beyond a well-defined value of the Batdorf parameter. Furthermore, we demonstrate how this convenient means of presenting the imperfection-sensitive buckling loads can be reinterpreted to develop practical design curves which provide safe, but not overly conservative, design loads for monocoque cylinders with a given maximum permitted tolerance of geometric imperfection. Hence, once the allowable manufacturing tolerance is specified during design or is measured post-manufacturing, the greatest expected knockdown factor for a shell of any geometry is defined. With the recent research interest in localized imperfections, we also attempt to reconcile their relation to the more classical, periodic, and eigenmode-based imperfections. Overall, this paper provides analytical and computational arguments that motivate a shift in focus in defect-tolerant design of thin-walled cylinders--away from the knockdown experienced for a specific geometric imperfection and towards the worst possible knockdown expected for a specified manufacturing tolerance. [ABSTRACT FROM AUTHOR]

A bimetallic steel bar (BSB) consisting of stainless-steel cladding and carbon steel substrate exhibits excellent corrosion resistance and good mechanical properties. The bimetallic structure of BSBs may affect their low-cycle fatigue performance, and current investigations on the above issue are limited. In this study, the low-cycle fatigue properties of bimetallic steel bars (BSBs) with inelastic buckling were investigated. Experiments and numerical studies were conducted to investigate the low-cycle fatigue capacity for BSBs, considering buckling. The buckling mode of BSBs is discussed. The hysteretic loops and energy properties of BSBs with various slenderness ratios (L/D) and fatigue strain amplitudes (εa) are investigated. With increases in the L/D and εa, the original symmetry for hysteresis loops disappears gradually, which is caused by the buckling. A predictive equation revealing the relation between the εa and fatigue life is suggested, which considers the effects of the L/D. A numerical modelling method is suggested to predict the hysteretic curves of BSBs. The effect of buckling on the stress and energy properties of BSBs is discussed through the numerical analysis of 44 models including the effects of the L/D, εa, and cladding ratios. The numerical analysis results illustrate that the hysteresis loops of BSBs with various εa values exhibit similar shapes. The increase in the cladding ratio reduces the peak stress and the dissipated energy properties of BSBs. The hysteresis loop energy density decreases by about 3% with an increase of 0.1 in the cladding ratio. It is recommended that the proportion of stainless steel inBSBs should be minimized once the corrosion resistance requirements are met. [ABSTRACT FROM AUTHOR]

This article discusses the influence of technological defects on the mechanical behavior of carbon-fiber reinforced polymer (CFRP) during buckling under compression. The study found that the presence of defects affected the elastic modulus and maximum load of the CFRP samples. Acoustic emission signals and digital image correlation were used to monitor the delamination process and fiber fracture. Another related study explores the effect of elevated temperature and preliminary thermal aging on the residual mechanical properties of a structural fiberglass, using acoustic emission signals to assess changes in mechanical behavior. Both articles provide valuable insights into the performance and durability of these materials. [Extracted from the article]

The effects of initial small-scale material nonlinearity on the pre-yield and pre-buckling response of externally pressurized metallic (plane strain) perfect rings (very long cylindrical shells) is investigated. The cylindrically curved 16-node element, based on an assumed quadratic displacement field (in surface-parallel coordinates) and the assumption of linear distribution of displacements through thickness (LDT), is employed to obtain the discretized system equations. The effect of initial small-scale material nonlinearity (assumed hypo-elastic) on the deformation and stress in the pre-yield and pre-buckling regime of a very long relatively thin metallic cylindrical shell (plane strain ring) is numerically investigated. These numerical results demonstrate that the enhanced responses for metallic rings due to initial small-scale nonlinearity are significant enough to not miss attentions from designers and operators of submersibles alike. [ABSTRACT FROM AUTHOR]

The present investigation has analyzed the buckling of bi-directional functionally graded conical micro-shells bearing axial loading. The dominant equations serve on the basis of the theory of first-order shear deformation in the modified couple stress theory (MCST). The Ritz technique is used so as to solve the governing equations. Bi-directional functionally graded material is the material used to construct the shell, and in a predefined composition profile, the volume fractions pertaining to the constituent materials constantly vary through the conical edge directions and thickness. The model predictions are compared and successfully validated using the ones available in the literature. According to the results, in comparison with the classical theory, the micro-shell buckling load is higher in the MCST. In addition, the contribution of a number of geometrical and mechanical parameters, for example, radius-to-thickness ratio, thickness-to-length scale ratio, length-to-radius ratio, semi-vertex angle, homogenization schemes, and material gradient indexes, to the buckling performance of conical micro-shells has been investigated. It is noteworthy that this investigation is the first effort to present a buckling analysis for the purpose of bi-directional functionally graded truncated conical micro-shells in accordance with the MCST. [ABSTRACT FROM AUTHOR]

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations. [ABSTRACT FROM AUTHOR]

The authors propose an intelligent computational method using the deep feedforward neural network integrated with an improved balance composite motion optimization algorithm to formulate a so-called iBCMO-DNN for solving the stochastic thermal buckling problems of functionally graded porous microplates. In the present approach, the deterministic behaviors of the functionally graded porous microplates were firstly analyzed by the combination of a unified higher-order shear deformation theory, modified strain gradient theory, and Ritz-type series solutions, and then stochastic responses under uncertainty of material properties are obtained by the iBCMO-DNN algorithm. The deep neural network with the long short-term memory model is used as a surrogate method to replace the time-consuming computational model, while the improved balance composite motion optimization is used to search for the optimal solutions. The obtained numerical results for various boundary conditions, uncertainty parameters, and three types of temperature distribution indicated that the proposed method achieves its accuracy and effectiveness in predicting stochastic thermal buckling of the functionally graded porous microplates. The improved balance composite motion optimization algorithm demonstrates a computational time ∼1.7 times faster than its predecessor. Furthermore, integrating a deep neural network into the improved algorithm reduces computational time to about 2/5 compared to the method without it. [ABSTRACT FROM AUTHOR]

Thermal buckling analysis of a simply supported sandwich cylindrical microshell with piezoelectric layers reinforced with graphene platelets is presented in the current study. The motion equations of the piezoelectric microshell are derived in reference to the first-order shear deformation hypothesis alongside the modified couple stress theory. The critical buckling temperature difference of piezoelectric graphene platelets reinforced cylindrical microshells is derived from adopting Navier's approach and the meshless method. The material properties of every layer for microcomposite shell layers reinforced by graphene platelets are estimated using Halpin–Tsai model. The comparison study is conducted to verify upcoming results. The goal is to investigate the effects of the applied voltage, the thickness of the piezoelectric layers, the distribution pattern, the weight fraction, the material length scale parameter, the length to radius ratio, and the thickness to radius ratio on the buckling of piezoelectric graphene platelets cylindrical microshell. [ABSTRACT FROM AUTHOR]

