Influence of elastic foundations and carbon nanotube reinforcement on the hydrostatic buckling pressure of truncated conical shells

In this study, the effects of elastic foundations(EFs) and carbon nanotube(CNT) reinforcement on the hydrostatic buckling pressure(HBP) of truncated conical shells(TCSs) are investigated. The first order shear deformation theory(FOSDT) is generalized to the buckling problem of TCSs reinforced with CNTs resting on the EFs for the first time. The material properties of composite TCSs reinforced with CNTs are graded linearly according to the thickness coordinate. The Winkler elastic foundation(W-EF) and Pasternak elastic foundation(P-EF) are considered as the EF. The basic relations and equations of TCSs reinforced with CNTs on the EFs are obtained in the framework of the FOSDT and solved using the Galerkin method. One of the innovations in this study is to obtain a closed-form solution for the HBP of TCSs reinforced with CNTs on the EFs. Finally, the effects of the EFs and various types CNT reinforcements on the HBP are investigated simultaneously. The obtained results are compared with the results in the literature, and the accuracy of results is confirmed.     

Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading

The nonlinear in-plane instability of functionally graded carbon nanotube reinforced composite (FG-CNTRC) shallow circular arches with rotational constraints subject to a uniform radial load in a thermal environment is investigated. Assuming arches with thickness-graded material properties, four different distribution patterns of carbon nanotubes (CNTs) are considered. The classical arch theory and Donnell’s shallow shell theory assumptions are used to evaluate the arch displacement field, and the analytical solutions of buckling equilibrium equations and buckling loads are obtained by using the principle of virtual work. The critical geometric parameters are introduced to determine the criteria for buckling mode switching. Parametric studies are carried out to demonstrate the effects of temperature variations, material parameters, geometric parameters, and elastic constraints on the stability of the arch. It is found that increasing the volume fraction of CNTs and distributing CNTs away from the neutral axis significantly enhance the bending stiffness of the arch. In addition, the pretension and initial displacement caused by the temperature field have significant effects on the buckling behavior.     

Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness

This work deals with a study of the dynamic and buckling analysis of polymer hybrid composite(PHC) beam. The beam has variable thickness and is reinforced by carbon nanotubes(CNTs) and nanoclay(NC) simultaneously. The governing equations are derived based on the first shear deformation theory(FSDT). A three-phase HalpinTsai approach is used to predict the mechanical properties of the PHC. We focus our attention on the effect of the simultaneous addition of NC and CNT on the vibration and buckling analysis of the PHC beam with variable thickness. Also a comparison study is done on the sensation of three impressive parameters including CNT, NC weight fractions, and the shape factor of fillers on the mechanical properties of PHC beams,as well as fundamental frequencies of free vibrations and critical buckling load. The results show that the increase of shape factor value, NC, and CNT weight fractions leads to considerable reinforcement in mechanical properties as well as increase of the dimensionless fundamental frequency and buckling load. The variation of CNT weight fraction on elastic modulus is more sensitive rather than shear modulus but the effect of NC weight fraction on elastic and shear moduli is fairly the same. The shape factor values more than the medium level do not affect the mechanical properties.     

Nonlinear stability of advanced sandwich cylindrical shells comprising porous functionally graded material and carbon nanotube reinforced composite layers under elevated temperature

The nonlinear stability of sandwich cylindrical shells comprising porous functionally graded material(FGM) and carbon nanotube reinforced composite(CNTRC)layers subjected to uniform temperature rise is investigated. Two sandwich models corresponding to CNTRC and FGM face sheets are proposed. Carbon nanotubes(CNTs) in the CNTRC layer are embedded into a matrix according to functionally graded distributions. The effects of porosity in the FGM and the temperature dependence of properties of all constituent materials are considered. The effective properties of the porous FGM and CNTRC are determined by using the modified and extended versions of a linear mixture rule, respectively. The basic equations governing the stability problem of thin sandwich cylindrical shells are established within the framework of the Donnell shell theory including the von K'arm'an-Donnell nonlinearity. These equations are solved by using the multi-term analytical solutions and the Galerkin method for simply supported shells.The critical buckling temperatures and postbuckling paths are determined through an iteration procedure. The study reveals that the sandwich shell model with a CNTRC core layer and relatively thin porous FGM face sheets can have the best capacity of thermal load carrying. In addition, unlike the cases of mechanical loads, porosities have beneficial effects on the nonlinear stability of sandwich shells under the thermal load. It is suggested that an appropriate combination of advantages of FGM and CNTRC can result in optimal efficiency for advanced sandwich structures.     

