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Abstract This study reports the formulation of a realistic aircraft wing model based on thin-walled composite beam theory. In this model, NACA 4-digit-series airfoils were selected for the wing-section. The circumferentially asymmetric stiffness lay-up was implemented and two different sets of coupling systems corresponding to the proposed model were utilized. The eigenvalue problem was solved by the extended Galerkin method and the natural frequencies were computed as a function of the ply angle. The results of the free vibration analysis along with the governing system of the proposed model contributes to the theory of anisotropic thin-walled beams, emphasizing the importance of thin-walled structures in the design of advanced aeronautical structures. Highlights • The formulation of a realistic aircraft wing model based on the thin-walled composite beam theory is presented by employing NACA 4-digit-series airfoils as the wing-section. • The free vibration analysis of this wing model is performed for two different sets of coupling systems, which feature Extension-Horizontal Bending-Horizontal Transverse Shear (E-HB-HTS) and Vertical Bending-Twist-Vertical Transverse Shear (VB-T-VTS). • The first four natural frequencies of E-HB-HTS and VB-T-VTS coupling systems are computed as a function of ply angle. • Various non-classical effects as well as the effects of a number of geometrical aspects on the natural frequencies are examined and discussed. • The transverse shear is found to have a significant effect on the natural frequencies of the E-HB-HTS coupling system than the ones of VB-T-VTS coupling system. [ABSTRACT FROM AUTHOR]

Highlights • Effect of transverse shear on plastic response due to localised blast is studied. • Theoretical solutions for displacement field are derived using plasticity theory. • Analytical results are validated against numerical ones. • Numerical models include pure Lagrangian and Coupled Eulerian–Lagrangian methods. • Pulse-shape-independent solutions are obtained based on effective parameters. Abstract Localised blast loads due to proximal charges are encountered in a variety of circumstances. This paper proposes an analytical solution for the dynamic plastic response of a rigid-perfectly plastic thick square plate subject to a localised explosion. The proposed model is an extension of the analytical model proposed by Micallef et al [1] to study circular plates which is adopted and modified in order to study impulsively loaded square plates where the effect of shear deformation is included. A piecewise continuous blast load function was assumed with axisymmetric spatial distribution of constant pressure in the central zone and exponentially decaying beyond it. Using the constitutive framework of limit analysis and incorporating the interactions between bending moment and transverse shear forces in the analyses, transverse displacement and response duration were examined on three classes of plates, classified according to the length to thickness ratio parameter ν. The results were furnished in terms of the impulsive velocity, which is a function of the localised blast load parameters. A theoretical solution for plates with ν > 2 was sought for the non-impulsive blast loads. Parametric studies were performed to elucidate the effect of loading parameters and plate thickness on the permanent deformation. The theoretical solutions have been found generic and can predict, by the correct choice of the load parameters, the dynamic response of most blast load scenarios brought about by proximal or distal charges. It was found that, for proximal impulsive blasts, the effect of transverse shear becomes irrelevant for even moderate values of ν , which effect is inconsequential on both central and endpoint displacements at discontinuous interface in the range of ν > 5. Since the short duration pulse is of concern, localised pressure loads affect only a small area of the plated structures. Thus, whilst the theoretical treatments also examine the fully clamped plates, the boundary conditions in such loads do not influence the overall response of the structure compared to the static or global blast loads. [ABSTRACT FROM AUTHOR]

Binder-stabilised preforms are being used increasingly in the production of large composite structures, such as wind turbine blades, to increase the throughput. The transverse shear behaviour of the preform is one of the driving factors in the development of wrinkling during manufacturing but has not previously been characterised in the literature. In this paper, the combined intra- and inter-ply deformations during transverse shearing of a binder-stabilised preforms for wind turbine blade manufacturing are characterised by a new test methodology. The results from two experimental campaigns are presented. In the first campaign, preform specimens are subjected to monotonic loading to a nominal transverse shear angle of 18.0° with three different deformation rates. The results show an increase in maximum load levels with greater deformation rates. In the second campaign, preform specimens are subjected to deformation-controlled cyclic loading with two different deformation amplitudes corresponding to a nominal transverse shear angle of 1.5° and 12.2°, respectively. During cyclic loading, permanent deformation is observed in all preform specimens and the maximum load at the 19th cycle is reduced to 48% of the maximum load at the first cycle for the tests with deformation amplitudes of 12.2°. The data generated in this study is freely available at https://doi.org/10.17632/9m78sg3zwn.1. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model is presented to study the failure strength of moderate thickness composite cylindrical shells under hydrostatic pressure. Considering the transverse shear effect on the mechanics of the moderate thickness cylindrical shell, the numerical model is proposed based on the First-order Shear Deformation Theory (FSDT). The Generalized Differential Quadrature (GDQ) method is applied to solve the 3D displacement and strain field of the static governing equations. Tsai-Wu tensor failure criteria is used to acquire the structural failure strength of the cylindrical shell. The calculated displacement and strain results are compared with the ones of FE analysis and show very good agreement of the distribution. The obtained failure strength based on proposed model is validated with an experimental test and the maximum error of the failure strength is 7.78%. The results and errors indicate that the proposed numerical model is valid and accurate enough for the failure strength analysis of the moderate thickness composite cylindrical shells under hydrostatic pressure. • Failure strength of moderate thickness composite shells under hydrostatic pressure are studied through a proposed numerical model based on FSDT. • The transverse shear effect is considered to build the numerical model and the generalized differential quadrature method is applied as the solver. • The solver is effective and the numerical solutions show good agreement of distribution through the comparison with FE and experimental test. • The obtained failure strength based on proposed model is validated with an experimental test and the maximum error of the failure strength is 7.78%. [ABSTRACT FROM AUTHOR]