Smart materials and structures at the nanoscale represent the main components in manufacturing plan for nano-electromechanical systems. In this research study, an unconventional shell model based upon the nonlocal couple stress (NCS) continuum mechanics accommodating the both softening and stiffening features of size dependency is formulated to analyze the buckling mode transition phenomenon in nonlinear stability characteristics of functionally graded (FG) piezoelectric nanoshells subjected to thermo-electromechanical load. To accomplish this objective, an efficient numerical strategy based upon the moving Kriging meshfree (MKM) technique is employed via different nodal distribution schemes, including Chebyshev, regular uniform and irregular ones. The established NCS-based numerical model has the capability to incorporate the buckling mode transition phenomenon as well as satisfying the function property of the Kronecker delta via imposing essential boundary conditions with no use of predefined mesh and directly at the associated nodes. It is also demonstrated that by changing the sign of electric actuation from negative to positive, the softening character of nonlocality as well as the strengthening character associated with the couple stress size dependency become a bit more significant. Furthermore, the roles of both unconventional stress tensors are more prominent in the value of the second bifurcation point in comparison with the first one. [ABSTRACT FROM AUTHOR]

Size-dependent functionally graded material thin plate buckling and post-buckling problems are considered using the framework of the MCST (Modified Couple Stress Theory). Based on modified couple stress theory and power law, the post-buckling deflection and critical buckling load of simply supported functionally graded material thin plate are derived using Hamilton's minimum potential energy principle. The analysis compares the simulation results of linear buckling and nonlinear buckling. Innovatively, a power-law distribution with scale effects is considered. The influences of scale effect parameters l and power-law index parameters k on buckling displacement, load, and strain energy of plates have been investigated. In this article, it is found that the critical buckling displacement, critical buckling load, and buckling strain energy increase with increases in the power-law index parameters k. The membrane energy decreases as the power-law index parameter increases. If the upper and lower layers are swapped, the opposite result is obtained. In comparison, the scale effect parameter is more influential than the power-law exponent. The critical buckling displacement in the x-direction is not affected by scale effects. The critical buckling load, the membrane energy, and buckling strain energy increase as the scale effect parameter increases. Scale effects increase material stiffness compared with traditional theory, and the power-law index parameters affect FGM properties such as elastic modulus, Poisson's ratio, density, etc. Both scale effects parameters and power-law index parameters have important effects on the mechanical behavior of materials. [ABSTRACT FROM AUTHOR]

AbstractThis study introduces a spatial shear deformable rectangular element formulation to investigate the size-dependent buckling behavior of porous graphene platelets (GPL) reinforced micro-shells within the framework of the modified couple stress theory (MCST) for the first time in the worldwide term. The rectangular element, characterized by 4 nodes with 19 degrees of freedom each and possessing weak continuity of order C1, incorporates a length scale parameter enabling size-dependent analyses of shells. The research considers three distinct functions for the distribution of porosity combined with three different patterns of the GPL distribution (called by patterns A to C) along the micro-shell thickness. The elastic modulus of the nanocomposite in the absence of porosity is obtained using the Halpin-Tsai micromechanics model. Subsequently, the study meticulously validates the modeling accuracy and then investigates variations in the critical buckling load with respect to porosity distribution functions, distribution patterns of GPL, porosity coefficient, weight percentage of GPL, geometric parameters of the cylinder, and the length-scale parameter. The results reveal that the combination of the GPL pattern A with the first symmetric type porosity distribution yields the highest critical buckling loads. On the contrary, if the pattern B is combined with the second symmetric type of porosity distribution, the lowest critical buckling load will be observed. Given the accuracy of the results obtained and the versatility of the finite element method (FEM) in handling complex geometries together with diverse boundary conditions, the developed element holds promise for analyzing shells of various shapes under different boundary conditions. [ABSTRACT FROM AUTHOR]

This article explores the impact of pre-tensioning force on the behavior of Buckling Restrained Brace (BRB) supported by a double pre-tensioning system. The study uses Finite Element Analysis (FEA) to investigate different configurations and pre-tensioning force values on traditional all-steel BRB members. The research aims to enhance rectangular BRBs with pre-tensioning systems and examines the impact of different parameters on their behavior. The findings of the study can contribute to the development and improvement of BRBs in seismic protection and structural engineering. [Extracted from the article]

We investigate the effect of defect geometry in dictating the sensitivity of the critical buckling conditions of spherical shells under external pressure loading. Specifically, we perform a comparative study between shells containing dimpled (inward) versus bumpy (outward) Gaussian defects. The former has become the standard shape in many recent shell-buckling studies, whereas the latter has remained mostly unexplored. We employ finite-element simulations, which were validated previously against experiments, to compute the knockdown factors for the two cases while systematically exploring the parameter space of the defect geometry. For the same magnitudes of the amplitude and angular width of the defect, we find that shells containing bumpy defects consistently exhibit significantly higher knockdown factors than shells with the more classic dimpled defects. Furthermore, the relationship of the knockdown as a function of the amplitude and the width of the defect is qualitatively different between the two cases, which also exhibit distinct post-buckling behavior. A speculative interpretation of the results is provided based on the qualitative differences in the mean-curvature profiles of the two cases. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to the analysis of large deflection and post-buckling behavior of cantilever nanorods under different load conditions. The proposed approach utilizes a variational method, incorporating the Gurtin–Murdoch surface elasticity theory and the consistent couple stress theory to account for size-dependency effects. By accounting for the strain energy contributions of the bulk material, surface layer, and load conditions, this approach expresses the behavior of the nanorods in terms of their intrinsic coordinates. A finite element method was used to solve this numerical problem, generating a system of non-linear equations that were iteratively solved using the Newton–Raphson method. The results obtained from the finite element method were confirmed by those from the shooting method. Also, it highlights the effectiveness of the variational model in predicting the large deflection and post-buckling behavior of cantilever nanorods while considering both surface stress and couple stress effects. Furthermore, the study investigated the influence of surface stress and couple stress on the response of the nanorods to point and uniform loads. The results showed that incorporating both effects enhanced the stiffness of the nanorods compared to scenarios in which these effects were neglected. In addition, the couple stress effect was found to have a greater influence on the stiffening of nanorods for the same value of unitless parameters compared to surface stress effects. These findings offer valuable insights into the large deflection and post-buckling behavior of cantilever nanorods and highlight the importance of surface stress and couple stress effects. The model proposed in this study has potential applications in advanced technological device designs by providing a comprehensive understanding of the mechanical response of nanorods, allowing for more accurate predictions and enhanced device performance. [ABSTRACT FROM AUTHOR]

