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• Novel mechanical characteristics of metamaterials are studied by theoretical analysis. • Dissipated energy per buckling event is studied. • Static and dynamic(re)programming characteristics are studied. • Potential energy landscape of programmable structure is studied. Metamaterials derive promising properties mainly from an internal micromechanical mechanism, rather than their chemical composition. Many interesting mechanical behaviors can be obtained by orderly assembling buckling elements. Elastic programmable properties, corresponding potential energy landscape and dynamic dissipation mechanism of elastic beam structures are studied in detail. To accomplish this work, a combination of theoretical models and extensive numerical calculations are applied to investigate a single element as well as homogeneous and gradient structures. This comprehensive investigation not only provides insights into the complex internal buckling behaviors and mechanisms of a specific unstable structure but also establishes conclusions that are applicable to other unstable structures having similar buckling behaviors. The potential energy of a serial combination of unstable elements is extremely wiggly, enabling multiple equilibrium configurations and resulting in multistable transformations and energy dissipation with elastic deformation and loading timescale independence. To the best of our knowledge, the most of programming properties investigated in this paper, the complex energy landscape, the deformation of internal elements, and programmable dynamic responses of gradient unstable structures have not been reported in previous papers. [Display omitted] [ABSTRACT FROM AUTHOR]

• Buckling behavior of spherical shells with patterned surface under indentation is investigated. • Shells with discontinuous protrusions exhibit unique multiple snap-through due to local buckling. • Mechanical response and buckling morphology can be controlled by tuning surface patterns. A well understanding of instability mechanics of soft shell structures is key issue due to its important implications in functional shape morphing, flexible electronics, soft robotics, nanotechnology, biological engineering, etc. Despite abundant studies, buckling analysis of flexible shells with patterned surface under indentation is rare, primarily because of the complexities of high nonlinearities in geometry, material, and surface contact. In this paper, buckling behavior of spherical shells with patterned surface under indentation is comprehensively investigated by using experimental, numerical and theoretical analyses. It is found shells with stripes show similar variation in the force-displacement curves and post-buckling morphologies like perfect shells. Unlike perfect ones, shells with discontinuous protrusions exhibit multiple snap-through due to local buckling under indentation. What is more, mechanical response and buckling morphology can be well controlled by tuning shell thickness as well as positions and sizes of protrusions. These results can not only deepen understanding of mechanism of spherical shell buckling under local loads, but also provide a designing guidance for flexible electronics, soft robotics, and other future devices. [Display omitted] [ABSTRACT FROM AUTHOR]

• Novel physics-driven neural networks are proposed for nonlinear micromechanics. • No labeled training data is needed for the proposed PDNNs. • Unphysical behaviors are avoided using a kinematic-based loss term. • Our PDNNs are computationally more efficient than the traditional PINNs. Micromechanical problems seek full-field solutions in response to external and/or internal thermal-mechanical loads, which have been increasingly encountered in material property and process assessments. Here we present a machine learning based strategy of solving micromechanics at finite strains. Deep neural networks (DNNs) are trained by employing the elastic energy together with other physical constraints to formulate the loss function. In particular, the crossover of material points, which can be a common issue for similar DNNs when applied to compression-dominant problems, is shown to be effectively addressed by including a kinematic penalty term that forces the DNN to maintain structural integrity and stability and avoid unphysical behavior. The generality and accuracy of the proposed physics-driven neural networks (PDNNs) are demonstrated through various micromechanical problems, including single crystal anisotropy elasticity, Eshelby's inclusion problem, buckling, and elastic homogenization of polycrystals. The effect of the choice of optimizers and hyperparameters on the PDNN training are discussed and the computational efficiency is also analyzed. It is shown that this novel PDNN framework can completely remove the need of labeled training data and exhibit improved performances as compared to the conventional physics-informed neural networks (PINNs) in terms of avoiding unphysical solutions and attaining higher computational efficiency. PDNNs can thus serve as a promising tool to solve some critical challenges associated with a wide range of nonlinear micromechanical problems. [Display omitted] [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold. On the one hand, it presents a methodology for the deterministic optimisation of a general class of variable-stiffness composite (VSC) structures, including a solution obtained by using laminæ with a curvilinear fibres-path and variable-thickness, by considering different design requirements under multiple load cases. The considered framework is the multi-level design methodology based on the polar parameters (PPs) to describe the macroscopic behaviour of the VSC structure. Particularly, only the first-level problem is addressed in this work: the design variables are, thus, the PPs and the thickness of the VSC laminate, whose spatial distribution is described via basis spline (B-spline) surfaces. The goal is to minimise the mass of the VSC structure subject to design requirements on feasibility, strength, first buckling load and maximum curvature of the fibres-path. This latter is formulated as an equivalent (conservative) constraint in the PPs space, regardless of the fibres-path within each lamina. Moreover, a general formulation of the gradient of the requirements related to buckling load and strength is proposed, which takes advantage from the main properties of B-spline entities and PPs. On the other hand, this paper aims to propose a new benchmark problem that is representative of a panel belonging to the fuselage of a standard civil aircraft subjected to multiple loading conditions. To this end, a wide campaign of numerical tests has been performed by considering a sensitivity analysis of the optimised solution to: (a) the integer parameters involved in the definition of the B-spline entities describing the distribution of the PPs and, possibly, of the thickness, (b) the type of VSC structure, (c) the type of deterministic optimisation algorithm. The results can be used as a database to assess the effectiveness of different design strategies against the optimised solutions presented in this paper. [Display omitted] • General framework for deterministic optimisation of variable-stiffness composites. • Multi-scale two-level optimisation strategy based on polar parameters. • Simultaneous anisotropy and thickness optimisation of the structural parts. • Application to a benchmark structure undergoing multiple loadings. • Multiple design requirements integrated in the problem formulation. [ABSTRACT FROM AUTHOR]

• The energy barrier concept is developed for evaluation of metastability of compressed spherical shells in the case of additional dynamic external perturbations. • Simple semi-analytical formulae are obtained for estimation of the energy barrier of perfect and imperfect spherical shells under external pressure. • They are validated by comparison with numerical and experimental data. • The energy barrier concept is applied for estimation of allowable pressure of imperfect spherical shells. The energy barrier concept is developed for the case of dynamic loading of spherical shells. Simple semi-analytical formulae were obtained for the energy barrier for perfect shells and structures with geometrical imperfections. They were applied to the case of spatial step pressure to estimate dynamic buckling load of geometrically imperfect shells. It has been shown that dynamic effect can be caught properly by separating additional energy which causes local buckling of the shell. The calculated dynamic knockdown factor was in good agreement with numerical solution and experimental data. The methodology and formulae were also developed for the metastability estimation of real structure and for establishing knockdown factor taking into account possible external perturbations. The suggested approach improves current NASA (SP-8032, 1969) recommendations for design buckling pressure which are overly conservative. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Two benchmarks are presented, for the validation of modelling/simulation aspects of stiffened panels subjected to buckling effects. • Different numerical strategies are presented to properly model the unstable behavior of the panels, including path-following approaches, geometric and material nonlinear effects. • The models account for initial geometric imperfections coming from friction stir welding joining operations. • Modelling and simulation guidelines are presented for subsequent researchers involved in the design process of stiffened panels for aeronautic applications. This work deals with the effective modelling and simulation of the behavior of stiffened panels, when subjected to compressive (buckling) loads. Within the Finite Element Method, two numerical strategies are compared, namely the Riks method and the displacement incremental control method, including damping effects. The capabilities and limitations of both approaches are explored for two distinct benchmarks: a panel with a blade stiffener, and a panel with a T shaped stiffener. In both cases, material (plasticity) and geometrical (large displacements) nonlinearities are considered, together with a modelling strategy based on shell elements. Following previous works of the authors, each panel accounts for initial geometric imperfections coming from friction stir welding joining operations. The paper shows a number of considerations that must be undertaken when choosing between one of the two modelling strategies. Both benchmarks involve a number of challenges from the point of view of modelling unstable structural behaviors, and therefore the proposed benchmarks can represent a valid set of case studies in the understanding of the capabilities of current numerical simulation codes. [ABSTRACT FROM AUTHOR]