Elastica of sandwich panels with a transversely flexible core—A high-order theory approach

The elastica behavior of an extensional sandwich panel with a “soft” core when subjected to in-plane compressive loads is presented and it is compared with the response of its extensional equivalent single layer (ESL) with shear deformations model. The field equations along with the appropriate boundary conditions for the sandwich and the ESL panels have been derived through a variational approach following the High-order SAndwich Panel Theory (HSAPT) approach that takes into account the vertical flexibility of the core. The governing equations include the effects of the extension of the mid-surfaces of the face sheets of the sandwich panel or the mid-plane of the ESL model which the classical elastica approach misses. The results of the elastica response of a clamped-simply-supported sandwich panel and its ESL counterpart are presented and compared. They include the response along the panel, deformed shapes and equilibrium curves of in-plane loads versus structural quantities such as displacements and internal stress resultants and stresses. These results reveal that the predicted buckling load of the ESL panel is larger than that of the sandwich panel and that deep in the non-linear range the upper face sheet wrinkles with increasing overall and edge displacements and a release of the load. Hence, the use of an equivalent single layer panel especially when a sandwich panel with a compliant core is considered may lead to unsafe and unreliable predictions when large displacements and large rotations are considered.     

Nonlocal thermal buckling and postbuckling of functionally graded graphene nanoplatelet reinforced piezoelectric micro-plate

This paper analyzes the nonlocal thermal buckling and postbuckling behaviors of a multi-layered graphene nanoplatelet(GPL) reinforced piezoelectric micro-plate. The GPLs are supposed to disperse as a gradient pattern in the composite micro-plate along its thickness. The effective material properties are calculated by the Halpin-Tsai parallel model and mixture rule for the functionally graded GPL reinforced piezoelectric(FG-GRP) micro-plate. Governing equations for the nonlocal thermal buckling a...     

Size-dependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory

In this paper, a size-dependent first-order shear deformable shell model is developed based upon the modified strain gradient theory (MSGT) for the axial buckling analysis of functionally graded (FG) circular cylindrical microshells. It is assumed that the material properties of FG materials, which obey a simple power-law distribution, vary through the thickness direction. The principle of virtual work is utilized to formulate the governing equations and corresponding boundary conditions. Numerical results are presented for the axial buckling of FG circular cylindrical microshells subject to simply-supported end conditions and the effects of material length scale parameter, material property gradient index, length-to-radius ratio and circumferential mode number on the size-dependent critical buckling load are extensively studied. For comparison purpose, the critical buckling loads predicted by modified couple stress theory (MCST) and classical theory (CT) are also presented. Results show that the size effect plays an important role for lower values of dimensionless length scale parameter. Moreover, it is observed that the critical buckling loads obtained based on MSGT are greater than those obtained based on MCST and CT.     

Instability of functionally graded micro-beams via micro-structure-dependent beam theory

This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded (FG) beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems (MEMS/NEMS) with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solution procedure, based on a generalized differential quadrature method (GDQM), is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geometric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young’s modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory.     

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress,the modified couple stress theory(MCST),and the nonlocal elasticity theories using the differential quadrature method(DQM)is presented.Main advantages of the MCST over the classical theory(CT)are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter.Based on the nonlinear von K′arm′an assumption,the governing equations of equilibrium for the micro-classical plate considering midplane displacements are derived based on the minimum principle of potential energy.Using the DQM,the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained.Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature.A parametric study is conducted to show the effects of the aspect ratio,the side-to-thickness ratio,Eringen’s nonlocal parameter,the material length scale parameter,Young’s modulus of the surface layer,the surface residual stress,the polymer matrix coefficients,and various boundary conditions on the dimensionless uniaxial,biaxial,and shear critical buckling loads.The results indicate that the critical buckling loads are strongly sensitive to Eringen’s nonlocal parameter,the material length scale parameter,and the surface residual stress effects,while the effect of Young’s modulus of the surface layer on the critical buckling load is negligible.Also,considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate.The results show that the critical biaxial buckling load increases with an increase in G12/E2and vice versa for E1/E2.It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude.Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios,it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.     