Flexible pipe is one of the most important types of equipment applied in the deep-water development of oil and gas and deep-sea metal mining. The carcass of an unbonded flexible pipe with a typical interlocked structure prevents buckling failure under external hydrostatic pressure. The process and principle of carcass layer deformation are described, and a three-dimensional finite element model with solid-shell elements is developed to simulate the cold forming process of a metal strap subjected to a series of rollers. The deflection and deformation behavior in the bend-rolling and interlocking process are investigated, and the residual stress due to deformation is calculated. Taking the carcass layer of a 4-inch internal diameter flexible pipe as an example, a three-dimensional finite element model of the carcass layer loaded with external hydrostatic pressure is developed. The buckling collapse of the carcass layer is evaluated considering different initial imperfections, including residual stress. The results show that the critical pressure can be 60% less than under ideal conditions when the geometric imperfection, material nonlinearity and residual stress due to deformation are considered, which indicates that the effect of residual stress on buckling collapse cannot be ignored. The numerical model and results provide an efficient method and basis for nonlinear buckling analysis and a collapse-resistant unbonded flexible pipe design for industry. [ABSTRACT FROM AUTHOR]

Present study deals with the nonlinear analysis of thermally induced deflection and snap-through buckling in functionally graded porous (FGP) curved nanotubes. It is assumed that the curved nanotube is rested on a two-parameter nonlinear elastic foundation. The curved nanotube is subjected to uniformly distributed transverse pressure loading and also uniform temperature rise. Distribution of thermomechanical properties in the thickness of curved nanotubes is radially graded according to a power law function. The even type of porosity distribution patterns is included into the formulation and all properties are considered as temperature dependent. The nonlocal strain gradient and uncoupled thermoelasticity theories are provided to analyze the geometrically nonlinear behaviors of curved nanotubes. The equilibrium equations are obtained based on the high-order shear deformation theory. To capture the large deformations, the von Kármán type of nonlinear kinematic assumptions is included. Two types of immovable boundary conditions are considered which are simply-supported and clamped-clamped. The equilibrium equations are reformulated and transferred into the dimensionless presentation. The closed-form expressions are provided to trace the thermal/mechanical load-deflection paths of curved nanotubes using the two-step perturbation technique. Numerical results of this study are compared with the available data in the literature for the macro-scale curved tubes. After that novel parametric results are provided to discuss the effects of nonlocal and length scale parameters, boundary conditions, porosity coefficient, foundation stiffness, power law exponent, and geometrical parameters. [ABSTRACT FROM AUTHOR]

Based on experimental data, this study presents a model of the dynamic growth of a thermally grown oxide (TGO) in thermal barrier coatings (TBCs) during thermal cycling. The model was solved using the finite element method. The thermal stress results of the model were compared with experimental results to verify the accuracy of the model. The stress analysis revealed that the combined effect of radial tensile stress and circumferential compressive stress can lead to the delamination of TBCs in a buckling form, which can induce the formation of cracks in TBCs along the axial direction. This observation was consistent with the conclusions drawn from the experimental results. Crack initiation and propagation result from the action of the maximum shear and radial stresses. In addition, the relationship between buckling failure and microscopic cracks was investigated. Thermal cycling induces radial and circumferential cracks, leading to buckling, delamination, and ultimate coating failure as the radial and circumferential cracks interact at the interface. [ABSTRACT FROM AUTHOR]

This study investigates the buckling behavior of functionally graded (FG) porous micro-shell covered with nanocomposite facesheets; graphene nanoplatelets (GPLs) are hired to reinforce and strengthen the faces. This micro-shell is under a hygrothermal environment and rested on Kerr foundations which consist of two rows of springs and one shear layer. Due to considering the size effect for this microstructure, modified couple stress theory is implemented in the strain energy. Reddy's theory in the Cartesian coordinate system is applied to analyze shear stress distribution through z-direction. In the end, the Navier's solution method is employed to solve equations analytically for simply supported edges. Moreover, the validity of the outcomes is confirmed by comparing them with a previous published study. After validation, the key findings of the research are examined; it highlights the influences of GPLs of facesheets and porous distribution on the stiffness of the structure, and the impact of Kerr foundation on the result is the most significant outcomes. The main implications show that the symmetric porosity distribution and FG V-A GPLs distribution make this engineering structure become stiffer which consequently leads to an increase in critical buckling load. [ABSTRACT FROM AUTHOR]

The forthcoming second generation of EN 1993‐1‐5 is bringing changes in terms of buckling and interpolation curves that allow the positive effects of torsional stiffness of closed‐section stiffeners to be taken into account. Regarding the determination of the critical buckling stress for global plate buckling, analytical or numerical methods may be used. FprEN 1993‐1‐5 provides a simplified analytical equation for determining the critical buckling stress of an equivalent orthotropic plate, which can also be found in the informative Annex A of EN 1993‐1‐5. The given equation does not take into account the torsional stiffness of longitudinal stiffeners with closed cross‐sections. The latter are often used in plated structures due to fabrication and strength benefits. This paper compares two methods for determining the elastic critical plate buckling stress that consider the positive effect of the torsional stiffness of closed‐section stiffeners. First, a newly proposed analytical method that accounts for the torsional stiffness of closed‐section stiffeners is derived on the same basis as the current equation in Annex A. Secondly, a numerical linear buckling analysis is performed on a large number of stiffened panels. The advantages and disadvantages of both methods are pointed out. Finally, both values are used to determine the ultimate resistance of plates and with GMNIA results from previous studies. [ABSTRACT FROM AUTHOR]

