This study investigated the effects of considering surface and nonlocal energy parameters on the buckling analysis of double piezoelectric nanoplate (DPNP) embedded in elastic foundations and thermal environments. Both in-phase and out-of-phase modes of buckling and various boundary conditions are studied and compared with each other. The governing equations were derived by drawing on the principle of virtual work and then solved by employing the finite difference method. Finite difference solution was validated using Navier's method and journal references. A parametric study was also launched in order to investigate the effects of the external electric voltage, nonlocal parameters, different boundary conditions, elastic foundations and thermal environments on the surface effect of DPNP buckling. The obtained numerical results showed that the influence of surface stress on in-phase and out-of-phase modes of buckling of the DPNP was enhanced by augmenting the nonlocal parameters and external electric voltage; on the other hand, it was found to be decreased by increasing elastic foundations and temperature changes. In addition, the value of surface stress effects for the in-phase mode was higher than that of the out-of-phase one.

In this study, the buckling behaviors of single-walled carbon nanocones (SWCNCs) under bending at finite temperatures are predicted using a proposed multiscale quasi-continuum approach based on the temperature-dependent higher order Cauchy–Born (THCB) rule. The hyper-elastic constitutive model is derived exactly in the context of the higher order gradient theory that incorporates the details of the interatomic interaction. The numerical simulations for the deformation of SWCNCs are implemented using the developed meshless computational framework based on moving least-squares interpolation, which can precisely reproduce the deformation process and buckling patterns of SWCNCs under bending. The underlying correlations of the critical bending angle with respect to the geometry of SWCNCs and temperature are revealed by the numerical results. Furthermore, our simulation captures the transformation from the local to the global buckling process of SWCNCs, accompanied with an average strain energy jump. Our results correspond with previous studies.

Prior to integrated circuit (IC) packaging, die performance must be verified using probe cards to screen for defective products. With the decrease in IC line width, the dimensions of the pads used for performance verification and the spacing between adjacent pads have also decreased. However, when the pad pitch is reduced to less than 30 μm, commonly used probe cards will face manufacturing problems in miniaturization. To resolve probe card manufacturing problems caused by the miniaturization of IC components, the use of an anisotropic conductive film (ACF) in probe cards was proposed in this study. Theoretical calculations and experimental testing of this probe structure were conducted to demonstrate the feasibility of this concept.

In theoretical calculations, composite material and buckling theory were utilized to evaluate the buckling behavior of the ACF. In experimental testing, photolithography and electroplating techniques were used to control the line width and spacing intervals of the micron-scale metal wires in the ACF. After the ACF was fabricated, the mechanical properties of the ACF during wafer testing were assessed. Theoretical analyses and experimental testing verified that ACFs can potentially be applied to the performance verification of IC products. In the ACF structure, multiple probes came into contact with each pad. Therefore, ACFs can potentially be applied to the performance verification of IC components with pad diameters of less than 20 μm. The results of this study directly benefit the miniaturization of ICs.

In the fields of engineering, nanoscience, and biomechanics, thin structural members, such as beams, plates, and shells, that are supported by an elastic medium are used in several applications. There is a possibility that these thin structures might buckle under severe loading conditions; higher-order, complicated elastic buckling modes can be found owing to the balance of rigidities between the thin members and elastic supports. In this study, we have shown a new and simple ‘power law’ relation between the critical buckling strain (or loads) and rigidity parameters in structural members supported by an elastic medium, which can be modelled as a Winkler foundation. The following structural members have been considered in this paper: i) a slender beam held by an outer elastic support under axial loading, ii) cylindrical shells supported by an inner elastic core under hydrostatic pressure (plane strain condition), and iii) complete spherical shells that are filled with an inner elastic medium.

This paper presents an analytical study on the buckling of cylindrical shells with arbitrary circumferential thickness variations under external pressure. Firstly, based on the thin shell theory and separation of variables, corresponding ordinary differential equations of laterally pressured cylinders are obtained. Secondly, the general asymptotic formula of buckling load, which is in terms of thickness variation parameter up to arbitrary order, is derived by combining the perturbation method and Fourier series expansion. Thirdly, the effects of uniform and circumferential modal thickness variations on the buckling of cylindrical shells under external pressure are investigated, respectively, and the results agree well with those available in literature. Particularly, the buckling load reduction of cylinders with circumferential modal thickness variation obtained by the proposed method coincides with the numerical results presented by Gusic et al. This analytical method is applicable for evaluating the stability of laterally pressured cylindrical shells with arbitrary circumferential thickness variations, once the thickness variation is known.

