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• A state-space-based mixed finite element method is established for dynamic analysis of composite beams. • This method is capable of dealing with both transversely multi-layered and axially jointed composite beams. • Stress singularities near the interfaces are resolved by ensuring both displacement and stress continuities across different materials. • Simultaneous arrangement of displacements and stresses provides reliable simulations of boundary conditions at both ends. A novel mixed finite element method is developed and implemented for analyzing the vibration and buckling behavior of general composite beams which consists both transversely layered and axially jointed materials. The governing state-space equations are derived using the Hamilton's principle, where both displacements and stresses are treated as fundamental variables. This semi-analytical method uses transfer relations in the transverse direction and finite element meshing in the longitudinal direction, overcoming the difficulties for general composite beams analysis and providing computational efficiency and analyzing flexibilities. The developed mixed finite element model ensures continuity of both displacements and stresses across the material interface, thereby resolving interfacial stress singularity issues and offering more reliable simulations of boundary conditions at both ends. The proposed method is formulated and validated for the free vibration and buckling analysis of general composite beams. Additionally, it is observed that material properties such as Young's modulus and density, as well as the stiffness of the interface connecting layers, have significant effects on the free vibration and buckling responses of the composite beams. Analysis of periodically distributed and bi-directional composite beams demonstrates the versatility of this method in handling two types of combination forms. The proposed method serves as a valuable reference for obtaining accurate vibration and buckling results while ensuring stress-compatibility for composite beams in practical applications. [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]

• 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]

• 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]

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]

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]

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]

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]

• 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]

In this work a finite element model is presented for buckling and nonlinear analysis of multilayer sandwich plates and shells, with a soft core sandwiched between stiff elastic layers. The finite element is obtained by assembling all element-layers through the thickness using specific assumptions on the displacement continuity at the interfaces between layers, but allowing for different behaviors of the layers. The stiff elastic layers are modelled using the classic plate theory and the core is modelled using Reddy׳s third order shear deformation theory. The present finite element model is a non-conforming triangular plate/shell element with 24 degrees of freedom for the generalized displacements. This model is applied in the solution of illustrative examples and the results are presented and discussed. [ABSTRACT FROM AUTHOR]

Buckling of cracked functionally graded plates resting on Pasternak foundation under tension has been studied. Classical plate theory in framework of the finite element method has been used. Shape functions for elements surrounding crack tips have been derived using previous solutions of displacement fields around crack tips. In-plane loads have been obtained by a pre-buckling solution using quarter-point elements around crack tips. Results show that an increase of foundation stiffness, leads to greater values of buckling loads. For longer cracks the effect of foundation stiffness on buckling load diminishes. For bi-axial loading such stiffness has less effect on buckling compared to uni-axial case. [ABSTRACT FROM AUTHOR]

The couplings of unsymmetric laminated structures and the comparatively low transverse shear stiffnesses significantly influence their stability behaviour. The aim of this work is to improve the purely analytical stability analysis of unsymmetric laminated structures. This problem can be reduced to one single plate with the use of the discrete plate theory. In this study, laminates under uniaxial compressive load are considered that are simply supported at all edges and have rotational restraints on the unloaded edges (SRSR) or have a free edge (SFSR). Therefore, the present study provides explicit solutions for the buckling load in two ways. Firstly, the first explicit solution for the buckling load of unsymmetric laminates with the mentioned boundary conditions is developed, which takes the bending–extension couplings into account in a direct way. The method is an energy-based method in the form of the Rayleigh-quotient for classical laminated plate theory (CLPT), first order shear deformation theory (FSDT) and third order shear deformation theory (TSDT). Secondly, the reduced bending (RBS) method is investigated for the first time in the framework of TSDT. The comparison of unsymmetric cross-ply and angle-ply laminates shows a good agreement with finite element analysis (FEA). Due to the high computational efficiency of the presented methods, they are excellently suited for pre-design and optimization of composite structures, with simultaneous high usability in practical application. [Display omitted] • First explicit buckling load for unsymmetric rotationally restrained laminates. • First reduced bending stiffness (RBS) method in the framework of TSDT. • Bending–extension couplings are taken into account in CLPT, FSDT and TSDT. • Pronounced transverse shear deformation in closed-form stability analysis. • High computational efficiency: very suitable for pre-design and optimization. [ABSTRACT FROM AUTHOR]