Background: The modelling of the sheet metal forming operations requires accurate and precise data of the material plastic behaviour along non-proportional strain paths. However, the buckling phenomenon severely limits the compressive strain range that could be used to deform thin metal sheets. Objective: The main aim of this paper was to propose an effective device, that enables to determine of accurate stress-strain characteristics of thin metal sheet specimens subjected to axial deformation without buckling and with a special emphasis on friction correction. Methods: In this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of X10CrMoVNb9-1 (P91) power engineering steel, and DP500 and DP980 dual-phase steels, under compression loading. The fixture enables monitoring of the friction between the specimen and supporting blocks during the test, and thus the precise stress response of the material could be determined. Results: The effectiveness of the fixture was evaluated under tension–compression cyclic loading and during the compression tests in which high-strength thin metal sheets were successfully deformed up to 10% without specimen buckling. Furthermore, the successful determination of a friction force variation between supporting blocks and the specimen during tests enabled to determine an actual force acting on the specimen. Conclusions: The proposed testing fixture was successfully assessed during the compression and cyclic tension–compression of high-strength thin metal sheets as no buckling was observed. Its advantage lies in adapting to change its length with specimen elongation or shrinkage during a test. The friction force generated from a movement of both parts of the device could be effectively monitored by the special strain gauge system during testing and thus its impact on the stress-strain characteristics could be successfully eliminated. [ABSTRACT FROM AUTHOR]

In the present work, the symmetric thermal buckling behavior of shear deformable heterogonous nano/micro circular porous plates resting on a two parameter foundation is studied. The material behavior of the nano plate is modeled by the modified couple stress theory. The plate material properties assumed to be graded across the thickness direction according to a simple power law, and have a uniform open void porosity. Using Mindlin's plate theory and the nonlinear von-Karman strain field and implementing the energy method, the plate stability equations together with the membrane equilibrium equation are derived and expressed in terms of the displacement field components. Then the nondimensionalized forms of the equations are derived using differential quadrature method (DQM). The resulting eigenvalue problem is solved to evaluate the plate critical buckling temperature difference. Convergence and comparative studies are carried out. Also the influences of some important parameters including length scale factor, porosity factor and Winkler& Pasternak stiffness coefficients are investigated. [ABSTRACT FROM AUTHOR]

This paper focuses on the size-dependent free vibration and buckling behaviors of the axially functionally graded (AFG) graphene platelets (GPLs) reinforced nanocomposite microbeams subjected to axially varying loads (AVLs). With various axial grading patterns, the GPL nano-reinforcements are distributed throughout the polymer matrix against microbeam length, and the improved Halpin–Tsai micromechanics model and the rule of mixture are adopted to evaluate the effective material properties. Eigenvalue equations of the microbeams governing the static stability and vibration are derived based on the modified couple stress Euler–Bernoulli beam theory via the state-space method, and are analytically solved with the discrete equilong segment model. The effects of axial distribution patterns, weight fraction, and geometric parameters of GPLs, as well as different types of AVLs, on the size-dependent buckling load and natural frequency are scrutinized in detail. The results show that the synchronized axial distributions of GPLs and AVLs could improve the buckling resistance and natural frequency more powerfully. [ABSTRACT FROM AUTHOR]

Small-sized structural elements such as beams, plates, and shells are usually used as nanomechanical resonators, nanoscale mass sensors, nanoelectromechanical actuators, and nanoenergy harvesters. At the nanoscale, the structures usually possess a high surface area-to-bulk volume ratio, leading to the free energy related to surface atoms becoming considerable compared to that of the bulk part. Earlier reports indicated several physical reasons for size-dependent phenomena, e.g., nonlocal stress, surface energy, and couple stress. To provide an in-depth insight into the mechanical behavior of small-scale structures, size-dependent continuum models including two or more physical factors have attracted the attention of the academic community. This research analyzes the thermal buckling and postbuckling characteristics of functionally graded carbon nanotube-reinforced (FG-CNTR) nanobeams with a tri-parameter, nonlinear elastic foundation and subjected to a uniform temperature rise. Chen-Yao's surface energy theory and Yang's symmetrical couple stress theory are combined to capture two types of size effects in nanobeams. The postbuckling model is formulated based on the Euler–Bernoulli deformation hypothesis and Euler–Lagrange equation. Using a two-step perturbation technique, the related postbuckling equilibrium path is determined. In numerical analysis, the impacts of surface energy, couple stress, elastic foundation, boundary conditions, geometric factor, layout type, and volume fraction of CNTs on the thermal buckling and postbuckling behaviors of nanobeams are revealed. It is indicated that considering couple stress or surface energy can lead to a significant increase in the postbuckling stability of nanobeams compared to the case in which it is not considered. In addition, there is a reverse competition between couple stress or surface energy effects on the thermal buckling responses of nanobeams. As the temperature rise will cause the material elastic moduli softening, the thermal buckling load–deflection curves of nanobeams with the temperature-independent case are much higher than those with the temperature-dependent cases. [ABSTRACT FROM AUTHOR]

Curved nanobeams are one of the essential components in manufacturing nano-electromechanical systems needing nonlinear stability design. In the current investigation, the nonlinear buckling characteristics of functionally graded porous reinforced curved (FGPRC) nanobeams having different degrees of curvature are analyzed by counting the higher-order gradients of the classical strain tensor as well as nonlocal-type interatomic interactions. In this regard, two independent length-scale constants within the framework of the nonlocal strain gradient theory (NSGT) of continuum elasticity are taken into account. Via employing the promising low computational cost and geometrically adaptable method of isogeometric collocation, various branches of NSGT-based equilibrium graphs of FGPRC nanobeams are plotted relevant to each considered degree of curvature. It is extrapolated that the quantity of graphene platelet (GPL) weight fraction has a negligible influence on the significance of nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect in the value of the maximum deflections or lateral loads at the detected limit points, especially attributed to a higher degree of curvature. Besides, it can be remarked that, in the FGPRC nanobeam owning a small degree of curvature, lessening the quantity of porosity index results in an increment in the significance of the nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect on the maximum deflection at both upper and lower limit points. However, in the FGPRC nanobeams owning medium and large degrees of curvature, it gets lesser at the upper limit point, but becomes higher at the lower limit one. [ABSTRACT FROM AUTHOR]