This work presents a general formulation and implementation in solid-shell elements of the refined zigzag theory and the trigonometric shear deformation theory in an unified way. The model thus conceived is aimed for use in the analysis, design and verification of structures made of composite materials, in which shear strains have a significant prevalence. The refined zigzag theory can deal with composite laminates economically, adding only two nodal degrees of freedom, with very good accuracy. It assumes that the in-plane displacements have a piece-wise linear shape across the thickness depending on the shear stiffness of each composite layer. The trigonometric theory assumes a cosine variation of the transverse shear strain. A modification of this theory is presented in this paper allowing its implementation with C 0 approximation functions. Two existing elements are considered, an eight-node tri-linear hexahedron and a six-node triangular prism. Both elements use a modified right Cauchy-Green deformation tensor C ¯ where five of its six components are linearly interpolated from values computed at the top and bottom surfaces of the element. The sixth component is computed at the element center and it is enhanced with an additional degree of freedom. This basic kinematic is improved with a hierarchical field of in-plane displacements expressed in convective coordinates. The objective of this approach is to have a simple and efficient finite element formulation to analyze composite laminates under large displacements and rotations but small elastic strains. The assumed natural strain technique is used to prevent transverse shear locking. An analytic through-the-thickness integration and one point integration on the shell plane is used requiring hourglass stabilization for the hexahedral element. Several examples are considered on the one hand to compare with analytical static solutions of plates, and on the other hand to observe natural frequencies, buckling loads and the non-linear large displacement behavior in double curved shells. The results obtained are in a very good agreement with the targets used. [ABSTRACT FROM AUTHOR]

• The classical shell theory is not applicable to the transverse shear kinematics of textile composite reinforcements. • A kinematic approach is presented to correct shear deformation without complicating the shell method. • Experimental comparisons show that the transverse shear of multi-layer textile fabric can be modeled accurately by the proposed approach. • The approach can be available for any user, together with any finite element software. During the draping of dry textile reinforcements, the high tensile stiffness of fibers and the possible slippage between them significantly modify the transverse shear deformation mechanism. In order to show the limits of classical shell elements (Kirchhoff and Mindlin shell) for textile reinforcements, four-point bending tests of multi-layer fibrous material were conducted and analyzed through experiment and simulation. In forming cases, the mid-surface deformation was obtained by a finite element stress resultant shell, which takes the in-plane shear and bending behavior into account. Based on the quasi-inextensibility of fibers, a kinematic modeling approach was then proposed to efficiently calculate the transverse shear strain. This approach has been implemented in Matlab software as a post-processing application, and can therefore be carried out by any user, together with any finite element software. Different bending tests and hemispherical forming experiments proved the effectiveness and correctness of the approach through comparisons between experimental and numerical results. [Display omitted] [ABSTRACT FROM AUTHOR]

Functionally graded plates whose material properties vary continuously through the thickness are modelled as exactly equivalent plates composed of up to four isotropic layers. Separate models are derived for analysis using classical plate theory, first-order and higher-order shear deformation theory. For cases where Poisson’s ratio varies through the thickness, the integrations required to obtain the membrane, coupling and out-of-plane stiffness matrices are performed accurately using a series solution. The model is verified by comparison with well converged solutions from approximate models in which the plate is divided into many isotropic layers. Critical buckling loads and undamped natural frequencies are found for a range of illustrative examples. [ABSTRACT FROM AUTHOR]

In recent years variable-stiffness (VS) technology has been shown to offer significant potential weight savings and/or performance gains for both monolithic and stiffened plate structures when buckling is a driving consideration. As yet, little work has been reported on VS sandwich structures. As such, a semi-analytical model is developed based on the Ritz energy method for the buckling of sandwich panels with fibre-steered VS face-sheets. The model captures both global and shear crimping instabilities and is shown to explain both types of buckling responses observed and the mode switching between them. Quantitative agreement with detailed three-dimensional finite element analysis was found to be within 13%. Subsequent parametric and optimisation studies, which were performed for many practical geometries using the developed model, reveal that, whilst VS sandwich panels show a significant improvement in global buckling performance, they suffer a reduction in shear crimping performance when compared to their straight-fibre counterparts. This behaviour is found to be due to the VS face-sheets creating a pre-buckling load redistribution where regions locally exceed the critical shear crimping load and induce the short wavelength instability at a reduced panel level load. For VS sandwich panels with modest to low transverse shear moduli of the core, shear crimping can become the critical mode diminishing performance benefits relative to straight-fibre configurations. Cores with sufficient rigidity, thus preventing shear crimping, showed improvements in critical buckling load in the order of 80% when using VS, however this improvement reduces to a negligible amount with decreasing core transverse shear moduli. The transverse shear flexibility and load redistribution are thus two key parameters that must be considered carefully in the design of sandwich panels, in order to exploit the benefits of VS fully in this novel structural configuration. [ABSTRACT FROM AUTHOR]