The present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

The imperfection sensitivity of cylindrical panels under compression loading is shown to be not only reduced but effectively eliminated using stiffness tailoring techniques. Shells are designed with variable angle-tow (VAT) laminae, giving their laminates variable-stiffness properties over the surface co-ordinates. By employing an asymptotic model of the non-linear shell behaviour and a genetic algorithm, the post-buckling stability was maximised with respect to the VAT design variables. Results for optimised straight-fibre and VAT shells are presented in comparison with quasi-isotropic designs. In the straight-fibre case, small improvements in the post-buckling stability are shown to be possible but at the expense of the buckling load. In the VAT case, on the other hand, considerable improvements in the post-buckling stability are obtained and drops in axial stiffness and load associated with buckling are reduced to negligible levels. The improvements are shown to be a result of a benign membrane stress distribution prior to buckling and a localisation of the buckling mode. The asymptotic results are compared with non-linear finite-element analyses and are found to be in good agreement. Potential future multi-objective optimisation studies are discussed.

This study examined the critical buckling characteristics of hydrostatically pressurized double-walled complete spherical shells. An analytical model based on small deflection thin shell theory is presented; the equations are solved in conjunction with variational principles. Axisymmetric and inextensional assumptions are not initially used in the exact formulation. This approach therefore avoids any discussion about the validity of the solution and allows the model to be extended to cover more generic nonaxisymmetric cases with relative ease. The analytical results are presented using illustrative buckling modes. Based on the developed formulation, only axisymmetric eigenmodes were found to occur despite the inclusion of the effect of interactions between outer and inner shells. Critical modes that are symmetric or antisymmetric about the equator may be determined depending on the combination of the stiffness connecting the outer and inner shells and the radius-to-wall thickness ratios.

In this article, the analyses of the natural frequency and buckling of orthotopic nanoplates, such as single-layered graphene sheets, resting on Pasternak's elastic foundations with various boundary conditions are presented. New functions for midplane displacements are suggested to satisfy the different boundary conditions. These functions are examined by comparing their results with the results obtained by using the functions suggested by Reddy (Reddy JN. Mechanics of Composite Materials and Structures: Theory and Analysis. Boca Raton, FL: CRC Press; 1997). Moreover, these functions are very simple comparing with Reddy's functions, leading to ease of calculations. The equations of motion of the nonlocal model are derived using the sinusoidal shear deformation plate theory (SPT) in conjunction with the nonlocal elasticity theory. The present SPT are compared with other plate theories. Explicit solution for buckling loads and vibration are obtained for single-layered graphene sheets with isotropic and orthotropic properties; and under biaxial loads. The formulation and the method of the solution are firstly validated by executing the comparison studies for the isotropic nanoplates with the results being in literature. Then, the influences of nonlocal parameter and the other parameters on the buckling and vibration frequencies are investigated.

This paper studies the buckling analysis for a ring-stiffened cylindrical shell consisted of functionally graded material (FGM) subjected to hydrostatic pressure and thermal loads. Material properties of the ring-stiffened FGM cylindrical shell are assumed to be temperature-dependent, and vary smoothly through the thickness direction of the structure according to a volume exponent. Based on the Donnell assumptions, buckling loads of the ring-stiffened FGM cylindrical shell are presented by utilizing the Galerkin method. Numerical results reveal that thermal loads, volume exponent and geometric parameters have significant effects on the buckling behavior of the ring-stiffened cylindrical shell.

In this paper, a Levy-type solution based on the modified couple stress theory isdeveloped to study the buckling behaviors of micro-plates. Based on this theory, lengthscale parameter is considered to capture the size effect of rectangular micro-plates.Minimum potential energy and adjacent-equilibrium criteria are exploited to obtain thestability equations and corresponding boundary conditions. Different boundary conditionswith two opposite edges simply supported and arbitrary boundary conditions along the otheredges are considered. To illustrate the new model, both uniaxial and biaxial loads areapplied and the critical buckling loads are defined for over a wide range of thickness,different length scale parameters and various boundary conditions. To show the accuracy ofthe formulations, present results are compared with available results in literature forspecific cases and a very good agreement is observed. Results reveal that the criticalbuckling load increases as the length scale parameter increases especially when thethickness of the micro-plates becomes in order of length scale parameter and this effectis more significant for free boundary condition.