• Comprehensive examination of prismatic shape memory alloy (SMA) beam-columns and their resistance against buckling. • Integration of analytical and semi-analytical methods to understand the process of straightening the column and prevent buckling. • Development of a mathematical model that provides a step-by-step explanation of the anti-buckling phenomenon. • Identification of nine different stages of stress-height diagrams resulting from the complex stress–strain behavior of SMA materials. • Derivation of corresponding forces and moments for each stage using analytical methods, facilitating the design of SMA structures. • Highlighting that achieving a uniform strain distribution across all sections of the column is the primary reason for beam-column straightening, rather than relying on an even distribution of stress. • Demonstrating that the process of achieving a uniform strain distribution led to a gradual decrease in the curvature of the beam-column, ultimately reaching zero curvature. The present paper focuses on studying the anti-buckling behavior of prismatic martensitic shape memory alloy (SMA) beam-columns. It combines analytical and semi-analytical approaches to investigate the process of column straightening for anti-buckling. We try to comprehensively describe this phenomenon and develop a mathematical model to formulate each step of the anti-buckling problem. Due to the complex stress–strain behavior of SMA material, nine different stages of stress-height diagrams may potentially occur during this effect; thus, for facilitating the design process of SMA structures, corresponding forces and moments to each stage, are analytically derived. Our demonstration establishes that the primary cause of beam-column straightening is not the uniformity of stress, but rather the achievement of uniform strain across all fibers of the cross-section. This uniform strain distribution implies that the curvature of the beam-column diminishes to zero. [ABSTRACT FROM AUTHOR]

Cutouts are commonly found in aerospace, ships, and marine structures, which have a great influence on mechanical properties such as stress concentration, natural frequency, and structural load-bearing performance of the structure. In this study, buckling behaviors of a square plate with a circular flanged cutout at the center are explored numerically, aiming to address the influence of different cutout parameters on the elastic and elasto-plastic buckling behaviors of the perforated plate. The flanged-perforated plate is subjected to uniaxial compressive loads, and the four edges are simply supported in the out-of-plane direction. The influence of various cutout parameters on the elastic and elasto-plastic buckling behaviors of the perforated plate is examined through a series of buckling analysis. In addition, structural weight reduction of the uniaxial compressed perforated square plates is carried out under the constraint of the elastic buckling stress of the plate structure. The findings indicate that different cutout parameters have a significant impact on the buckling performance of the plate. Perforated plates with flanging exhibit higher buckling strength than those without flanging, and variations in plate geometric parameters (such as the plate slenderness ratio and cutout radius ratio) are associated with increases in elastic buckling stress and elasto-plastic ultimate strength. The results of this paper can provide references for the design of flanged-cutouts in engineering. [ABSTRACT FROM AUTHOR]

Although it is often asserted that, in view of their reduced length, axially compressible beams have a higher buckling load than their inextensible counterparts, a detailed analysis demonstrates that this is not necessarily the case. The argument to arrive at this conclusion is made in terms of relatively straightforward concepts of elasticity and structural mechanics. It is shown that for certain classes of materials, the reduced prebuckling length is more than compensated for by a softening of the elastic response, leading to a reduction of the Euler critical load. [ABSTRACT FROM AUTHOR]

The prebuckling deformation of structures is neglected in most of the conventional buckling theory (CBT) and numerical method (CNM), because it is usually very small in conventional concepts. In the preceding paper (Su et al., 2019), we found a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation became large and essential for determining the critical buckling load, and developed a systematic buckling theory for 3D beams considering the effects of finite prebuckling deformation (FPD). For bulk structures that appear vastly in the advanced structures, a few buckling theories consider the effects of the prebuckling deformation in constitutive equations by energy method, which are significantly important but not straightforward and universal enough. In this paper, a systematic and straightforward theory for the FPD buckling of bulk structures is developed with the use of two constitutive models. The variables for the prebuckling deformation serve as the coefficients of the incremental displacements, deformation components, and stress in the buckling analysis. Four methods, including the CBT, CNM, DLU (disturbing-loading-unloading method) method and FPD buckling theory, are applied to the classic problems, including buckling of an elastic semi-plane solid and buckling of an elastic rectangular solid, respectively. Compared with the accurate buckling load from the DLU method, the FPD buckling theory is able to give a good prediction, while the CBT and CNM may yield unacceptable results (with 70% error for the buckling of an elastic semi-plane solid). [ABSTRACT FROM AUTHOR]

Hoop stresses are produced due to the electromagnetic forces in the winding. Free buckling of winding turns can lead to failure of the transformer. Design issues are a major reason for the catastrophic failure of 11kV/433kV distribution transformers. In a distribution transformer (DT), the LV winding is generally of helical type and is asymmetrical. Asymmetry in the transformer design causes change in the direction and magnitude of the forces. In this work, a comprehensive analysis of the short-circuit forces has been done for a DT with a double-layer helical winding with all three of the limbs modelled and phases energized. The forces are computed using magnetostatic analysis of a 315kVA DT. The transformer has been modelled in 3D CAD software and forces are computed using 3D finite element method (FEM) and the results obtained are compared to that obtained from first principals. The windings are assessed for the presence of hoop stresses in its turns, and along with it the safety factor is computed for free-bucking using von-Mises equivalent. The intent is to find the weak section of the double layer helical winding from short circuit forces a transformer is designed to withstand. Such simulations of energy conversion create a robust and sustainable design, which can prevent catastrophic failure and reduce the environmental impact due to major repairs or replacement of equipment. [ABSTRACT FROM AUTHOR]

In this work, a nonlocal strain gradient model for the buckling analysis of functionally graded Euler–Bernoulli beam subjected to thermo-mechanical loads is developed. The governing equations are derived by incorporating the effects of nonlocal and strain gradient parameters. Thermal properties over the cross section are graded using the power law. The resulting sixth-order differential equation is solved analytically for various boundary conditions. The effect of strain gradient and nonlocal parameters on the variation of critical buckling temperature under three different boundary conditions and three different thermal loading conditions is studied. The proposed model compares well with the existing literature in the limiting sense of no nonlocal and gradient effects. [ABSTRACT FROM AUTHOR]

In this article, the numerical and experimental results for buckling analysis of a nanocomposite beams reinforced by nanorods are studied and compared. The Chebyshev-Ritz method is used to calculate the buckling numerically and compare it with the buckling test. Epoxy resin, glass's fiber, and nanorods are used to make composites. These nanorods are made using recycled materials. Also, bending and tensile tests are used to obtain the properties of these composites. In addition, the effect of various parameters such as Young's modulus, temperature change, Poisson's ratio, and boundary conditions, the strain gradient parameter, and different shape function is investigated. The addition of nanorods increases the strength and stiffness of composites and increases the critical buckling load. Actually, the made nanorods are used as a reinforcement in matrix, thus in the made nanocomposites, fracture and buckling tests are done and the results indicate that the inclusion of nanorods (0.32%) increases the critical buckling load by 16.4%. A facile hydrothermal method to synthesis the nano rodes has a less cost with the other methods, thus by adding a small percentage of it to the composite, the stiffness of the structure increases. According to the results and the significant increase in Young's modulus and critical buckling load and the cost-effectiveness of carbon nanorods (CNRs) made from recycled materials, these environmentally friendly reinforcements can be used in various industries such as machine body construction, automobile manufacturing, shipbuilding and construction of type's turbines. Highlights • Using potato peels and hydrothermal methods, CNRs produced. • These CNRs are useful, and production is cheap and no harm environmental. • Buckling sample include of glass fiber, without and with CNRs and epoxy resin. • Third order shear deformation beam theory and Chebyshev-Ritz are used • Theoretical and experimental buckling critical load are compared. [ABSTRACT FROM AUTHOR]