• First attempts to model soft machines driven by buckling actuators. • Simulation provides missing information vital for real designs. • Results aid the design and control of soft machines. Buckling of elastomeric materials is recoverable and can be harnessed to provide useful functions. Soft machines enabled by buckling actuators have been demonstrated experimentally, while no efforts have been conducted to model these actuators and machines numerically. This paper fills this blank and presents numerical modelling of buckling actuators and the derived soft machines. Key design parameters are obtained through the simulation, which are missing and typically difficult to be obtained in experiment. The numerical results are helpful to understanding the working mechanism of buckling actuators, and shed light on design and control of soft machines enabled by buckling actuators. The idea and the strategy can be developed further for the design of other soft machines. [ABSTRACT FROM AUTHOR]

• An analytical model formulated to capture the transition features. • Different transition paths were found when the line forces were applied at different locations. • Total value of the required line forces fluctuated with the radius of the axisymmetric line forces. • The required line forces were minimum when they were applied at distances of about half of disk radius away from disk centre. The transition processes of nanostructure-induced bistable disks triggered by line forces are analytically and experimentally investigated. An analytical model based on the Ritz method is formulated to optimise the placement of axisymmetric line forces for converting the bistable disks between the two stable configurations. Different transition paths are captured for the bistable disks upon applying the line forces at different locations. The transition features, including the snapping forces and transition types, of the bistable disks under different line forces are analysed with respect to the design parameters, such as the nanostructured region ratio, accumulated plastic deformation and disk slenderness. Strategies for placing the line forces to achieve the shape transitions using small line forces or small total forces are proposed. Transition tests of manufactured bistable disks reveal a local buckling phenomenon when the line forces are placed around the disk centre, which is also predicted by numerical modelling. The experimental investigation validates the analytical studies, which are also verified by numerical models. This study provides information for the design of mechanical actuations to achieve the shape reconfiguration of bistable disks. [ABSTRACT FROM AUTHOR]

• Improved variant of the reduced stiffness method is presented, the localized reduced stiffness method (LRSM). • The LRSM is a versatile and effective lower-bound method for the design of buckling critical thin-walled shells. • Physical explanation for the plateau or lower-bound buckling load of cylinders under axial compression is identified. • The LRSM is applied and validated with experimental results for different shells and different load cases. • The LRSM is easy to implement in commercial finite element codes and delivers 24% to 176% higher KDFs for the buckling load when compared with currently used empirical guidelines. Thin-walled shells like cylinders, cones and spheres are primary structures in launch-vehicle systems. When subjected to axial loading, bending or external pressure, these thin-walled shells are prone to buckling. The corresponding critical load heavily depends on deviations from the ideal shell shape. In general, these deviations are defined as geometric imperfections, and although imperfections exhibit comparatively low amplitudes, they can significantly reduce the critical load. Considering the influence of geometric imperfections adequately into the design process of thin-walled shells poses major challenges for structural design. The most common procedure to take into account the influence of imperfections is based on classical buckling loads obtained by a linear analysis which are then corrected by a knockdown factor. The knockdown factor represents a statistical lower-bound with respect to data obtained experimentally for different types of thin-walled shells. This article presents a versatile and simple numerical design approach for buckling of critical shell structures. The new design procedure is based on the reduced stiffness method and leads to significantly improved critical load estimations in comparison to lower-bounds obtained empirically. An analysis example is given which is based on the launch-vehicle stage adapter (LVSA) of NASAs Space Launch-system (SLS). [ABSTRACT FROM AUTHOR]

• There are three failure modes including necking, buckling and fatigue cracking for HDPE specimen under cyclic loading. • Necking and buckling are dependent on the specimen temperature increase due to the competition between inelastic deformation accumulation and heat transfer with surroundings. • An approach is proposed based on constitutive model and heat transfer analysis to calculate the specimen temperature increase with cycles. • A methodology is established based on the calculated specimen temperature to predict the failure mode of HDPE specimen under cyclic loading. Failure analysis is a critical process for the lifetime evaluation of high density polyethylene (HDPE) under cyclic loading since HDPE may encounter different failure modes under different service environments. However, there are only a few investigations on the failure mechanism and failure mode of HDPE in cyclic-loading tests. The objective of this paper is to understand the failure mechanism and propose an approach to predict the failure mode of HDPE under cyclic loading. On the mechanism analysis, our results demonstrated that there could be three failure modes including necking, buckling and fatigue cracking for HDPE under cyclic loading. Both necking and buckling were strongly dependent on the increase of the specimen temperature, which led to the reduction of both yield stress defining necking and tangent modulus governing buckling. On the mode prediction, the yield stress and the tangent modulus could be computed as the functions of specimen temperature which was calculated by FEM heat transfer analysis considering heat generated by inelastic deformation energy and heat transferred with surroundings. Then, necking was predicted by comparing the decreased yield stress with the applied peak stress, and buckling was predicted by comparing the declined buckling stress proportional to tangent modulus with the absolute of the applied valley stress. The proposed methodology was validated as the predicted results were well matched with the experimental data for the tests of HDPE under different cyclic loadings. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• An accurate buckling analysis of FG porous GPLRC cylindrical shells is proposed. • Pre-buckling deformations and in-plane boundary conditions are considered. • Unified governing equations are established based on Donnell's theory and HSDT. • Highly accurate critical buckling loads and buckling mode shapes are obtained. • Effects of the material properties on stability of shells are detailedly discussed. Abstract By considering the pre-buckling effect and in-plane constraint, an accurate nonlinear buckling analysis of a functionally graded porous graphene platelet reinforced composite cylindrical shells under axial compressive load is performed. The stability equation is established according to a unified shell theory including the classical thin shell theory and the high-order shear deformation theory. Three types of porosity distributions and graphene platelet reinforced patterns are considered, and the modified Halpin–Tsai model and rule of mixtures are employed to determine their effective material properties. Explicit expressions of buckling equations for clamped or simply supported boundary conditions are obtained by the Galerkin's method. Highly accurate critical buckling loads and analytical buckling mode shapes are obtained simultaneously. A comparison between theoretical prediction and experiment is presented to verify the present method and very good agreement is reported. The influences of material properties on the buckling behaviors are also extensively investigated. It is recommended that the symmetric dispersion pattern is the optimal material distributions for both graphene platelets and porous, and the largest possible weight fraction, specific surface area and average thickness of graphene platelets could induce a better anti-buckling performance for the nanocomposite shell. Graphical abstract Image, graphical abstract An accurate nonlinear buckling analysis for functionally graded (FG) porous graphene platelet reinforced composite (GPLRC) cylindrical shells is performed by considering the pre-buckling effect and in-plane constraint. Highly accurate critical buckling loads and analytical buckling mode shapes are obtained by a unified shell theory. [ABSTRACT FROM AUTHOR]