Abstract: Three-dimensional reinforced sandwich structures are generally designed in order to provide optimal out-of-plane mechanical properties, beside traditional sandwiches which generally display satisfactory specific flexural properties but fatally insubstantial stiffnesses in the through-thickness direction. This paper deals with sandwich structures manufactured with polymeric foam core reinforced thanks to the technology (which is based on transverse needling) and specially investigates the compression behavior through the thickness direction. The compressive longitudinal moduli of such sandwiches are shown to be significantly improved in the presence of fibrous orthogonal reinforcements but the experimental estimations rather differ from analytical predictions that can be easily obtained using classical mixture laws. These discrepancies are mainly due to the buckling phenomenon, inherent in the geometry of the reinforcements, and the associated imperfection sensitivity. This work is thus devoted to the prediction of the critical loading of such a sandwich structure under through-thickness compression. A closed-form analytical expression is first derived from a general 3D elastic bifurcation analysis, then compared to finite element numerical solutions (obtained by both linearized buckling and incremental post-buckling analyses) for validation purposes, and finally confronted to experimental results. The buckling phenomenon is actually proved to be mainly responsible for the final collapse of the through-thickness reinforced sandwich. [Copyright &y& Elsevier]

Abstract: This paper presents an analytical study on the influence of in-plane forces on the dynamic characteristics of a plate with grooves in different sizes. A sub-structuring approach, the reverse receptance method, is applied to solve the eigenvalues of an in-plane forces loaded plate with two parallel grooves and two orthogonal grooves, respectively. On considering coupling and interaction between two orthogonally connected grooves, the point receptance arrays are employed. Accuracy is evaluated by comparing the analytical solutions with numerical results obtained from the finite element model. Parametric study reveals, the deeper the groove, the lower the natural frequencies and buckling loads of the grooved plate will be. With in-plane tensions applied and increased linearly, the grooved plate is stiffened gradually and its natural frequencies increase accordingly. With equal bi-axial tensions, the natural frequencies of the grooved plates increase twice as much as those with uni-axial tension do. With in-plane compressive forces on the plate, the situations are reversed. The lowest natural frequency of a grooved plate with sufficient tensions can be higher than that of a non-grooved unloaded plate. When the groove size and the loading condition are the same, the orthogonal grooves decrease the natural frequencies and the buckling loads of a plate more than the parallel grooves do. The in-plane forces do not affect the mode shapes of the grooved plate; but the grooves do. The analytical evaluation demonstrates the accuracy and applicability of the proposed approach. [Copyright &y& Elsevier]

Abstract: A point receptance array is proposed to study behaviors of panel structures with stiffeners. Although the overall objective is intended to develop a general algorithm for large structural members with stiffeners of arbitrary arrangements, the present study focus on an analytical evaluation of the accuracy of the approximation. To simplify the formulations, a thin plate with two diagonally connected beam stiffeners is selected. By solving governing differential equations for the plate and beam, point receptances that represent the interaction and compatibility conditions at the plate–beam interfaces are analytically obtained. Buckling modes of the stiffened plate are obtained by solving an eigenvalue problem. Accuracy of the approach is verified by a comparison of the analytical solution with data obtained from a direct finite element model. A parametric study was also performed. Good agreement indicates that the point receptance is a viable approach for general applications. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses the results of a finite element (FE)-based study of the compressive instabilities of axial fiber tows in 2D triaxial braided carbon fiber composites (2DTBC). A 3D FE model of an axial tow is used in conjunction with the ABAQUS commercial FE code. To accommodate unstable snap-back post-peak behavior, an arc-length solution technique is adopted to solve the FE equations. Explicit account of the braid microstructure (geometry and packing) and the measured inelastic properties of the matrix (the in-situ properties) are accounted for via the use of the FE method. This type of detailed modeling is necessary for developing a mechanism-based failure prediction capability. The computational model provides a means to assess the compressive strength of the axial fiber tow and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameters that affect compressive strength of a 2DTBC. [Copyright &y& Elsevier]

Abstract: Thermal post-buckling analysis of uniform, isotropic, slender and shear flexible columns is presented using a rigorous finite element formulation and a much simpler intuitive formulation. The ends of the columns are axially restrained to move and consequently any temperature rise above the stress free condition of the column produces an equivalent constant compressive mechanical load that causes the column to buckle at a critical temperature. Further increase in temperature beyond critical temperature results in the thermal post-buckling phenomenon. As a result of constraints imposed on the axial displacement at the ends of the column, the post-buckling phenomenon is governed by the von-Karman strain displacement relation applicable to one dimensional problems. Empirical formula for ratio of nonlinear axial load to critical load (equivalent constant mechanical load for a given temperature rise) as a function of the central deflection are obtained using both the rigorous finite element and intuitive formulations for various boundary conditions. The boundary conditions considered are the classical such as hinged–hinged, clamped–clamped and clamped–hinged conditions and nonclassical boundary conditions like the hinged–guided or the clamped–guided conditions. Post-buckling analysis results pertaining to nonclassical boundary conditions are meagre in the literature. It is observed that results obtained from both the formulations are in excellent agreement for all boundary conditions considered. Also the accuracy and simplicity of the intuitive formulation is aptly demonstrated to slender and shear flexible columns. [Copyright &y& Elsevier]