The paper deals with generalised vector finite integral transformation designed for the solution of initial boundary value problems described by systems of linear differential equations in partial derivatives. Described structural algorithm method provides for the construction of adjoint and invariant operators, that in contrast to the method of eigen function expansion can be considered non-selfadjoint boundary value problems with asymmetric matrix coefficients in the system of equations. An essential feature of the proposed method is the ability to produce all the components of the solution including two vectors of sound functions without any a priori information. The proposed procedure is demonstrated as a new method of analytical solution of the nonstationary problem for a shell of revolution with an arbitrary meridian. [ABSTRACT FROM AUTHOR]

The homogenization of the honeycomb sandwich core enables to obtain an equivalent homogeneous solid and its elastic moduli thus to make numerical modeling very efficient. In the present paper, the in-plane shear, torsion, in plane-shear coupled with torsion and transverse shear are studied with skin effect: the honeycomb core’s deformation is constrained by two fairly rigid skins, so the core’s stiffness is largely increased. An analytic homogenization method, using trigonometric function series is proposed to study the influence of the honeycomb thickness on the elastic properties, and the upper and lower bounds of their equivalent elastic moduli can be given directly by the analytical homogenization models (H-models). A very good agreement has been achieved between numerical results issued from the H-models and 3D FE modeling. [ABSTRACT FROM AUTHOR]

This study investigates the flexural–torsional coupled vibration of thin-walled composite beams. We first derived the thin-walled beam theory for an arbitrary cross-section and applied it to a biconvex cross-section. The flexural–torsional coupled motion is generated featuring a symmetric lay-up composite configuration. The natural frequencies are determined by solving the eigenvalue problem, which are obtained both for the warping restraint and the free-warping models. The variations of the natural frequencies with respect to the ply angle orientation are computed for selected values of thickness, slenderness and aspect ratios. We find that the natural frequencies have a tendency to increase with increasing slenderness and thickness ratios, while they tend to decrease with increasing aspect ratio. We also observed that omission of the transverse shear effect, particularly at the ply angles between 60° and 120°, led to an overestimation of the natural frequencies of the first and the second modes for higher slenderness ratios, while overlapping results are obtained for any thickness or aspect ratios regardless of including/omission of transverse shear deformation. Overall, we point out that the geometrical aspects have a substantial influence on dynamic characteristics in the design of thin-walled composite beams. [ABSTRACT FROM AUTHOR]

To improve the poor transverse shear resistance of corrugated sandwich cores, the present study uses a combined analytical and numerical approach to exploit the idea of filling core interstices with polymer foam. For foam-filled corrugated cores under transverse shear, four collapse modes are considered: elastic buckling, plastic buckling or yielding/fracture of corrugated strut, interfacial debonding/sealing off between corrugation platform and face sheets, and foam shear failure. Analytical models are constructed to determine the transverse shear stiffness and strength. To estimate the elastic/plastic buckling strength of a corrugated strut, the foam insertions are treated as a superposition of Winkler type elastic foundations to support the strut against buckling. Finite element simulations are carried out to validate the model predictions, with good agreement achieved. The sensitivity of transverse shear strength and failure mode to corrugation angle, strut slenderness and strain hardening of strut parent material is systematically studied; collapse mechanism map is constructed, and minimum weight design is carried out. Whether the sandwich is made of metal or fiber-reinforced composite, it is demonstrated that the foam-filled corrugated core exhibits radically enhanced transverse shear response, outperforming competing core topologies such as hollow pyramidal lattices and square honeycombs on the basis of equal mass. [ABSTRACT FROM AUTHOR]

This paper deals with the plastic buckling behavior of two-layer shear-deformable beam–columns with partial interaction. The Timoshenko kinematic hypotheses are considered for both layers and the shear connection (no uplift is permitted) is represented by a continuous relationship between the interface shear flow and the corresponding slip. A set of differential equations is obtained from a general 3D plastic bifurcation analysis, using the above assumptions. Original closed-form expressions of the buckling loads and the corresponding modes of the composite beams under axial compression are derived for various boundary conditions, considering that both layers (or possibly only one) behave plastically at the critical point. The particular case of Euler–Bernoulli beams can be deduced from these general expressions by neglecting the influence of shear deformability. The proposed analytical solutions are favorably compared against the predictions of a FE model based on a co-rotational two-layer beam formulation which accounts for interlayer slip and inelasticity. Parametric analyses are performed and the effect of the elastoplastic moduli is particularly emphasized. [ABSTRACT FROM AUTHOR]