Highlights • Three dimensional deformation shapes of compressed beam in circular constraints. • Four deformation modes as axial displacement increases. • Critical axial displacement between deformation modes. • Geometrical parameters influence the mode transition. Abstract This paper studies the three dimensional buckling and post buckling process of compressive long elastic beam confined by cylindrical lateral constraint without friction. Based on theoretical analysis and numerical simulations, four stages are identified and characterized as the compressive axial displacement increases from zero: initial two dimensional shape, small three dimensional shape, three dimensional helix shape and three dimensional alpha shape. Critical axial displacement at the transition points between four deformation shapes are studied, and the effect of geometrical parameters such as beam length and constraint size on critical displacement are examined. Special emphasis is paid to identify the transition points from three dimensional helix shape to three dimensional alpha shape, and the transition can be divided into jump regime (sharp transition) and no-jump regime (smooth transition) based on the criterion whether number of helical periods is larger or smaller than one. At the same time, critical number of helical periods in three dimensional helix shape is linearly correlated with a nondimensional geometrical parameter. Graphic abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Highlights • The buckling problem of a multiply connected bar-chain (MCB) system is investigated. • The MCB model has rigid bars connected by both direct and indirect neighbouring rotational springs that simulate the long range interactions between bars. • The buckling loads of the MCB with two-neighbour and N-neighbour interactions are analytically obtained for simply supported and clamped boundary conditions. • A nonlocal continuum model is constructed to predict the buckling behavior of MCB system with short and long range interactions. • The length scale of the nonlocal beam model is calibrated with respect to the rotational spring stiffnesses of MCB. Abstract This paper investigates the buckling problem of a multiply connected bar-chain (MCB) system. Unlike the Hencky bar-chain that comprises rigid bars connected to each other by rotational springs, this MCB model has rigid bars connected by both direct and indirect neighbouring rotational springs that simulate the long range interactions between bars. The buckling loads of the MCB with two-neighbour and N-neighbour interactions are analytically obtained for simply supported, clamped-clamped and clamped-free boundary conditions. By continualizing the discrete equations associated with MCB, a nonlocal continuum model is constructed to predict the buckling behavior of nonlocal bars with short and long range interactions. It is shown that this continualized nonlocal model (CNM) is equivalent to a stress gradient type of Eringen's nonlocal media. By comparing the solutions between CNM and MCB, it is shown that CNM is a simple nonlocal continuum model that is able to capture the scale effect of a generalized lattice that includes multiple interactions among its components. The closed form expression of the length scale of CNM is derived in terms of the rotational spring stiffnesses of MCB. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Highlights • Delamination and buckling of a thin film thermoelectric generator composed of pn-junction are examined. • Strong nonlinear relationship between the temperature field and the electric current field are considered. • Delamination energy release rate for different temperature loads and electric current densities are obtained. • Critical temperature difference of delamination and buckling initiations are identified. Abstract This paper investigates the problem of delamination and buckling of thermoelectric pn-junctions, which have many potential civil and military applications including thermal protection systems in space industry. Based on the compatibility equations of deformation, equilibrium equations of axial force and the strain compatibility equation at the interface of the bonding part are derived. Analytical solution of the delamination energy release rate is obtained. It is noted that there is no energy release rate when the magnitude of the temperature difference between the right end and the left end of the pn-junction is zero. The energy release rate can decrease or increase with the coefficient of thermal expansion. Distributions of the critical temperature differences for the delamination propagation and buckling are presented graphically. The critical temperature differences decrease continually with delamination and buckling lengths. Either a higher temperature difference or a higher electric current density can result in a bigger delamination energy release rate, a larger buckling deflection and a strong axial force. The buckling deflection increases but the axial force decreases with the increase of buckling length. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Highlights • FEM based model with and without van der Waals interaction is developed and validated for SWCNTs and DWCNTs. • FEM modeling of VACNTs with and without van der Waals forces are presented. • Influence of arrays size of VACNTs on elastic modulus is studied. • Influence of arrays size, intertube spacing and tube diameter on buckling strength of VACNTs is studied. Graphical abstract Image, graphical abstract Abstract Vertically aligned carbon nanotubes (VACNTs) have been explored widely in various applications due to their unique anisotropic properties. However, its application is limited due to large aspect ratio of nanotubes which lead to buckling phenomena. In this paper, we perform a finite element analysis to predict the variation of elastic modulus and critical buckling load of VACNTs. While elastic modulus is obtained from the slope of stress–strain variation of tubes when one end is fixed and another end is subjected to longitudinal loading, critical buckling load is found using eigenvalue analysis corresponding to first buckling mode. We also perform study to show size dependence of elastic modulus and buckling load of single walled carbon nanotubes (SWCNTs) using FEM approach and compare the results with MD results found in the literature. After validating FEM approach with available results of single-walled and double-walled carbon nanotubes, we apply the same method to arrays of VACNTs. It is found that elastic modulus of VACNTs increases from 1.18 TPa to 2.02 TPa when the size increases from 4 to 36 tubes and then it becomes nearly size independent. The variations of critical buckling load versus other parameters such as tube diameter, intertube spacing, etc., are also obtained. It is found that with the increase in diameter, there is a steep rise in the buckling load for the case of VACNTs arrays. In order to show the influence of non-linear van der Waals force in VACNTs, we compare the above results with and without the presence of van der Waals force and discuss its significance. The modelling and analysis presented in the paper can be used to optimise the number density of VACNTs for different applications. [ABSTRACT FROM AUTHOR]