[Display omitted] • The attempt of building FEA model dedicated to damage prediction. • Comparison of PFA and experimental damage evaluation in 1:1 macro- and microscale. • Analysis of ply stacking sequence effect on damage initiation and propagation. • Ply clusters reduce delamination range at the expense of intense crack development. • PFA model predicts well the localization of damage onset but not the damage types. Fibre reinforced polymers are widely used materials in terms of their mechanical properties. The application of proper stacking-sequence of layers allows to obtain desirable properties of composite structure, and affect its failure mechanisms. The aim of this work was to evaluate the stacking sequence influence in the axially compressed glass-fibre reinforced epoxy thin-walled columns. To highlight the differences, the comparative failure analysis was performed. The macroscopic observation and the analysis of X-ray µCT images presented numerous damage types for particular stacking sequences. Also, the progressive failure analysis model, which takes the manufacturing conditions into account, was implemented. The novelty of the analysis approach lies in direct comparison of experimental and numerical results in scale 1:1 – both in macroscale and microscale. The analysis indicated the most sensitive points of the studied columns in terms of damage initiation. The most dominant failure mode was delamination. It was noted ply clustering allows one to limit the damaged area in cost of increased matrix failure. It was also noticed that symmetric and asymmetric stacking sequences possess insignificant differences in the damaged area. The changes of stacking sequences have the effect on the development of translaminar, interlaminar and intralaminar cracks likewise. The comparison of experimental failure analysis and finite element method showed that the PFA model predicts the approximate localization of the failures. [ABSTRACT FROM AUTHOR]

• Local buckling behavior of omega-stringer-stiffened panels under shear load. • Simple closed-form analytical solution for the eigenvalue problem. • Laminated composite plates with bending-twisting coupling. • Results in good agreement with finite element analyses. The local shear-buckling behaviour of omega-stringer-stiffened composite panels is analysed introducing a novel approximate analytical computational model. This type of stability analysis is critical for thin-walled structures like the proposed panel, which is applied, among other things, mainly in aerospace structures and marine vessels. In this context, computationally efficient methods are especially necessary for preliminary design phases that often involve optimization and extensive parameter studies. In the present work, a simple analytical model for the critical shear-buckling load is developed and evaluated taking bending-twisting coupling and different load directions into account. The modelling approach is based on energy methods and employs the principle of the stationary value of the total elastic potential. Hereby, the buckling shape functions are based on a combination of a polynomial term and a trigonometric Timoshenko-type term, where the latter is commonly used for closed-form analytical shear-buckling analysis. The approximate computational model is evaluated for four different laminate configurations and a wide range of different panel dimensions in comparison to finite element analyses. The parameter studies yield promising results with errors very acceptable in the context of preliminary design. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a finite element model for the static and dynamic stability of a rotating pretwisted aerofoil cross-section two-bladed packet subjected to uniform radial periodic force. The effects of various parameters such as shroud dimensions, pretwist angle, stagger angle, rotational speed and distance of shear center from the centroid on the stability of the blade packets are presented. The numerical results show that pretwist angle and the coupling effect are important in high-frequency modes depending on shear center distance from the centroid on dynamic stability regions. The increase in stagger angle makes the pretwisted two-bladed packet less stable. However, the increase in rotational speed makes the pretwisted two-bladed packet more stable. [Copyright &y& Elsevier]

Abstract: In this paper, lower and upper bounds of the buckling load of a composite beam with two non-overlapping delaminations are obtained by developing analytical models. The characteristic equation governing the delamination buckling is derived by using Euler–Bernoulli beam theory, performing proper linearization and by imposing the appropriate continuity and boundary conditions. The effects of the differential stretching and the bending–extension coupling are considered. The accuracy of the approach is verified by comparing results with previously published data and a separately carried out finite element analysis. The effects of the dimensions of the delaminations, their thicknesswise and spanwise locations on the lower and upper bounds of the buckling load are investigated in detail. The longer of the two non-overlapping delaminations dominates the buckling behavior. Composite beams with anti-symmetric non-overlapping delaminations withstand lower buckling loads than the composite beams with symmetric non-overlapping delaminations. The lower and upper bounds of the buckling load will be useful to gauge the working range of bridging and give guidelines for practical applications. [Copyright &y& Elsevier]