Abstract: Variable angle tow (VAT) laminates have previously shown enhanced buckling performance compared to conventional straight fibre laminates. In this study, an analytical method is developed for the buckling analysis of a novel blade stiffened VAT panel to allow this potential to be more fully exploited. The prebuckling and buckling analysis, performed on a representative section of a blade stiffened VAT panel, are based on a generalised Rayleigh–Ritz procedure. The buckling analysis includes a first order shear deformation theory by introducing additional shape functions for transverse shear and is therefore applicable to structures with thick skins relative to characteristic length. Modelling of the stiffener is achieved with two approaches; idealisation as a beam attached to the skin’s midplane and as a rigidly attached plate. Comparing results with finite element analysis (Abaqus) for selected case studies, local buckling errors for the beam model and plate model were found to be less than 3% and 2% respectively, whilst the beam model error for global buckling was between 3% and 10%. The analytical model provides an accurate alternative to the computationally expensive finite element analysis and is therefore suitable for future work on the design and optimisation of stiffened VAT panels. [Copyright &y& Elsevier]

Abstract: This paper presents the development of a new three-dimensional brick finite element by the use of the strain based approach for the linear analysis of plate bending. The developed element has the three essential external degrees of freedom (U, V and W) at each of the eight corner nodes as well as at the centroidal node. The displacement field of the developed element is based on assumed functions for the various strains satisfying the compatibility equations and the static condensation technique is used for the internal node. The performance of this element is evaluated on several problems related to thick and thin plate bending in linear analysis. The obtained results show the good performances and accuracy of the present element. [Copyright &y& Elsevier]

Abstract: The manufacture of advanced composite panels with variable fibre angles can lead to laminates with a flat profile on one side and a smooth, curved profile on the other. When modelling these laminates in two-dimensional form the flat plate assumptions may no longer accurately capture the structural behaviour. In this paper the buckling behaviour of laminates with one-dimensional fibre variations and symmetric stacking sequences is investigated. The assumptions of modelling the three-dimensional profile as a flat plate or a cylindrical panel are assessed, taking into account the effects of transverse shear deformation. The governing differential equations are solved in the strong form using the Differential Quadrature method and validated by 2D finite element models. The validity of the two modelling approaches is assessed by comparing the solutions to a 3D finite element model capturing the actual shape of the laminate. It is suggested that the buckling event of these variable angle tow, variable thickness laminates is characterised more accurately by “shell-like” than by “plate-like” behaviour. The idea of investigating the effects of two-dimensional fibre orientations with their associated doubly curved topologies is proposed. [Copyright &y& Elsevier]

Abstract: The present paper provides algorithms to be used in calculating longitudinal dispersion coefficients using ADCP data driven by either vertical or transverse velocity gradients in large river, and describes software components capitalizing on these ADCP measurement capabilities to provide the longitudinal dispersion coefficients based on in-situ measurements. The paper couples in an innovative way the wealth of data provided by ADCPs with robust and theoretical algorithms to compute longitudinal dispersion coefficient relying only on actual velocity data, rather assuming horizontal or vertical velocity models due to traditional lack of field data. The paper clearly provides the promise of ADCP data and the associated analytical algorithms for estimating longitudinal dispersion coefficients. We also compared longitudinal dispersion coefficients obtained with the theoretical formula using ADCP with those from the other available alternative empirical formulas, and found that empirical formula overestimated the longitudinal dispersion coefficient in large river. Therefore, further use of the software and the embedded procedures can uniquely support in-situ measurement campaigns designed to document important aspects of the dispersion processes and formulation of reliable knowledge that circumvent the empirical approaches of the past. [Copyright &y& Elsevier]

Abstract: This paper deals with the buckling behavior of two-layer shear-deformable beams with partial interaction. The Timoshenko kinematic hypotheses are considered for both layers and the shear connection (no uplift is permitted) is represented by a continuous relationship between the interface shear flow and the corresponding slip. A set of differential equations is obtained from a general 3D bifurcation analysis, using the above assumptions. Original closed-form analytical solutions of the buckling load and mode of the composite beam under axial compression are derived for various boundary conditions. The new expressions of the critical loads are shown to be consistent with the ones corresponding to the Euler–Bernoulli beam theory, when transverse shear stiffnesses go to infinity. The proposed analytical formulae are validated using 2D finite element computations. Parametric analyses are performed, especially including the limiting cases of perfect bond and no bond. The effect of shear flexibility is particularly emphasized. [Copyright &y& Elsevier]

Abstract: The dynamic instability problem of symmetrically laminated cross-ply plates, compressed by time-dependent stochastic membrane forces, is investigated. The effect of shear deformation is included in the formulation. By using the direct Liapunov method, bounds of the almost sure instability of cross-ply plates are obtained. Furthermore, it is shown how the viscous damping coefficient, variances of the stochastic forces, ratio of the principal lamina stiffnesses, number of layers, plate aspect ratio, and cross-ply ratio influence the instability regions. A special attention is given to the proper choice of two shear correction factors of the laminated plate. Numerical calculations are performed for the Gaussian process with a zero mean and variance as well as for the harmonic process with an amplitude A. [Copyright &y& Elsevier]