点阵增强型复合材料夹层结构的力学性能实验与分析

采用真空导入成型工艺,制备出在面板与芯材界面上具有创新构型的点阵增强型复合材料夹层结构。对其面板拉伸性能、夹层结构剪切与平压性能进行了实验研究,得出点阵增强型复合材料夹层结构经树脂柱增强后,剪切与平压性能均得以提高的结论。对不同跨高比复合材料夹层结构开展了三点与四点弯曲实验,研究其典型受力破坏形态与机理。基于Eshelby等效夹杂原理,采用Mori-Tanaka方法求解了点阵增强型复合材料夹层结构经树脂柱增强后的剪切性能。利用经典夹层梁理论和非线性有限元模拟方法,预估了试件抗弯刚度与受弯极限承载力,理论分析与实验结果较吻合。     

Thermal buckling and post-buckling response of imperfect temperature-dependent sandwich FGM plates resting on elastic foundation

Post-buckling behaviour of sandwich plates with functionally graded material (FGM) face sheets under uniform temperature rise loading is considered. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation, which acts in both compression and tension. The derivation of equations is based on the first-order shear deformation plate theory. Thermomechanical non-homogeneous properties of FGM layers vary smoothly by the distribution of power law across the thickness, and temperature dependency of material constituents is taken into account. Using the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect sandwich plates with FGM face sheets are derived. The boundary conditions for the plate are assumed to be simply supported in all edges. The governing equations are reduced to two coupled equation in terms of stress function and lateral deflection. Employing the single mode approach combined with Galerkin technique, an approximate closed-form solution is presented to calculate the critical buckling temperature and post-buckling equilibrium path of the plate. Presented numerical examples contain the influences of power law index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation coefficients.     

Non-linear behavior of delaminated unidirectional sandwich panels with partial contact and a transversely flexible core

The paper presents the results of an investigation of the non-linear behavior of delaminated sandwich panels with a compressible core. The delaminated zone, at one of the face-core interfaces, consists of through-the-width crack, which is free of shear stresses but is capable of accommodating partial contact with compressive stresses only within the debonded zone. The governing non-linear equations along with the appropriate boundary conditions and the continuity conditions are derived through variational principles. The governing equations include moderate deformations type of kinematic relations, and include the high-order effects due to the transverse flexibility of the core. The governing equations along with the stress and displacements fields for the core and the appropriate continuity conditions are presented. The effects of the non-linear response and the partial contact are described through some numerical cases of three points bending typical sandwich panels with inner delaminations in the vicinity of a concentrated load, in the vicinity of a stiffened core and, finally, far from the load. Numerical results in the form of displacements, bending moments, shear stresses in the core and vertical interfacial normal stresses at the upper and lower face-core interfaces along the panel length and at the delamination crack tips are presented. Buckling curves of load versus various extreme structural parameters are included. The analyses show that a full contact type of delamination transforms into a partial contact area with buckling of the compressed face sheet, as the load is increased and it is associated with extreme large displacements and stresses.     

基于修正偶应力和高阶剪切变形理论的变截面微梁的自由振动

基于修正偶应力和高阶剪切理论建立了仅含有一个尺度参数的Reddy变截面微梁的自由振动模型,研究了变截面微梁自由振动问题的尺度效应和横向剪切变形对自振频率计算的影响。基于哈密顿原理推导了动力学方程与边界条件,并采用微分求积法求解了各种边界条件下的自振频率。算例结果表明,基于偶应力理论预测的变截面微梁的自振频率均大于经典梁理论的预测结果,即捕捉到了尺度效应。另外,梁的几何尺寸与尺度参数越接近,尺度效应就越明显,而梁的长细比越小,横向剪切变形对自振频率的影响就越明显。     

Thermal buckling analysis of truss-core sandwich plates

Truss-core sandwich plates have received much attention in virtue of the high values of strength-to-weight and stifness-to-weight as well as the great ability of impulseresistance recently. It is necessary to study the stability of sandwich panels under the influence of the thermal load. However, the sandwich plates are such complex threedimensional(3D) systems that direct analytical solutions do not exist, and the finite element method(FEM) cannot represent the relationship between structural parameters and mechanical properties well. In this paper, an equivalent homogeneous continuous plate is idealized by obtaining the efective bending and transverse shear stifness based on the characteristics of periodically distributed unit cells. The first order shear deformation theory for plates is used to derive the stability equation. The buckling temperature of a simply supported sandwich plate is given and verified by the FEM. The efect of related parameters on mechanical properties is investigated. The geometric parameters of the unit cell are optimized to attain the maximum buckling temperature. It is shown that the optimized sandwich plate can improve the resistance to thermal buckling significantly.     