The novelty of this study is to model and investigate the free and forced thermal vibration and buckling behaviors of a porous functionally graded magneto-electro-elastic (MEE) nanoplate made of barium-titanate and cobalt-ferrite and subjected to moving loads. In the modeling, the strains are assumed to originate from classical mechanics, thermal expansion, electroelastic, and magnetostrictive properties, nonlocal elasticity, and strain gradient elasticity, and the motion equations of MEE nanoplate are obtained by Hamilton's principle Considering various cases, the effects of thermal stresses, magneto-electro-elastic coupling, externally applied electric and magnetic field potential, nonlocal properties (nonlocal and material size parameters), porosity volume fraction on the free vibration and buckling behavior have been studied. Additionally, the forced response to the moving load for various cases of the velocity of the load is also investigated. It is observed that the free-response and buckling of the nanoplate vary with the material composition, externally applied electrical and magnetic fields, temperature rise, and porosity volume fraction. Furthermore, it is also noticed that the velocity of the load is the most influential factor in the forced response of the MEE nanoplate. Moreover, the material composition of the nanoplate characterizes the magneto-electro-elastic response depending on the amounts of barium-titanate (electro-elastic) and cobalt-ferrite (magnetostrictive). The stiffness of the MEE nanoplate can be controlled by regulating the intensities of electric and magnetic fields. This property can keep the bending and buckling stability of the nanoplate exposed to severe thermal and high-speed moving loads. [ABSTRACT FROM AUTHOR]

In this paper, free vibration analysis and temperature-dependent buckling behavior of porous functionally graded magneto-electro-thermo-elastic material consisting of cobalt ferrite and barium titanate were modeled and analyzed. A high-order sinusoidal shear deformation theory was used to accurately model the anisotropic material behavior. The study examined the porosity role variation across thickness in the buckling and free vibration behavior of nanobeams, as well as the effects of magneto-electro-elastic coupling, thermal stresses, nonlocal properties, externally applied electric and magnetic field potential, and porosity volume fraction. [ABSTRACT FROM AUTHOR]

• A new exact buckling model based on MGE for thin-walled microbeams is proposed. • Besides the classical flexural–torsional coupling, two new coupling effects are found. • The first new coupling effect is the higher-order flexure–flexure coupling. • The second new coupling effect is the higher-order flexural–torsional coupling. More and more thin-walled micro-beams, including the I-section thin-walled micro-beams, are applied in MEMS. The buckling of a thin-walled micro-beam exhibits some different phenomena from that of a large scale thin-walled beam, such as the size effect, and the coupling effects caused by strain gradient. To investigate the influence of the coupling effects and size effect on the buckling of thin-walled micro-beams, a new buckling model is proposed. Based on modified gradient elasticity (MGE), the governing equations and boundary conditions of the new model are derived from the variational principle. The governing equations and boundary conditions can be simplified to the classical Vlasov's theory, the MGE Bernoulli–Euler beam model, MGE Bernoulli–Euler beam model considering bi-directional flexure respectively. Solved by the feature expansion method, the size effects of the thin-walled micro-beam can be captured by the new model, that is the buckling load increases with internal length scales. Besides the classical flexural–torsional coupling effect, two new coupling effects, such as the higher-order flexure–flexure coupling and the higher-order flexural–torsional coupling, are also captured by the new model. These two new high-order coupling effects of the new model reduce the critical buckling load of thin-walled micro-beams. The higher-order flexural–flexural coupling effect is far greater than the other two coupling effects, and the higher-order flexural–flexural coupling effect is on the same order of magnitude as the effect of MGE (size effect), with the former being negative and the latter positive. The size effect and higher-order coupling effect cannot be ignored and need to be considered carefully for the buckling of thin-walled micro-beams. [Display omitted] [ABSTRACT FROM AUTHOR]

This article deals with the linear and nonlinear buckling behavior of porosity-dependent functionally graded (FG) non-uniform microtubes. The modified couple stress theory is determined to consider small-scale effects on the micro-size tube which is modeled, based on the Euler–Bernoulli beam theory in conjunction with the employment of the conservation energy principle to derive the nonlinear governing equations regarding the nonlinear Von-Kármán strains. The main contribution of this article is the impact of cross-sections on the static behavior of cylindrical beams with four applicable cross-sections, involving the exponential, linear, and convex in comparison of uniform section for the radial distribution of ceramic and metal material based on the power-law function. Also, the pinned, clamped, and combination of these boundary conditions are defined as the boundary supports, and the generalized quadrature method (GDQM) is utilized as the numerical solving technique along with the iteration method to solve the nonlinear equations. Finally, the obtained results extracted to investigate the impact of various parameters, involving the nonlinear amplitude, power FG index, porosity parameter, small-scale parameter, and different cross-sections on the buckling treatment of cylindrical beam. [ABSTRACT FROM AUTHOR]

This paper aims to study imperfect nanotubes' buckling behavior made of functionally graded materials with porosity and non-uniform cross-section. The nonlocal strain gradient theory is used to define the size effect in nano-scale, and also new higher order tube model and first-order shear deformation theory are utilized to develop the nanotube's formulation. The results are obtained using the generalized differential quadrature method and are compared to the Timoshenko theory with very satisfying convergence. The boundary conditions are considered as clamped, clamped-simply supported, and also simply supported. The results illustrate the effects of the FG power index, porosity, rates of cross-section change, nonlocal, and strain gradient parameters on the buckling behavior of the FG tapered porous nanotube. [ABSTRACT FROM AUTHOR]