Abstract: A combined analytical and experimental approach is presented to characterize both mode-II and mixed mode fracture of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending load, and closed-form solutions of compliance and energy release rate of the mode-II (four-point symmetric end-notched flexure) and mixed (four-point asymmetric end-notched flexure) mode fracture specimens are provided. The transverse shear deformation in each sub-layer of bi-material bonded beams is included by modeling each sub-layer as an individual first order shear deformable beam, and the effect of interface crack tip deformation on the compliance and energy release rate are taken into account by applying the interface deformable bi-layer beam theory (i.e., the flexible joint model). The improved accuracy of the present analytical solutions for both the compliance and energy release rate is illustrated by comparing with the solutions predicted by the conventional rigid joint model and finite element analysis. The fracture of Carbon fiber-reinforced polymer-concrete bonded interface is experimentally evaluated using both the four-point symmetric and asymmetric end-notched flexure specimens, and the corresponding values of critical energy release rates are obtained. Comparisons of the compliance rate-changes and resulting critical energy release rates based on the rigid joint model, the present theoretical model, and numerical finite element analysis demonstrate that the crack tip deformation plays an important role in accurately characterizing the mixed mode fracture toughness of hybrid material bonded interfaces under four-point bending load. The improved solution of energy release rates for the four-point symmetric and asymmetric end-notched flexure specimens by the flexible joint model can be used to effectively characterize hybrid material interface, and the fracture toughness values obtained for the Carbon fiber-reinforced polymer-concrete interface under mode-II and mixed mode loading can be employed to predict the interface fracture load of concrete structures strengthened with composites. [Copyright &y& Elsevier]

Abstract: Fiber-reinforced polymer (FRP) sandwich deck panels with sinusoidal core geometry have shown to be successful both in new construction and the rehabilitation of existing bridge decks. This paper is focused on an experimental study of the strength evaluations of a honeycomb sandwich core under out-of-plane compression and transverse shear. The sinusoidal core is made of E-glass Chopped Strand Mat (ChSM) and Polyester resin. The compressive, tensile and shear strengths were first obtained from coupon tests. The out-of-plane compression tests were performed on representative single-cell volume elements of sandwich panels, and the tests included “stabilized” samples to induce compression failure, and “bare” samples to induce local buckling of the core. Finally, four-point bending tests were conducted to study the structural strength behavior under transverse shear. Two types of beam samples were manufactured by orienting the sinusoidal wave either along the length (longitudinal) or along the width (transverse). Both typical shear failure mode of the core material and delamination at the core–facesheet bonding interface were observed for longitudinal samples. The failure for transverse samples was caused by core panel separation. For both single-cell and beam-type specimen tests, the number of bonding layers, i.e., the amount of ChSM contact layer and resin used to embed the core into the facesheet, and the core thickness are varied to study their influence. The experimental results described herein can be subsequently used to develop design guidelines. [Copyright &y& Elsevier]

Abstract: The paper describes the transverse shear properties of a novel centresymmetric honeycomb structure evaluated using analytical and finite element models. The cellular structure features a representative volume element (RVE) geometry allowing in-plane auxetic (negative Poisson’s ratio) deformations, and multiple topologies to design the honeycomb for multifunctional applications. The out-of-plane properties are calculated using a theoretical approach based on Voigt and Reuss bounds. The analytical models are validated using a full scale Finite Element technique to simulate transverse shear tests, a quarter FE of the RVE with periodic shear conditions and an FE homogenisation method for periodic structures. The comparison between the analytical and numerical models shows good convergence between the different set of results, and highlights the specific deformation mechanism of the multi re-entrant honeycomb cell. [Copyright &y& Elsevier]

Abstract: A phenomenological definition of classical invariants of strain and stress tensors is considered. Based on this definition, the strain and stress invariants of a shell obeying the assumptions of the Reissner–Mindlin plate theory are determined using only three normal components of the corresponding tensors associated with three independent directions at the shell middle surface. The relations obtained for the invariants are employed to formulate a 15-dof curved triangular finite element for geometrically nonlinear analysis of thin and moderately thick elastic transversely isotropic shells undergoing arbitrarily large displacements and rotations. The question of improving nonlinear capabilities of the finite element without increasing the number of degrees of freedom is solved by assuming that the element sides are extensible planar nearly circular arcs. The shear locking is eliminated by approximating the curvature changes and transverse shear strains based on the solution of the Timoshenko beam equations. The performance of the finite element is studied using geometrically linear and nonlinear benchmark problems of plates and shells. [Copyright &y& Elsevier]

Primary structures of aerospace applications are often constructed as stringer frame stiffened shell structures because of their high load carrying capacity. Recent research activities on the design of such shells have shown that the design is a demanding task due to the mostly interdependent design variables. Furthermore, the calculation of panel instability is only possible with numerical simulation software demanding high computational costs. Recently, an efficient approach was developed with promising results. This work is taken up to be analysed in more detail. Study structures with differentiating stiffnesses are defined. Findings show high deviations in the prediction of panel instability for increasing axial stiffness of the shell. The reason is found to be the insufficient consideration of prebuckling deformations resulting from the reduced structural model. Improvements to the method are suggested: The reduced structural model is changed and the formerly Ritz formulation is converted into a finite element formulation. One panel of the shell is discretized by the derived one dimensional element. The influence of skin buckling on the structural behaviour is taken into account. An adapted smeared stiffener theory is used in an iterative calculation routine. Geometrically non-linear verification computations are conducted using commercial finite element simulation software. The suggested adjustments lead to a capturing of the size effect and a significant improvement of the method. Excellent results for the prediction of panel instability with reasonable error margins are delivered. • Smeared stiffener theory expanded by the effective width of the skin fields. • Reduction to one panel insufficient for the depiction of the structural behaviour. • Discretization of one panel shell to a one dimensional element. • Suggested method shows superior prediction capability of the panel instability load. [ABSTRACT FROM AUTHOR]