Highlights • Numerical study of different cone geometries with semi-vertex angle ß = 10°…75°. • New improved shell buckling design factors for conical shells in form of a simple analytic equation. • Different equivalent cylinder approaches investigated. • Imperfection sensitivity of Interstage ½ of Vega launch-system analyzed. Abstract Thin-walled conical shells are used as adapters between cylindrical shells of different diameters in launch-vehicle systems. Conical shells carry heavy payloads and are consequently subjected to axial compression. The buckling load of these shells is very sensitive to imperfections (geometry, loading conditions) which results in a critical disagreement between theoretical and experimental results for axially loaded conical shells. The design of these stability critical shells is based on classical buckling loads obtained by a linear analysis which are corrected by a single knockdown factor (0.33 - NASA SP-8019) for all cone geometries. This practice is well established among designers and hasn't changed for the past 50 years because the buckling behavior is till today not very well understood. Within this paper an analytical and numerical lower-bound procedure for conical shells under axial compression is proposed. Data of previous experimental testing campaigns are used to validate the new design criteria for different conical shell geometry configurations. The whole design concept is demonstrated by means of the Interstage 1/2 of the Vega launcher and it is concluded that a revision of the current design recommendation for conical shell structures may results in a significant weight reduction potential. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper deals with the representative challenging buckling problem of a fully free plate under biaxial compression by a distinctive symplectic superposition method, which yields the benchmark analytic solutions by converting the problem to be solved into the superposition of two elaborated subproblems that are solved by the symplectic elasticity approach. The solution is advanced in the symplectic space-based Hamiltonian system rather than in the classic Euclidean space-based Lagrangian system, which shapes the main advantage of the method that a direct rigorous derivation is qualified for obtaining the analytic solutions, without any assumptions or predetermination of the solution forms. Comprehensive new analytic results for both the buckling loads and mode shapes are presented and validated by the finite element method. The fast convergence and accuracy of the method make it applicable to analytic modeling of more plate problems. [ABSTRACT FROM AUTHOR]

• A buckling-regulated origami material is proposed by synergy design of multiple origami features. • The properties of both developable and undevelopable origami are improved in proposed buckling-regulated materials. • A mechanical model for predicting the property of the buckling-regulated origami material is established. Origami is an emerging class of structural materials that can display remarkable physical and mechanical properties due to its unique deployability, while simple combination of deployable and undeployable features lead to more fantastic mechanical properties because of the extended design freedom. To further exploit the application potential of multiple origami features, a buckling-regulated origami material is proposed in this work by synergy design instead of simple combination of different origami features. In details, three buckling-regulated mechanisms are incorporated into the origami materials using synergy design, i.e., controlling global bulking via deployable folding, controlling local buckling through cell structure arrangement, and reproducing high energy-absorbing deformation mode using undeployable features. According to the synergic effect of multiple origami features, the buckling-regulated origami material improves both the resistance of deployable origami and instability of undeployable deformation. To validate this, the corresponding origami materials are manufactured by 3D printing technology, and experimentally tested. The manufactured origami materials show anticipated properties under quasi-static compression, i.e., high resistance and protracted steady plateau. Furthermore, due to the structural characteristics of origami and the tailorability of mechanical properties, it may inspire new innovations in designing other multi-functional metamaterials. [Display omitted] [ABSTRACT FROM AUTHOR]

A general framework is presented for evaluating stress triaxiality fields using five different configurations of Dirichlet boundary conditions. The latter ones were measured via stereocorrelation for a simple shear test on a thin sample where buckling was mitigated with an anti-buckling fixture. Friction and material parameters displayed negligible influence on the stress triaxiality fields. Accounting for the anti-buckling fixtures provided the most realistic stress triaxiality fields, but was computationally demanding. Prescribing all out-of-plane displacements, noisier but trustworthy stress triaxiality fields were also obtained by using much less computational resources. [Display omitted] • Minor frictional and material parameter impact on stress triaxiality fields • Including anti-buckling device in model yielded valid stress triaxiality fields • Trustworthy stress triaxiality fields by prescribing all out-of-plane displacements [ABSTRACT FROM AUTHOR]

In this study, we investigate buckling and postbuckling of etching-induced wiggling in a bilayer structure consisting of mask and masked layers. To show effects of explicit modeling of etching process, two mask–masked ridge models with and without etching (Models w/E and w/oE) are analyzed using finite element analysis. The etching process is explicitly introduced via step-by-step eigenvalue buckling analysis. Although Model w/oE predicts a constant value of the critical wavelength of wiggling regardless of the change in ridge width, Model w/E predicts a shorter wavelength depending on the decrease in ridge width and the increase in intrinsic compressive stress in the mask layer. In postbuckling analysis, Model w/oE predicts a monotonic increase in the wiggling amplitude with the constant wavelength, whereas Model w/E predicts saturation of the wiggling amplitude owing to the decreasing wavelength. In the explicit modeling of etching process, the wiggling behavior shows completely opposite tendencies. Dimensional analysis is performed to obtain empirical equations, which are compared with an experiment. [ABSTRACT FROM AUTHOR]

In this paper a physically based and deterministic design procedure for spherical shells under external pressure is introduced. Within the new design concept the membrane energy of a sphere is incrementally reduced by means of perturbation cutouts, until a bending energy dominate state is identified. The threshold between membrane energy state and bending energy state represents a robust plateau for the buckling pressure. A comprehensive numerical investigation was performed in order to study the influence of radius-to-thickness ratio (R/t) as well as the dome height-to-base radius ratio (H/r). The results verify that both geometric properties ratios significantly influence the lower-bound buckling pressure, especially if plastic buckling occurs. Improved shell buckling design factors are given in the form of an simple analytic equation. The corresponding threshold KDFs were validated with a large number of buckling experiments and deliver much higher KDFs than currently used empirical guidelines. Based on the new design criterion lower-bound estimation for the buckling pressure of a tori-spherical bulkhead and the inner dome of the cryogenic upper stage ESC-A from the European space launch-vehicle Ariane 5 are determined. [ABSTRACT FROM AUTHOR]

Understanding the buckling behaviors of rods confined in a finite space is of paramount importance in a diversity of engineering fields. In this paper, theoretical analyses, numerical simulations and experimental measurements are combined to investigate the buckling and postbuckling of a long rod confined in a circular tube. Under uniaxial compression, the initially straight rod first buckles into a sinusoidal shape, followed by the occurrence of snap-through instability or helical buckling, which leads to a complicated, three-dimensional configuration consisting of serially connected sinusoids and helices. A new theoretical model is presented to analyze the sinusoidal and helical buckling processes of the confined rod. The complete load–displacement curve of the buckled system during loading and unloading can be well predicted by the present theory. The critical conditions are obtained for the occurrence of the sinusoidal buckling and the sinusoid–helix transitions of buckling modes. It is found, both theoretically and experimentally, that the morphological evolution during unloading exhibits distinctly different features from that during loading due to the peculiar energetic features of snap-through instability. A flexible multibody dynamics method on the basis of the geometrically exact beam theory is employed to numerically explore the buckling behavior of slender rods and to reveal the underlying energetic mechanisms. The theoretical, numerical, and experimental results agree with each other very well. The theoretical model and the numerical method presented in this work are expected to analyze some other problems of confined rods, beams, and their combined systems. [ABSTRACT FROM AUTHOR]

We present a physics-based finite element simulation of self folding of a hydrogel bilayer with programmed holes. Introducing holes in a bilayer modifies the topology and boundary of the bilayer. Early state swelling of a hydrogel bilayer forms rolled tubes along the periphery of the bilayer and adds the local rigidity along the boundary. Our numerical simulation shows that formation of rolled edges switches the deformation mode of hydrogel bilayer from slow and gradual bending to fast and sudden buckling or folding. On demand folding is thus possible by tuning the location, size and shape of holes. The uncovered folding mechanism is leveraged to design a number of soft self-folding machines. The results throw light on design and simulation of soft self-folding machines. [ABSTRACT FROM AUTHOR]