Abstract: Supercavitating vehicles are characterized by substantially reduced hydrodynamic drag with respect to fully wetted underwater vehicles. Drag is localized at the nose of the vehicle, where a cavitator generates a cavity that completely envelops the body (supercavity). The size of the supercavity and the magnitude of the drag at the cavitator are greatly affected by the vehicle''s velocity and by the shape and size of the cavitator. This paper investigates the benefits of an adaptive cavitator, capable of adjusting its size with the speed of forward motion of the vehicle. Objective of the cavitator size variation is to maintain the minimum cavity length and the minimum drag at any given speed. The localized drag and the propulsion required to sustain the vehicle''s motion can cause the vehicle to buckle. In addition, propulsion acts as a follower force and may be a source of flutter-type instabilities when the vehicle is accelerating. The insurgence of buckling and flutter is investigated to identify limiting operating conditions. The analysis is performed by using a finite element model developed to predict stability limits. The case of pulsating thrust is also addressed through the application of the method of infinite determinants, also known as Bolotin''s method. [Copyright &y& Elsevier]

Abstract: In this paper static and dynamic stability of rotating asymmetric cross-section two-bladed packets subjected to uniform radial periodic force are studied using the finite element method. The effects of various parameters such as shroud dimensions, stagger angle, rotational speed and distance of shear center from the centroid on the stability of the blade packets are presented. The numerical results indicate that the coupling effect is important in frequency modes depending on shear center distance from the centroid. The increase in stagger angle makes the two-bladed packet less stable. However, the increase in rotational speed makes the two-bladed packet more stable. [Copyright &y& Elsevier]

Abstract: A generalized layer-wise stochastic finite element formulation is developed for the buckling analysis of both homogeneous and laminated plates with random material properties. The pre-buckled stresses are considered in the derivation of geometric stiffness matrix and the effect of variation in these stresses on the mean and coefficient of variation of buckling strength is studied. The mean buckling strength of plates under uniform stress assumption exactly matches with those reported in the literature. However, it is shown that the actual mean buckling strength of plates can be significantly different based on the pre-buckled stress analysis which depends on boundary constraints, principal material directions, aspect and thickness ratios of plates. The statistics of buckling strength is determined using a Taylor series expansion based mean centered first order perturbation technique. The stochastic finite element solutions obtained using layer-wise plate theory is also validated with analytical solutions presented in this paper. Parametric studies are conducted for different aspect ratios, ply orientations and boundary conditions. [Copyright &y& Elsevier]

Abstract: A finite element model is presented to study the static and dynamic stability of a pre-twisted Timoshenko beam having asymmetric aerofoil cross-section subjected to an axial periodic force. The change in the effects of coupling due to centre of flexure distance from the centroid and the shear coefficient on the stability due to the pre-twist angle is considered. It is concluded from the results that the pre-twist angle has an influence on the effects of coupling and the shear coefficient. [Copyright &y& Elsevier]

Abstract: The buckling characteristics of sandwich plates having laminated stiff layers are studied for different types of partial edge loadings using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piecewise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. It is quite interesting to note that this plate model having all these refined features requires unknown parameters only at the reference plane. To have a generality in the present analysis, finite element technique is adopted and it is carried out with newly developed triangular element, as existing finite elements cannot accommodate this plate model. So far, no solution exists in the literature for the problem of sandwich plate subjected to partial edge loading. The present analysis is first validated for the case of an isotropic plate subjected to partial edge compression and then it is extended to analyze sandwich plates. Few results are presented. [Copyright &y& Elsevier]

The finite element method is applied to study the static and dynamic stability of an aerofoil cross-section rotating blade subjected to an axial periodic force. The effects of coupling due to the center of flexure (shear center) distance from the centroid, rotational speed, stagger angle and disk radius on the stability are considered. Critical load parameters are calculated and dynamic instability regions of the blade with different reference values are illustrated graphically. The numerical results indicate that the coupling effect is very important in the third and fourth modes depending on dY distance. The increase in stagger angle makes the blade less stable. However, the increase in rotational speed and disk radius make the blade more stable. [Copyright &y& Elsevier]