Shell theory solutions for radial buckling of multiply-concentric hollow cylinders are presented. Multi-cylindrical systems are those composed of two or more concentically mounted hollow tubes, wherein the annular space mediates inter-tube forces, attractive or repulsive depending on structural details of composites. Reflecting the multiple core-shell structures, the systems often exhibit peculiar radial buckling modes, which should be relevant to macro scale applications for deep water oil and gas transportation andmicroscale realization in lipid bilayer tubes. In this article, we focus on an illustrative example of such the multiply-tubular systems with nanometric dimension, the so-called multiwalled carbon nanotubes (MWNTs). Theoretical analysis based on a thin shell theory allows us to find anomalous radial buckling behaviors of MWNTs driven by hydrostatic pressure. The obtained buckling modes are characterized by petal-like wavy cross sections, which is what we call the radial corrugation of MWNTs. An important observation is the mechanical consequence of stiff core-tube insertion into the innermost hollow region of a given MWNT. The insertion results in a significant variance in the critical buckling pressure, above which the MWNT undergoes radial corrugation. The insertion-induced-variance in the critical pressure is due to the primary role of inter-tube interaction between adjacent constituent tubes, as explained within our theoretical model.

Pour situer l’origine d’une anomalie récurrente sur une coque en sandwich tri-coucherotomoulé, une analyse d’instabilité par voilement global est développée. Cette voie estsuggérée par la caractérisation de la géométrie du défaut observé et parl’imprédictibilité de son apparition. Le problème thermomécanique est posé dans un cadrenon-linéaire en se restreignant à l’évolution au refroidissement en phase solide après quela fraction cristallisée ait atteint le niveau de saturation. Dans le modèle proposé, lesnon-linéarités liées à l’évolution des propriétés matérielles en fonction de latempérature et celles associées au contact unilatéral moule/pièce sont considérées. Larésolution du problème thermomécanique instationnaire est réalisée par la méthode deséléments-finis au moyen du code Abaqus/Explicit. Le recalage de l’évolution thermique estconduit par un schéma de prédiction-correction de la conductance sur l’interface decontact. Pour l’analyse de la stabilité sous l’effet du chargement thermomécanique, nousappliquons la méthode de perturbation linéaire et les résultats de simulation confirmentbien la nature de défaillance suspectée. Les deux premiers modes de voilement calculéssont en bon accord avec les observations dans les conditions réelles du processus.

L'objet de ce travail est de présenter les premiers résultats de modélisation et simulation du comportement vibratoire non-linéaire d'une plaque circulaire stratifiée munie de couches en matériau piézoélectrique, élément principal d'un capteur de masse MEMS. La modélisation permet de prendre en compte (i) le couplage électromécanique lié à la pastille piézoélectrique, (ii) la structure stratifiée des membranes, (iii) l'état précontraint au repos de la membrane et le flambage éventuel et (iv) les vibrations non-linéaires qui produisent un effet raidissant ou assouplissant. Le modèle non-linéaire et sa résolution, par méthode de continuation et équilibrage harmonique, sont présentés, pour dégager le comportement de la membrane en régime forcé.

Dans certains procédés de mise en forme, tel que le laminage, l'apparition des contraintes résiduelles est inévitable et peut engendrer le flambage qui se traduit en défauts géométriques. Ceci exige la modélisation de ce phénomène d'instabilité mécanique afin de bien définir la forme et l'amplitude de ces défauts. Cela nécessite un modèle complet ayant des capacités pour le calcul du post-flambage. Dans le présent article, on présente un modèle de flambage possédant la faculté de détecter la charge critique de flambage et la forme post-flambée d'une plaque sous contraintes résiduelles. Des applications à des cas académiques et un cas de laminage seront aussi traités.

The applications of skew plates in the construction of aerospace structures are well known. The critical buckling load and post-buckling strength are two important design parameters of skew composite laminates. In this study, the refined buckling and nonlinear postbuckling solutions of a homogenous isotropic skew plate based on polynomial expansions of various degrees have been examined. Numerical results based on high-order Rayleigh-Ritz solutions are presented for certain type of oblique plates.