When subjected to a constant applied load and elevated temperature, structural steel columns may buckle after a certain duration due to increasing creep-induced deformation, and such mode of failure is referred to as creep buckling. This paper presents an analytical method to simulate the creep buckling behaviour of steel columns at elevated temperatures by incorporating the Fields-and-Fields creep model and a nonlinear constitutive model of steel at elevated temperatures. Fire and creep buckling tests on Q690 high-strength steel columns are selected to validate the proposed method, and a good agreement between the experimental and analytical results is achieved. This demonstrates that the proposed method can provide an accurate assessment of the lateral deflection of steel columns at elevated temperatures accounting for the creep effect. Time- and strain-hardening formulations are separately incorporated into the analysis. The obtained results indicate that the strain-hardening formulation is more suitable for cases with stress variations. The study also unveils the failure mechanism of creep buckling, which indicates that the creep-induced lateral deflection of an axially loaded steel column at elevated temperatures is initiated by the gradient of stress and strain distributions on the cross-section of the column triggered by the initial imperfection. The parametric study results show that the creep buckling time of the steel column decreases as the load ratio, elevated temperature, and initial imperfection increase; however, the creep buckling time increases as the slenderness ratio increases. [ABSTRACT FROM AUTHOR]

The present paper provides an analysis to obtain the critical buckling load and vibration frequencies of the sandwich cylindrical panel with functionally graded (FG) face sheets and FG porous core resting on an elastic foundation, subjected to mechanical load and in thermal environments. The panel is formulated within the framework of the nonlocal strain gradient theory for shell model and classical shell theory. Based on Hamilton's principle and Galerkin's method, the effects of nonlocal and strain gradient parameters, materials and geometrical characteristics, porosity, temperature and elastic foundation on buckling load, fundamental frequencies, and dynamic response of the panel are considered. [ABSTRACT FROM AUTHOR]

This study investigates the buckling of microbeams with variable cross‐sections and middle supports in a thermal environment. Based on classical theories and modified couple stress, the size‐dependent behavior of the microbeam is modeled, and the intermediate support is simulated elastically. A temperature‐dependent relationship will also be assumed for the material properties of the microbeam. The governing equations will be derived using Hamilton's principle based on the modified Couple stress theory and the nonlinear thermal field. Using an analytical approach, buckling loads and deformation of microbeams will be determined. The accuracy of the answers will be investigated to demonstrate the effectiveness of the method used and the correctness of the results obtained. A comparison will be made between the obtained results and the results available in the scientific literature to prove the accuracy of the formulation and the method used. A parametric study will then be conducted to determine the effect of boundary conditions, the flexibility of the middle support, temperature distribution, and geometric characteristics on the buckling loads of microbeams. [ABSTRACT FROM AUTHOR]

In the realm of high-pressure vessel simulation, conventional finite element method (FEM) approaches, as per ASME standards, may inadequately predict the behavior of flat surfaces under elevated temperatures. This study challenges the efficacy of shell-type mesh modeling for high-temperature flat plates, demonstrating that the thermal conditions within such high-pressure vessels can induce thermal instability and buckling, not accounted for by traditional FEM methods recommended by ASME. Through comprehensive analytical investigations, we reveal that traditional shell-type meshing techniques, while suitable for certain applications, fail to capture the intricate thermal stresses and deformation patterns inherent in high-temperature flat plate configurations. Our analysis delineates distinct stability regimes governed by key design parameters, including plate thickness, operating temperature, and geometric dimensions, profoundly impacting the structural integrity of heating plates under thermal loading. Specifically, we found that increasing the plate thickness enhances resistance to thermal buckling, clamping the plate edges raises the critical buckling temperature, and selecting materials with lower thermal expansion coefficients improves stability. These findings provide engineers with critical insights necessary for optimizing the design and performance of high-temperature equipment. This includes the design of high-pressure vessels with flat surfaces for heating materials, flanges in high-temperature environments, and fins in heat exchangers across various industries such as oil and gas, pyrolysis, and power plants. The findings presented herein serve as a valuable reference for engineers seeking to comprehend and mitigate instability phenomena in solid mechanics, offering practical guidance for developing robust and reliable high-temperature structures in demanding industrial environments. [ABSTRACT FROM AUTHOR]

This article presents the nonlinear investigation of the thermal and mechanical buckling of orthotropic annular/circular single-layer/bilayer nanoplate with the Pasternak and Winkler elastic foundations based on the nonlocal strain gradient theory. The stability equations of the graphene plate are derived using higher-order shear deformation theory (HSDT) and first-order shear deformation theory (FSDT) considering nonlinear von Karman strains. Furthermore, this paper analyses the nonlinear thermal and mechanical buckling of the orthotropic bilayer annular/circular nanoplate. HSDT provides an appropriate distribution for shear stress in the thickness direction, removes the limitation of the FSDT, and provides proper precision without using a shear correction coefficient. To solve the stability equations, the differential quadratic method (DQM) is employed. Additionally, for validation, the results are checked with available papers. The effects of strain gradient coefficient, nonlocal parameter, boundary conditions, elastic foundations, and geometric dimensions are studied on the results of the nondimensional buckling loads. Finally, an equation is proposed in which the thermal buckling results can be obtained from mechanical results (or vice versa). [ABSTRACT FROM AUTHOR]

Collapse in steel structures is often controlled by loss of load carrying capacity of steel columns due to interactive buckling, which involves interactions between local and global (i.e., lateral and lateral torsional) buckling. Commonly used concentrated plastic hinge or fiber-based elements do not simulate the physics of this response, potentially leading to inaccuracy in performance assessment. A nonlinear fiber-beam-column element [termed the Torsion Fiber Element (TFE)] to simulate monotonic interactive buckling in steel beam-columns is presented. The element, implemented in the OpenSees platform, incorporates St. Venant as well as warping torsion through enrichment of strain interpolation functions, in addition to axial and flexural deformation modes. Local buckling is represented through a softening multiaxial constitutive relationship. The efficacy of this approach is examined by comparing its results against those obtained from continuum finite element simulations as well as experimental data on beam-columns subjected to monotonic loading. The comparisons indicate that the element can functionally represent the physics underlying interactive buckling, resulting in effective prediction of the overall monotonic load-deformation response, as well as internal deformation and stress fields. Limitations of the element in its current form are summarized, along with prospective improvements. [ABSTRACT FROM AUTHOR]