The collapse behavior of a non-uniform circular shallow arch is analytically studied for both fixed-fixed and pinned-pinned boundary conditions. The non-uniformity is characterized by three piecewise constant stiffness regions. The equilibrium equations are derived based on the least potential energy principle and the resulting solutions are presented by proper non-dimensionalization in a form independent of total length of the whole arch by identifying two modified slenderness parameters. Detailed parametric study of both stiffer center case and stiffer end case has been conducted to investigate the influence of various geometric parameters and distinctly different collapse behaviors are found for different boundary conditions. Some criteria are derived to identify the snap-through buckling. Moreover two limiting cases of extreme non-uniformity(rigid end case and rigid center case) are studied via the augmented potential energy with introduced Lagrangian multipliers. Through an asymptotical analysis, a finite modified slenderness parameter is shown to suffice to ensure the occurrence of snap-through buckling for rigid end case with pinned boundary conditions when the dimension of center region is approaching to zero. It is shown rigorously that the same conclusion holds even when there is some rotational restraint at the pinned ends. For rigid center case, closed-formed criteria are derived for snap-through buckling. Finally analysis has been carried out on the case where one part of the arch has large bending rigidity but moderate stretching rigidity. This paper aims to enhance the understanding of collapse behavior of non-uniform shallow arch under a central concentrated load for various boundary conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the parametric instability of functionally graded graphene reinforced nanocomposite plates that undergo a periodic uniaxial in-plane force and a uniform temperature rise. The plate is composed of multiple graphene platelet reinforced composite (GPLRC) layers in which graphene platelets (GPLs) are uniformly distributed in each individual layer with GPL concentration varying layer-wise across the plate thickness. The modified Halpin–Tsai model that takes into account the GPL geometry effect is employed to calculate the Young's modulus of the GPLRC. Based on the first-order shear deformation theory, the governing equations are deduced and then are solved by using the differential quadrature approach integrated with the Bolotin's method. A parametric study is undertaken to show the influences of GPL distribution pattern, concentration and geometry, temperature change, static in-plane force, plate geometry and boundary condition on the parametric instability of functionally graded multilayer GPLRC plates. It is found that the addition of a small amount of GPL reinforcements considerably increases the critical buckling load and natural frequencies but reduces the size of unstable region. The reinforcing effect is the best when the surface layers of the plate are GPL-rich. [ABSTRACT FROM AUTHOR]

This paper presents analytical study of a non-uniform shallow arch under a central concentrated load. The non-uniformity is characterized by three constant stiffness regions. The least potential energy principle is used to obtain the equilibrium equations. The anti-symmetric buckling axial compression and buckling modes are shown to be identical with those of Euler-Bernoulli beam. The initial imperfection effect is also investigated theoretically and a parametric study on the different geometric parameters has been carried out on the snap-through symmetric buckling load and anti-symmetric buckling load. The comparison against the finite element analysis shows the accuracy of the theoretical model. We show that the stiffer center case is always economically better than the stiffer end case. The two limiting cases with largest degree of non-uniformity are analytically analyzed by using the augmented potential energy with the Lagrangian multiplier. The closed-form condition for the occurrence of symmetric snap-through buckling is presented for one limiting case. This paper serves to enhance the understanding of the effect of the non-uniformity of shallow arch on its load carrying capacity. [ABSTRACT FROM AUTHOR]

A non classical analytical model is presented for free vibration of the cracked rectangular isotropic and functionally graded micro plates in the presence of thermal environment. The new approach is based on the combination of classical plate theory and the modified couple stress theory. The crack terms are based on the Line Spring Model whereas the thermal environment is accommodated in the form of thermal moment and in-plane forces. The solution for fundamental frequencies of the cracked plate is obtained by discounting geometric nonlinearity. A non classical relation for geometrically linear thermal buckling phenomenon of a cracked micro-plate is also proposed. The variation of critical buckling temperature and fundamental frequency with uniform rise in temperature of the cracked plate is studied for various crack length ratios, gradient index and internal material length scale parameter. Furthermore the variation of the buckling coefficient with plate aspect ratio and thickness of the cracked micro-plate is established. A comparison is presented between the classical results and present results as affected by thermal environment and microstructure of the plate. It is concluded that the presence of cracks affects the critical buckling temperature and fundamental frequencies of micro plates. The consideration of size effect increases the buckling temperature which shows the significance of the internal material length scale parameter in the presence of thermal environment. [ABSTRACT FROM AUTHOR]

The present paper investigates the biaxially compressed buckling and postbuckling behaviors of functionally graded multilayer composite plates reinforced with a low content of graphene nanoplatelets (GPLs) that are randomly oriented and uniformly dispersed in the polymer matrix within each individual layer. The material properties of the GPL-reinforced composite (GPLRC), which are graded along the thickness direction due to a layer-wise change in GPL weight fraction, are evaluated through a micromechanics model. Theoretical formulations are based on the first-order shear deformation plate theory and von Kármán-type nonlinear kinematics and include the effect of an initial geometric imperfection. A two step perturbation technique is employed to determine the asymptotic postbuckling solutions and the biaxial compressive postbuckling equilibrium paths of both perfect and imperfect plates simply supported on all edges. The effects of GPL weight fraction, distribution pattern, geometry and size as well as total number of layers on the buckling and postbuckling behaviors of functionally graded GPLRC plates are examined in detail. [ABSTRACT FROM AUTHOR]

This paper presents an analytical investigation on the free vibration, static buckling and dynamic instability of laterally-restrained zed-section purlin beams when subjected to uplift wind loading. The analysis is carried out by using the classical principle of minimum potential energy. By assuming the instability modes, the kinetic energy and strain energy of the beam and the loss of the potential energy of the applied load are evaluated, from which the mass, stiffness and geometric stiffness matrices of the system are derived. These matrices are then used to carry out the analyses of free vibration, static buckling and dynamic instability of the beams. Theoretical formulae are derived for the free vibration frequency, critical buckling moment, and excitation frequency of the beam. The effects of the section size of the beam and the static part of the applied load on the change of dynamic instability zone are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, a generalized discrete elastica including both bending and shear elastic interactions is developed and its possible link with nonlocal beam continua is revealed. This lattice system can be viewed as the generalization of the Hencky bar-chain model, which can be retrieved in the case of infinite shear stiffness. The shear contribution in the discrete elastica is introduced by following the approach of Engesser (normal and shear forces are aligned with and perpendicular to the link axis, respectively) and that of Haringx (shear force is parallel to end section of links), both supported by physical arguments. The nonlinear analysis of the shearable-bendable discrete elastica under axial load is accomplished. Buckling and post-buckling of the lattice systems are analyzed in a geometrically exact framework. The buckling loads of both the discrete Engesser and Haringx elastica are analytically calculated, and the post-buckling behavior is numerically studied for large displacement. Nonlocal Timoshenko-type beam models, including both bending and shear stiffness, are then built from the continualization of the discrete systems. Analytical solutions for the fundamental buckling loads of the nonlocal Engesser and Haringx elastica models are given, and their first post-buckling paths are numerically computed and compared to those of the discrete Engesser and Haringx elastica. It is shown that the nonlocal Timoshenko-type beam models efficiently capture the scale effects associated with the shearable-bendable discrete elastica. [ABSTRACT FROM AUTHOR]