Abstract: The static behaviour of Bi-Steel beams was simulated using a finite element model. The model was compared to test results showing good agreement. It was then used in parametric studies of transverse shear capacity and uniformly distributed load cases of Bi-Steel beams. It was possible to isolate the transverse shear failure mode and prevent other failure modes from using the FE model. This enabled the comparison and verification of the proposed design equations for transverse shear. Based on parametric studies, modifications to the design method were also proposed to accommodate udl cases. [Copyright &y& Elsevier]

Abstract: This paper presents a set of closed form solutions for the elastodynamic structural response of thin cylindrical tubes to internal moving pressures with specific profiles. The solution set includes newly derived expressions for transverse shear and axial strains plus modified expressions for the reflected structural waves. These expressions are used to study the amplification of flexural and shear stress waves caused by internal gaseous detonation and shock loading. It is shown how the three different critical speeds at which the resonance of the structural waves occur can be computed. The development of stress waves in a thin aluminum tube is studied over a wide range of speeds and the magnitudes of dynamic amplification factors are determined. In particular, the occurrence of transverse shear resonance at the second critical speed is studied. The peak value of the shear stress at this speed is found to be significantly higher than the finite element results reported by other researchers. Finally, an adjusted form of the general solution is used to investigate the response of a thin tube to internal shock loading. The predicted vibrational spectrums were in very good agreement with the experimental results reported in the literature. [Copyright &y& Elsevier]

Abstract: The exact analytical solution of buckling in beams with multiple delaminations is presented. In order to investigate analytically the influence of axial and shear strains on buckling loads, the geometrically exact beam theory is employed with no simplification of the governing equations. The critical forces are then obtained by the linearized stability theory. The parametric studies are designed so that they give us fundamental understanding of the effects of the delamination number, length and position on the buckling load. The effect of shear is found to be of substantial importance. [Copyright &y& Elsevier]

Abstract: This work deals with the development of a new four nodes rectangular finite element for the linear analysis of plate bending with transverse shear effect. The displacements field of the element has been developed by the use of the strain-based approach and it is based on the assumed independent functions for the various components of strain insofar as it is allowed by the compatibility equations. The element possesses three essential external degrees of freedom at each of the four corner nodes and satisfies the exact representation of the rigid body modes of displacements. This element is found to be numerically more efficient than the corresponding displacement-based element and its precision is evaluated through a series of tests cases related to thick and thin plates. [Copyright &y& Elsevier]

This work concerns with experimental studies on buckling of thin-walled circular cylindrical shells under transverse shear. The buckling loads are also obtained from finite element models, empirical formulae and codes and are compared. Experiments are conducted on 12 models made of stainless steel by rolling and longitudinal seam welding. In situ initial geometric imperfection surveys are carried out. The tests are conducted with and without axial constraint at the point diametrically opposite the loading. Theoretical analyses are carried out using ABAQUS finite element code. Two finite element models considered are: (i) geometry with real imperfection (FES-I) and (ii) critical mode imperfect geometry (FES-II). In the former, the imperfections are imposed at all nodes and in the latter, the imperfection is imposed by renormalizing the eigen mode, using the maximum measured imperfection. General nonlinear option is employed in both the cases for estimating the buckling load. Galletly and Blachut’s expressions, design guidelines of Japan for LMFBR main vessel expressions (empirical formulae), ASME and aerospace structural design codes are used for comparing with experimental loads.The comparisons of experimental, numerical and analytical buckling loads reveal the following. The numerical results are always higher than the experimental values; the percentage difference depends on the wall thickness. FES-II predicts somewhat a lower load than that of the FES-I. The Japanese guidelines predict the lowest load, which is conservative. Experimental loads are lower than that predicted by both ASME and aerospace structural design codes. [Copyright &y& Elsevier]

Corrugated board usually exhibits low transverse shear stiffness, especially across the corrugations. In the present study the transverse shear is included in an analysis to predict the critical buckling load of an edge-loaded orthotropic linear elastic sandwich plate with all edges simply supported. In the analysis, effective (homogenised) properties of the corrugated core are used. Classical elastic buckling theory of orthotropic sandwich plates predicts that such plates have a finite buckling coefficient when the aspect ratio, i.e. the ratio between the height and width of the plate, becomes small. However, inclusion in the governing equilibrium equations of the additional moments, produced by the membrane stresses in the plate at large transverse shear deformations, gives a buckling coefficient which approaches infinity when the aspect ratio goes to zero. This improvement was first included in the buckling theory of helical springs by Harinx [Proc. Konjlike Nederland Akademie Wettenschappen, vol. 45, 1942, Amsterdam, Holland, pp. 533–539, 650–654] and later applied to orthotropic plates by Bert and Chang [J. Eng. Mech. Division, Proc. Am. Soc. Civil Engrs. 98 (EM6) (1972) 1499–1509]. Some inconsistencies in the latter analysis have been considered. The critical buckling load calculated with corrected analysis is compared with a predicted load obtained using finite element analysis of a corrugated board panel, and also with the critical buckling load obtained from panel compression tests. [Copyright &y& Elsevier]