Wrinkling of sandwich wide panels/beams based on the extended high-order sandwich panel theory: formulation, comparison with elasticity and experiments

There exist several high-order sandwich panel theories, most notably, the first to be introduced high-order sandwich panel theory (HSAPT) assumes a constant shear stress in the core. Recently, the extended high-order sandwich panel theory (EHSAPT) was introduced, its novelty being that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core, and the rotation at the centroid of the core) instead of just one (shear stress in the core) of the earlier theory. In this paper, the EHSAPT formulation for predicting the critical wrinkling load is presented for a simply supported sandwich of general asymmetric construction. The cases of (i) applying the loading just on the face sheets with a linear core assumption and (ii) applying uniform strain loading throughout the thickness of the panel and a nonlinear core assumption are examined. The results are compared with a benchmark elasticity solution. In addition, edgewise compression experiments were conducted on glass face/Nomex honeycomb core and the ensuing wrinkling point is compared with the theoretical predictions. A comparison is also made with earlier edgewise compression experiments on aluminum face/granulated-cork core reported in literature. Other wrinkling formulas that are included in the comparison are: Hoff–Mautner and the HSAPT.     

Torsional buckling of an elastic thick-walled tube made of rubber-like material

The elastic stability of a rubber-like, thick-walled tube which is subjected to finite torsional deformation is investigated both theoretically and experimentally. The analysis is based on the theory of finite elastic deformations, in cojunction with the method of small displacements superposed on large elastic deformations. The governing field equations are solved by a numerical scheme which determines the critical buckling torque and the associated buckling mode of the tube. The predicted results compare closely with the experimental measurements of the buckling of thick-walled silicone rubber tubes tested under finite twist.     

Postbuckling of pressure-loaded shear deformable laminated cylindrical panels

IntroductionInrecentyears,fiber_reinforcedcompositelaminatedpanelshavebeenwidelyusedintheaerospace,marine ,automobileandotherengineeringindustries .Theproblemofbucklingandpostbucklingofcylindricalpanelsunderaxialcompressionortorsionhasbeenextensivelystudied .Incontrast,theliteratureoncylindricalpanelsunderpressureloadingisrelativelyspares.Thesestudiesincludealinearbucklinganalysis (Singeretal.[1]) ,anonlinearbucklinganalysi(YamadaandCroll[2 ]) ,anelastoplasticbucklinganalysisusingreducedstif…     

热荷载作用下Timoshenko功能梯度夹层梁的静态响应

在精确考虑轴线伸长和一阶横向剪切变形的基础上建立了Timoshenko功能梯度夹层梁在热载荷作用下的几何非线性控制方程.采用打靶法数值求解所得强非线性边值问题,获得了两端固支功能梯度夹层梁在横向非均匀升温作用下的静态热过屈曲和热弯曲变形数值解.分析了功能梯度材料参数变化、不同表层厚度和升温参数对夹层梁弯曲变形、拉-弯耦...     

基于等几何有限元法的功能梯度微板热力耦合屈曲预测

基于修正偶应力理论和Kirchhoff板理论,建立了功能梯度微板热力耦合屈曲等几何有限元模型。该模型仅包含一个材料尺度参数,能够描述尺度效应现象,且满足修正偶应力理论的高阶连续性要求。基于虚功原理推导了功能梯度微板热力耦合屈曲等几何有限元方程。通过对板的典型算例分析,讨论了材料尺度参数、边长比及梯度指数对板稳定性的影响。结果表明,本文模型预测的屈曲载荷总是大于宏观理论的结果,即捕捉到了尺度效应现象;随着临界屈曲力的增加,临界屈曲热载荷线性减少;此外,边长比和梯度指数也对微板的稳定性产生一定影响。     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.