Sandwich structures have several potential applications in structural engineering because of the different material properties of the skin and core. In particular, sandwich structures with heteromorphic cores can satisfy the special requirements of engineering and structural design. In this study, to enhance the critical thermal buckling behavior of sandwich structures with heteromorphic cores, we developed a free-form optimization system based on a gradient method to optimize the core shapes under a volume constraint. The free-form optimization system combined with a finite element method code and an in-house program consists of thermal buckling analysis, initial thermal stress analysis, the derivation of the sensitivity function, velocity analysis, and shape update. According to the optimal results of the design examples, the developed free-form optimization system could significantly enhance the thermal buckling behavior of sandwich structures. In particular, by simply specifying the constraint conditions in the velocity analysis, we could maintain the initial shape of the specified parts in the heteromorphic core during the free-form optimization process to satisfy special requirements. [ABSTRACT FROM AUTHOR]

In this research paper a refined shear and deformation theory for buckling of functionally graded FGM plates under mechanical loading is presented. The shear stress variation through the thickness in a parabolic form is accounted for in this theory, and satisfies the condition of the transversal shear stress null on the upper and bottom edges of the plate without using shear correction coefficients. Unlike the conventional other shear stress and deformation theories, only four unknowns involved in the proposed refined theory, which has many resemblances to traditional plate theory. boundary conditions, equilibrium equations and stress expressions. The properties of the functionally graded plate are varying following a power law distribution of the fraction’s volume of the constituents. Equilibrium equations are derived from the virtual works principle. The solution of simply supported functionally graded plates is deduced and their results are compared against those of first-order theory and higher-order theories. It can be said that the suggested theory is effective and accurate in determining the buckling behavior of FGM plates. [ABSTRACT FROM AUTHOR]

The present investigation involved the modeling and analysis of the thermomechanical buckling behavior of sandwich nanoplates with foam core layers. The study employed the utilization of the new higher order deformation theory and nonlocal strain gradient elasticity theory. The modeling of foam core involves separate consideration of uniform and symmetric open cell foam distribution types, while the face plates are predicted to exhibit FGM and isotropic layers. A total of six sandwich plate types were modeled and analyzed. The thermomechanical buckling behavior of sandwich nanoplates is significantly influenced by the sandwich type, volumetric foam ratio of the core layer, and its distribution along the foam core height, as demonstrated in prior analyses. The study revealed that the incorporation of foam structure resulted in an elevation of the buckling temperature during the thermo-mechanical response of the nanoplate. At low temperatures, the uniform foam model had lesser thermal buckling than the symmetrical foam model. However, this trend changed after reaching ΔT = 350–360 K levels. The study is expected to yield significant insights into the development and application of nanosensors, transducers, and nanoelectro mechanical systems that are designed to operate in high-temperature settings. [ABSTRACT FROM AUTHOR]

• The temperature-dependent material properties of BaTiO 3 and CoFe 2 O 4 were defined in the model for the first time. • Sinusoidal higher-order shear and nonlocal strain gradient theories are employed to model the dynamic behavior. • The free vibration and buckling behavior of a magneto-electro-elastic (MEE) laminated nanoplate were investigated. • The effects of nonlinear thermal field, electric and magnetic potentials are presented. • The faceplate composition and electric/magnetic potentials are helpful to keep the MEE nanoplate in adjusted response. This study investigated the free vibration and buckling behavior of a magneto-electro-elastic (MEE) sandwich porous nanoplate under nonlinear thermal loads and electric and magnetic potentials. The equation of motion of the nanoplate consisting of barium-titanate and cobalt-ferrite components, with a functionally graded (FG) porous core and two face plates, was modeled by a sinusoidal higher-order shear (SHSDT) and the nonlocal strain gradient (NSGT) theories. Due to the significant effect of the temperature in the dynamics of the magneto-electro-elastic nanoplate, the temperature-dependent material properties of barium-titanate (BaTiO 3) and cobalt ferrite (CoFe 2 O 4) were defined and applied to the modeling for the first time in the literature. The laminated plate consists of upper and lower surface auxiliary plates and a main FG core plate. The core plate consists of functionally grading cobalt-ferrite and barium-titanate, while face plates can be in three different material compositions consisting of pure cobalt-ferrite, pure barium-titanate, or a combination of the two. It has been shown in this study that the dynamic behavior of the core plate, exposed to high temperatures, can be controlled through auxiliary surface plates. Especially in nanosensor applications, the disadvantage of thermal load can be reduced by the electric and magnetic field's strength applied to the surface plates. This study will make an essential contribution to the design and application of nanosensor or nanoelectromechanical systems, especially by controlling nanosensor responses in high-temperature applications. [ABSTRACT FROM AUTHOR]

This paper presents the state of art in the field of composite shells with focus on stress analysis, buckling and post‐buckling responses under mechanical and thermal loading. Many researchers have investigated the buckling and post‐buckling responses of cylindrical, conical, spherical, thin and thick composite shells with single and doubly curved shells under mechanical and thermal loading. From the literature it can be inferred that hydrostatic pressure, axial compression and thermal environment influence the buckling behavior of laminated composite shell significantly. An effort is taken to review the research on buckling and post‐buckling responses of cylindrical and conical shaped shells under mechanical and thermal loading and their behavior during buckling and post‐buckling conditions. POLYM. COMPOS., 39:4231–4242, 2018. © 2017 Society of Plastics Engineers [ABSTRACT FROM AUTHOR]

The present work uses a new three-dimensional framework for thermo-electro-mechanical buckling analysis of functionally graded piezoelectric cylindrical nano/micro-shells subjected to axial mechanical compression, an external applied voltage and uniform temperature rising. To account thickness stretching effect, three-dimensional shear and normal deformation theory is employed. Size dependency is modeled based on modified couple stress theory. Principle of virtual work is used to derive governing equations. The solution procedure is developed based on Navier's technique for simply-supported boundary conditions. The importance of the present new framework is justified through comparison between present results and corresponding previous lower-order analysis. The full numerical results are presented in terms of significant parameters of the problem such as some dimensionless geometric parameters, temperature change, dimensionless length scale parameter and applied voltages. [ABSTRACT FROM AUTHOR]

The nonlocal strain gradient and classical shell theories are used to derive the governing equations of functionally graded cylindrical nanopanels (open cylindrical shells). The properties of the nanopanel are graded as a power-law distribution through the thickness direction. The linearization stability equations are obtained using an adjacent equilibrium criterion. Governing equations are solved by Galerkin method to investigate the effects of the material length scale parameter, the nonlocal parameter, the geometric parameters, and the material properties on the buckling behavior of functionally graded cylindrical nanopanels. Numerical results are compared and discussed with available data. The solution of the closed cylindrical shell is recovered when the span angle is taken as 360 degrees. [ABSTRACT FROM AUTHOR]