In this study an attempt has been made to incorporate the effect of transverse shear on the stability of moderately thick/very thick composite laminated plates under in-plane compressive and shear loading using a Simple Higher Order Shear Deformation Theory based on four unknown displacement functions (u0,v0,wb,ws) instead of five which is commonly used in most of the higher order theories. The finite element method is employed to study the initial buckling load of laminated plates. The change in initial buckling response of thick rectangular antisymmetric laminates with respect to the fibre orientation angle has been studied. The interaction curves (between Nx and Nxy for different parameters of the laminates) are studied in detail. [Copyright &y& Elsevier]

In this paper, we analyze dynamic behavior of a piezothermoelastic laminate considering the effect of damping due to interlaminar shear and the effect of transverse shear. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all egdes simply supported and to be subjected to mechanical, thermal and electrical loads varying arbitrarily with time. Behavior of the laminate is analyzed based on the first-order shear deformation theory. The effect of damping due to interlaminar shear is incorporated into our analysis by introducing the interlaminar shear stresses which satisfy the Newton’s law of viscosity. Solutions of the following quantities are obtained: (1) natural frequencies of the laminate, (2) weight functions for the deflection and rotations and (3) unsteady deflection due to loads varying arbitrarily with time. Moreover, numerical examples of the solutions are shown to examine the effects of damping and transverse shear on dynamic behavior of the laminate and how the voltage applied to the laminate decreases the deflection due to mechanical or thermal loads. [Copyright &y& Elsevier]

The paper presents the linear transient response analysis of laminated stiffened plates. The work is based on a new laminated stiffened plate element recently developed which can accommodate any number of arbitrarily oriented stiffeners within the plate element and obviates the need to use the mesh lines along the stiffeners. Thus the mesh generation is not constrained by the disposition of the stiffener and is based more on the choice of stress resolution sought. The formulation is based on the first order shear deformation theory. The dynamic response analysis of a few laminated plates stiffened with blade/I-section/hat stiffeners under step load are carried out. Though some investigations have been reported on transient response of unstiffened laminated plates, the literature on laminated stiffened plates has not been reported. [Copyright &y& Elsevier]

A generalized, finite-element-based, cross-sectional analysis for nonhomogenous, initially curved and twisted, anistropic beams is formulated from geometrically nonlinear, three-dimensional (3-D) elasticity. The 3-D strain field is formulated based on the concept of decomposition of the rotation tensor and is given in terms of one-dimensional (1-D) generalized strains and a 3-D warping displacement that is obtained from the formulation, not assumed. The warping is found in terms of the 1-D strains via the variational asymptotic method (VAM). In this paper a Timoshenko-like model is presupposed for a beam with cross-sectional characteristic length h , wavelength of deformation given by l , and the magnitude of the radius of initial curvature and/or twist is taken to be of the order R . First, a solution for the asymptotically correct refinement of classical anisotropic beam theory for initially curved and twisted beams through O( h 2 / R 2 ) is obtained. Next, the O( h 2 / l 2 ) correction is computed. It is known that Timoshenko-like theory is not capable of capturing all the O( h 2 / l 2 ) corrections for generally anisotropic beams. However, if all the O( h 2 / l 2 ) terms are known, then the corresponding Timoshenko-like theory is uniquely defined. Numerical results are presented to illustrate the trends of the various classical (extension-twist, bending-twist, and extension-bending) and nonclassical couplings (extension-shear, bending-shear, and shear-torsion) as the initial twist and curvatures are varied. [ABSTRACT FROM AUTHOR]

Finite element analysis is performed to study the effects of layerwise in-plane displacements on fundamental frequencies and specific damping capacity for composite laminated plates. The cross-ply and angle-ply composite laminated plates with simply-supported boundary conditions are considered. The strain energies of each stress component are computed to quantify the amount of the transverse shear deformations for thin and thick plates. The results show that the length-to-thickness ratios, cross-ply ratios, and fiber orientations have a great influence on the in-plane displacement responses. It is also shown that the layerwise in-plane displacements should be taken into account for the dynamic analysis of thick composite plate. [Copyright &y& Elsevier]

Peridynamics is a nonlocal theory which can easily handle discontinuities such as cracks, while it is computationally more expensive compared with finite element method (FEM). Beams and shells, as the main units of structural idealization, can tremendously improve the computational efficiency for complex structures. This study presents new peridynamic (PD) beam and shell models with the effect of transverse shear deformation based on the micro-beam bond and the Timoshenko beam theory. Interpolation method is used for describing axial, torsional, bending and transverse shear deformations as well as the corresponding strain energy densities of the micro-beam bond. The micro moduli for PD beam and shell models can be solved spontaneously. The deflections of the PD models for thin/thick beams and shells are captured accurately due to the high-order relationships between the transverse forces/bending moments and the deflections/rotational angles of the micro-beam bond. Also, no restrictions are needed on the material parameters in the PD models. The simulation results prove the high precision of the presented PD beam and shell models. • The PD beam and shell models with transverse shear effect are presented. • The micro-beam bond is completely similar to the Timoshenko beam element in FEM. • The transverse deformations of thick beam/shell have the same accuracy as the thin models. • No restrictions on the material parameters are needed. [ABSTRACT FROM AUTHOR]