• A novel design approach for stiffening of aircraft fuselage panels is introduced. • Advantage of Voronoi-type stiffeners greatly increases as compression loads increase. • More than 60% stiffener mass saving is achieved compared to conventional stiffeners. • Notable predictability with artificial neural network optimization scheme is shown. Designing lighter airframes is one of the crucial pursuits of aviation for structural and operational efficiency. Owing to the expansion of the boundaries for manufacturing technologies, the utilization of exotic structures inspired by nature in aviation has gained popularity in recent years. In this study, a bio-inspired structural stiffening concept employing Voronoi cells is proposed to reinforce a fuselage panel subjected to compression loads. In this regard, a genetic optimization algorithm based on artificial neural networks (ANNs) is used to establish the optimized design of Voronoi cell reinforced fuselage panels with minimum weight. Since stiffening with Voronoi cells causes serious nonlinearity in the estimation of buckling strength, a layer/neuron count optimization scheme consisting of nested loops and condition blocks is developed for each panel with different local Voronoi cell densities. Comparisons with conventional panel stiffeners such as isogrid, orthogrid and stringer structures demonstrate that Voronoi-type stiffeners provide much lighter design solutions at the same critical buckling load levels. Additionally, it is also presented that the advantage of Voronoi cell reinforcements significantly increases as the critical buckling load level increases. Therefore, the results provided in this study signify a great potential for the usage of Voronoi cells as bio-inspired stiffener members for lightweight structural designs. [Display omitted] [ABSTRACT FROM AUTHOR]

On the basis of the nonlocal strain gradient theory, a size-dependent Euler–Bernoulli beam model is formulated and devoted to investigating the scaling effect on the post-buckling behaviors of functionally graded (FG) nanobeams with the von Kármán geometric nonlinearity. The developed beam model can incorporate the scaling effect of both nonlocal long-range force and microstructure-dependent strain mechanism. To simplify the redundancy of the governing equation and derive the closed-form solutions, a physical neutral surface is applied for removing the bending-stretching coupling due to geometric nonlinearity and the coupling rigidity between the extensional and bending rigidities of the though-thickness FG material. The closed-form solutions for the post-buckled configuration and the critical buckling force (CBF) are deduced in the case of hinged-hinged boundary conditions. The effects of scaling parameters and material property variation on the post-buckled configuration and the CBF are investigated in detail. It is found that the stiffness-hardening or stiffness-softening effect is dependent of the values of scaling parameters. [ABSTRACT FROM AUTHOR]

Buckling of the rectangular thin plates is a class of problems of fundamental importance in mechanical engineering. Although various theoretical and numerical approaches have been developed, benchmark analytic solutions are still rare due to the mathematical difficulty in solving the complex boundary value problems of the governing high-order partial differential equation. Actually, most available solutions can be categorized as either “accurate” for the plates with two opposite edges simply supported or “approximate” for those without two opposite edges simply supported. In this paper, we present the first work on the symplectic superposition method-based analytic buckling solutions of the rectangular thin plates. A Hamiltonian system-based variational principle via the Lagrangian multiplier method is proposed to formulate the thin plate buckling in the symplectic space. Then the governing equation is analytically solved for some fundamental subproblems which are superposed to yield the final solutions of the original problems. For each problem, a set of equations are produced with respect to the expansion coefficients of the quantities imposed on the plate edges. The existence of the nontrivial solutions of the equations sets the requirement that the determinant of the coefficient matrix be zero, which leads to a transcendental equation with respect to the buckling loads. The buckling mode shapes are obtained by substituting the nontrivial coefficient solutions into the mode shape solutions of the subproblems, followed by superposition. Four types of buckling problems are studied for the plates with combinations of clamped and simply supported edges, without two opposite edges simply supported. The developed method as well as the accurate analytic results is well validated by the finite element method and very few analytic results from the literature. [ABSTRACT FROM AUTHOR]

This paper presents the Hencky bar-chain model (HBM) that allows for the presence of internal elastic springs. With the development of this general HBM, one can analyse beam-like structures with repetitive cells with allowance for internal damaged sections or bracing members. In this paper, we have derived formulas for the internal rotational and lateral spring stiffnesses of HBMs based on the finite difference model (FDM). In addition, the analytical buckling loads and vibration frequencies of the HBM and FDM with internal elastic springs are presented for the first time. These analytical solutions converge to the exact solutions for continuum beams when the HBM segmental number approaches infinity. The solutions can also be used to calibrate the Eringen's small length scale coefficient e 0 in the nonlocal beam theory based on their phenomenological similarities. [ABSTRACT FROM AUTHOR]

Grid structures are extensively used in many engineering structures as an orthotropic layer with at most in-plane anisotropy. In this study, the laminated grids structures are considered. These structures are composed of various numbers of thin composite grid layers. This concept yields to numerous laminated grid configurations with disparate coupling effects, which can be used to tailor the stiffness, compare to conventional grids. In the present study, four known grid patterns with equal weight and thickness constitute the laminated grids. The genetic algorithm (GA) is employed to optimize the stacking sequence and pattern composition of the laminated grid. The buckling load is taken as a fitness function and the pattern and orientation of the grid layer are considered as the design variables. The first-order shear deformation and classical laminated plate theories are considered along with Ritz method to obtain the elastic buckling loads. The optimization results are presented for various boundary conditions and aspect ratios. The results show, using the laminated grid considerably improves the axial buckling load of the plates. Moreover, the plate boundary conditions and aspect ratios play an imperative role in the optimum pattern and stacking sequence of the laminated grid plates. [ABSTRACT FROM AUTHOR]

Buckling of anisotropic piezoelectric cylindrical shells subjected to axial compression and lateral pressure is investigated based on the new modified couple stress theory and using the shear deformation theory with the von Kármán geometrical nonlinearity. By applying the principle of minimum potential energy, the governing equations and boundary conditions are derived. Unlike the classical continuum model, the present model is size-dependent, and the size effects are captured using the new modified couple stress theory. The critical buckling load is obtained for simply supported, clamped-simply supported and clamped piezoelectric cylindrical shells. A detailed numerical study is carried out to discuss the effects of different parameters, such as material length scale parameter, thickness ratio, length ratio, load interaction parameter and the external electric voltage on the critical buckling load. The critical buckling load is found to be significantly size-dependent, especially for large values of thickness and small values of length ratio. Besides, the influence of load interaction parameter is found to be negligible for large values of length and small values of thickness ratio. [ABSTRACT FROM AUTHOR]

A new model depicting the full phase of tubular string buckling in vertical wellbores is proposed. The buckling modes of the tubular string are divided into: no buckling, 2D lateral buckling, 3D lateral buckling, continuous contact buckling and helical buckling. For the 2D lateral and 3D lateral buckling, the tubular string is respectively depicted by two and four suspended sections; for the continuous contact and helical buckling, the tubular string includes four suspended sections and one continuous contact section. With the suspended and continuous contact sections respectively depicted by beam-column model and buckling differential equation, the general buckling configurations of the entire tubular string are deduced. Substituting relevant continuity, boundary and stability conditions, the tubular string buckling problem is converted into a system of nonlinear equations. Solving these equations with iteration method, the critical buckling loads and the buckling configurations under different buckling modes for a weightless tubular string are obtained. Later, the weightless model is extended to the case for a tubular string with weight. On the basis of the new buckling model, the axial force and torque transfer along the tubular string under the coupling effect of friction force and buckling is discussed. The results show that the existence of tubular string weight increases the complexity of buckling mechanism and calculation. The continuous contact between the tubular string and wellbore reduces the axial force and torque transfer along the tubular string. To increase the axial force and torque transfer and inhibit buckling, the installation of stabilizers of low friction and buckling inhibition on the buckling-prone sections is wiser than unilaterally increasing the diameter and thickness of the tubular string. Compared with the previous results, the new model provides a more sophisticated description of tubular string buckling in vertical wellbores. [ABSTRACT FROM AUTHOR]

Postbuckling and postbuckled vibration characteristics of sandwich plate subjected to non-uniform in-plane loadings is investigated in this article. The core compressibility effects are considered in the model by assuming fourth and fifth order expansions for the transverse and tangential displacement of the core. The exact stress distributions within the panel are determined by panel prebuckling analysis for the applied parabolic and partial edge loadings. Multi-term Galerkin's method is employed to reduce the governing partial differential equation to a set of non-linear ordinary differential equations in the case of dynamic analysis and to a set of non-linear algebraic equations in the case of static stability analysis. Newton-Raphson method in conjunction with Riks approach is used to trace the postbuckling path. Free vibration frequencies of the sandwich plate about a static equilibrium state are obtained by solving the associated linear eigenvalue problem. From numerical study it is observed that the postbuckling path becomes more softening type with increase of aspect ratio. Moreover, unloaded fixed edge of SCSC sandwich plate gives more rigidity than unloaded simply supported edge of CSCS. The prebuckling and postbuckling frequency increases with increase in edge restraint, and in postbuckling range, frequency increases with increase of in-plane load. [ABSTRACT FROM AUTHOR]

In this article, buckling response of functionally graded nano-plate based on exponential shear deformation theory is presented. The theory presented herein is built upon the classical plate theory. In this displacement-based, refined shear deformation theory, an exponential functions are used in terms of thickness co-ordinate to include the effect of transverse shear deformation and rotary inertia. The number of unknown displacement variables in the proposed theory are same as that in first order shear deformation theory. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the functionally graded rectangular nano-plate. The material properties of the plate are assumed to vary according to the Power Law form in the thickness direction. The governing equations and corresponding boundary conditions are derived by implementing Hamilton's principle. To show the accuracy of the formulations, our research results in specific cases are compared with available results in the literature and a good agreement will be observed. Finally, the effect of various parameters such as nonlocal parameter, Power Law indexes, aspect ratio, and the thickness ratio on the non-dimensional critical buckling load of rectangular FG nano-plates are presented and discussed in detail. [ABSTRACT FROM AUTHOR]

• A novel buckling-guided 3D assembly method is introduced. • Buckling behavior of a laminated thin circular ring is investigated. • Scaling laws for the critical current of buckling are provided. • The scaling law for measurement of elastic moduli of planar materials is provided. Buckling-guided transformations of thin-film materials into three-dimensional (3D) architectures are extensively utilized in electronic microsystems. However, the mechanically-guided assembly technique exploits a prestretched substrate, such that low-stiffness precursors would fail to realize global buckling due to the difficulty in overcoming interfacial adhesion (i.e., Van der Waals forces). Here, based on finite element analysis (FEA), a novel buckling-guided 3D assembly method by electromagnetic actuation is introduced through investigating the buckling behavior of a laminated thin circular ring. In this method, interfacial adhesion could be notably reduced by replacing soft substrates with rough platforms, thereby allowing formation of 3D structures with ultralow stiffnesses. Scaling laws for the critical current of buckling and the effect of joule heating are developed to guide controlled deformations and ensure rational designs. Numerical demonstration of a morphable, reconfigurable four-petal rose suggests the applicability and advantages of the proposed Lorentz force-guided 3D assembly method. In addition, we show that simultaneous measurement of the elastic moduli and thickness of planar materials could be possible based on the established scaling law for critical buckling current. The results presented here serve as design guidelines for applying electromagnetically-actuated buckling behavior of thin-film materials in future applications such as soft grippers and biomedicine. [Display omitted] [ABSTRACT FROM AUTHOR]

Discrete Element Method (DEM) simulations are used to model the elastic properties of a continuous material. The preparation route of the particle packing is shown to have a significant effect on the macroscopic properties. We propose simple relations, generalized from the mean field solution, that are able to fit DEM results. These relations introduce only basic microstructural features such as the coordination number and the packing density. When the tangential to normal stiffness ratio increases above unity, the material becomes potentially auxetic. Buckling is also explored with DEM, and results on cylindrical bars are compared to the classic Euler results for critical stress. [ABSTRACT FROM AUTHOR]

This paper investigates the torsional wrinkling behavior of an annular thin film. Non-dimensional nonlinear von Karman buckling equations are established, which are solved by introducing a compound series method to acquire the post-wrinkling characteristics. The proposed theoretical model can accurately predict the critical wrinkling behavior and post-wrinkling characteristics of the annular thin film, which are verified by the experimental measurement based on the digital image correlation (DIC) technique. The theoretical results show that the post-wrinkling stress is intimately associated with the wrinkle configuration in the post-wrinkling stage. The hoop post-wrinkling stress along the wrinkle texture direction of the annular thin film dictates the wrinkle evolution. The wrinkle number remains constant in the elastic regime, which is determined by the critical buckling load factor. The results provide good guides to tune or control the wrinkles in the thin film. [ABSTRACT FROM AUTHOR]

A new accurate four-variable shear deformation plate theory is introduced in this paper to illustrate the hygrothermal vibration and buckling of FGM sandwich plates resting on Winkler–Pasternak elastic foundations. Based on the suggested theory, the equations of motion are derived from Hamilton׳s principle containing the hygrothermal effects. This theory involves only four unknown functions and accounts for quasi-parabolic distribution of transverse shear stress. In addition, the transverse shear stresses are vanished at the top and bottom surfaces of the sandwich plate. A power law distribution is used to govern the gradation of material properties through the plate thickness. Various types of FGM sandwich plates are considered. To check the validity of the theory and formulations, the obtained results are compared with the previous results. Comparison studies reveal that the results of the proposed theory are more accurate than those of other shear deformation plate theories. Parametric study is performed to show the influences of moisture condition, temperature rise, elastic foundation coefficients and power law index on the buckling and natural frequency of FGM sandwich plates. [ABSTRACT FROM AUTHOR]

The effects of creep of the core material on the global and local geometrically nonlinear behavior of sandwich panels under axial and/or lateral loading conditions is presented, within the framework of the high-order sandwich theory (HSAPT). The theoretical model combines the concepts of the hereditary (convolution) integral of viscoelasticity based on the principle of superposition, with the HSAPT. From the expansion of the relaxation moduli into Prony series, an incremental exponential law that corresponds to the rheological generalized Maxwell model is obtained, and which allows for a step-by-step time analysis that accounts for the change in deformations and stresses with time. The results show that creep of the core leads to a significant reduction in the local and global buckling capacity of sandwich panels. It is shown that sandwich panels under a combined axial and lateral loading can undergo global buckling with time due to creep, under a sustained load that is less than 50% of their buckling load. Similar trend is also observed for the local buckling (wrinkling) of the compressed face sheet when the panel is subjected to a sustained uniformly distributed load. In both cases, buckling commenced at a relatively low stress levels but it is associated with an unlimited increase of the stresses with time that eventually lead to material failures and total failure of the sandwich panel. [ABSTRACT FROM AUTHOR]

This paper aims to develop a new non-classical Bernoulli–Euler model, taking into account the effects of a set of size dependent factors which ignored by the classical continuum mechanics. Among those factors are the microstructure local rotation, long-range interactions between a particle and the other particles of the continuum and the surface energy effects. The model used the modified couple-stress theory to study the effect of the local rotational degree of freedom of a specific particle. Furthermore, the surface elasticity model developed by Gurtin and Murdoch has been used to determine the surface energy effects on the behavior of the particle. The effects of the local rotation and surface energy are investigated in the framework of nonlocal elasticity theory, which is employed to study the nonlocal and long-range interactions between the particles. In addition, Poisson׳s effect incorporated in the newly developed beam model. The equations of equilibrium and complete boundary conditions of the new beam are derived using the principle of virtual work. The developed model is validated, by comparing the obtained results with benchmark results. To illustrate the new model, analytical solutions for the static bending and critical buckling load are obtained. Numerical results reveal the significant effects of the nonlocal, microstructure, surface energy, length-to-height ratio and Poisson on the static bending and critical buckling load of nanobeams. [ABSTRACT FROM AUTHOR]

We study the stability of thin walled circular cylindrical shells subject to radial pressure loading. Towards this end, we first develop the equations of motion of these shells with predominant radial deflections. We identify additional terms in the shell equations of motion which have mostly been neglected in existing studies and ascertain their importance in predicting the correct static buckling pressure. For finite cylinders, incorporation of these terms results in the best prediction of the static buckling pressure. Furthermore, we also find that the assumed relationships between the in-plane displacements of a generic point and the in-plane displacements of the mid-surface, which change from one shell theory to the other, play a critical role in determining the correct onset of the buckling instability under radial loading. In particular, the Donnell shell theory which is very popular for the study of dynamic problems related to cylindrical shells does not predict the correct buckling pressure. We find that the Flügge–Luré–Byrne theory is best suited for this purpose. Accordingly, the shell equations with the additional terms and the in-plane displacements related as per the Flügge–Luré–Byrne shell theory have been used for the study of parametric instability of a cylinder subject to a uniform radially fluctuating pressure. Stability charts with respect to different combinations of the forcing parameters viz. the static component of the pressure, the amplitude and frequency of the fluctuating component of the pressure have been presented which can serve as design guideline for shells subject to fluctuating radial loads. [ABSTRACT FROM AUTHOR]

In this paper, recently developed inverse trigonometric zigzag theory by the authors is extended for the stability analysis of laminated composite and sandwich plates. The model satisfies the inter-laminar continuity at layer interfaces as well as the traction free boundary conditions at top and bottom surfaces of the plate. This theory assumes the non-linear distribution of transverse shear stresses. Green–Lagrange non-linear strain–displacement relations are used to represent geometric nonlinearity in buckling analysis. An efficient C 0 finite element is employed for discretization of the laminate. Numerical results on buckling load parameters are evaluated for laminated composite and sandwich plates covering with different features such as aspect ratios, span thickness ratios, modular ratios, loading and boundary conditions. To ensure the potentiality of the present theory, the evaluated results are validated with the three dimensional elasticity results and the existing results based on different deformation theories as well. Higher modes with corresponding mode shapes are also presented for laminated composite plates. The exemplary results with minimum percentage error with respect to exact results ascertain the accuracy and efficiency of the present theory. [ABSTRACT FROM AUTHOR]

In the present study, the buckling behaviour of laminated composite skew plates with different boundary conditions subjected to linearly varying in-plane loads are presented. The skew plate is modelled based on higher order shear deformation theory, which accurately predicts the buckling behaviour for the thick plate. The in-plane stress distribution within the skew plate due to linearly varying in-plane load is equal to the applied in-plane edge load in the pre-buckling range. Using these in-plane stress distributions, the total potential energy functional is formulated. Total potential energy is a function of the total strain energy of skew plate and potential energy due to in-plane stress distributions. The total strain energy of skew plate contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total potential energy functionals mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Using a Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total potential energy functional is converted into sets of algebraic equations. Finally, these algebraic equations are rearranged as a linear eigenvalue problem, which is solved to obtain the critical buckling loads. The numerical results are presented for different skew angles, boundary conditions, length to thickness ratios, aspect ratios and in-plane loadings. It is observed that the critical buckling load increase with the increase of skew angle as well as change in the mode shape at a lower aspect ratio with the increase of skew angle. [ABSTRACT FROM AUTHOR]

A new size-dependent beam model is introduced on the basis of hyperbolic shear deformation beam and modified strain gradient theory. The governing differential equations and corresponding boundary conditions are obtained with the aid of minimum total potential energy principle. The static bending and buckling behaviors of simply supported microbeams embedded in an elastic medium are investigated. The interactions between the microbeam and elastic medium are simulated by Winkler foundation model. Navier solution procedure is employed to obtain analytical solutions for deflections under sinusoidal load and critical buckling loads. The effects of material length scale parameter, length-to-thickness ratio, shear correction factors and Winkler modulus on the bending and buckling responses of microbeams are discussed in detail. The results are comparatively presented with the results of other beam theories. It is observed that the new results predicted by the present model and the results evaluated by sinusoidal shear deformation beam model are in good agreement. [ABSTRACT FROM AUTHOR]

Computer simulations are becoming increasingly important for the optimisation of various processes since they can significantly reduce the development time and costs. The discrete element method (DEM) offers a powerful tool for simulating the interactions of large numbers of particles. The method has proven its usefulness for many applications where granular and spherical particles are handled. Very recently DEM, was used to simulate the interactions of tubular particles. While the existing linear elastic models could describe the reversible bending and denting of these particles in a realistic way for small deformations, they are inadequate for describing the bending and compression behaviour at higher forces. In this region, buckling phenomena become important. Therefore, new phenomenological models, inspired by the collapse of steel tubes due to ovalisation of the cross section and the formation of plastic hinges, have been implemented for metal and synthetic plastic tubes. Using these models virtual, bendable tubes were created in the DEMeter++ software. The DEM parameters were calibrated for copper and PVC tubes based on combined bending and denting tests conducted using an Universal Testing System. The simulations were in good agreement with the measurements ( R 2 > 0.91 ). This realistic DEM model of bending can, in future research, be used to simulate the processing of large numbers of tubular particles (e.g. the processing of crop stems). [ABSTRACT FROM AUTHOR]