This paper presents the derivation of nondimensional buckling equations of sandwich cylindrical shells made of composite facesheets with a shear deformable core. The procedure yields an analytical solution in terms of a series of nondimensional parameters for the axial buckling load investigating the influence of the core transverse shear. The developed equations and the nondimensional parameters are used to study the buckling response of different shells, and the calculated buckling loads are compared to the buckling values obtained by neglecting the transverse shear. Graphs and tables are presented to show the effects of the nondimensional parameters on the nondimensional buckling load. The results are verified by finite element analyses using the commercial code Abaqus. • Analytical formulation studies transverse shear influence on buckling loads. • Shells of different scale are compared using the nondimensional buckling load. • Nondimensional equations present a similar format as the dimensional equations. • Analysis and results can be used to design sandwich composite cylindrical shells. [ABSTRACT FROM AUTHOR]

• In this study, a new theoretical approach for predicting the equivalent shear modulus G C * of the lattice core has also been proposed. The analytical prediction of the natural vibration frequency, accounting for the transverse shear effects, agrees well with the FE results. • Also, plots of the variation of the first-order natural frequency f 1 with strut diameters exhibit a convex shape, suggesting that there is a maximum value of the frequency f 1 for a given facesheet thickness t f . • A designer can predict the maximum of 1st natural frequency of lattice sandwich beam. In this study, the vibration characteristics of a sandwich lattice beam have been studied using an analytical approach and finite element(FE) analyses. In the analytical approach, a sixth-order partial differential equation for expressing the motion in terms of the transverse displacement has been solved, which is assumed that the sandwich core is deformed mainly by the shear load. Here, a new theoretical approach for predicting the equivalent shear modulus G C ∗ of the lattice core is proposed. The analytical prediction of the natural frequency, accounting for transverse shear, agrees well with the FE results. Also, the vibration response of the first-order natural frequency f 1 exhibits a upwardly convex curve as the strut diameter increases, suggesting that there is a maximum value of the frequency f 1 for a given facesheet thickness t f . Moreover, it is observed that the maximum frequency of the sandwich lattice beam is always greater than that for a continuum beam, which ensures the effectiveness of the lattice core in enhancing the vibration response. Therefore, vibration suppression in aircraft structures can be achieved by introducing lattice sandwich panels. [ABSTRACT FROM AUTHOR]

This study presents a new state-based PeriDynamic (PD) model of a composite laminate with arbitrary laminate layup; it captures all types of material couplings in the presence of transverse shear deformation. It consists of normal and shear bonds instead of fiber and matrix bonds to allow arbitrary fiber orientations. Also, rotational degrees of freedom are included in the equilibrium equations in order to evaluate the transverse shear angle and curvature. Mindlin-Reissner plate theory, employed in this model, permits the use of existing composite constitutive law which leads to the coupling between different deformation modes. In addition, a quasi-local boundary condition applied only to the first row of material points avoids the approximation of nonlocal boundary values. The accuracy of this model is verified against benchmark solutions, and validated by comparison with experimental results. [ABSTRACT FROM AUTHOR]

Stringer frame stiffened shell structures are frequently used as primary structures of aerospace applications. They show a high load carrying capacity combined with a low mass. The design is complex because of three reasons: Firstly, there exists a high number of design variables making the design of such a shell very demanding using numerical methods such as the finite element method. Secondly, such a shell can exhibit different local instabilities before failing globally. And thirdly, the calculation of the panel instability load is not fully possible yet, especially when using closed and therefore torsional stiff stringer stiffener. Within this paper, a novel approach for the calculation of the panel instability load of stringer frame stiffened shell structures with torsional stiff stringer under axial compression is introduced. The novelty is expressed in the consideration of transverse shear and prebuckling deformations. It is shown that in contrast to unstiffened shell structures both aspects cannot be neglected and have a significant influence on the buckling load. The classical smearing method is expanded and used in a consecutive utilization of the Ritz method to calculate the panel instability load. Geometrically non-linear finite element analyses are performed to validate the novel approach and establish a domain of applicability. The suggested approach delivers excellent results for the prediction of the panel instability load. [ABSTRACT FROM AUTHOR]

• A new exact analytical buckling model of sandwich panel. • The shear deformation of facings is non-negligible especially for wrinkling. • The boundary of material parameters that need to consider the shear effect. In this paper, a new exact analytical solution of buckling of sandwich panels/beams is presented. The transverse shear deformation of the face-sheet (caused by the interlayer shear effect), which has been usually neglected in previous works, is considered for the first time in our theoretical framework. In the constituent phases of the sandwich plates, the core is assumed to be isotropic, and the faces are assumed to be orthotropic, so the model can be applied to sandwich plates with composite faces. Next, the solution is compared with different results in the literatures, and the finite element computations is then carried out as a standard for measuring the accuracy. It is shown that the present solution leads to better accuracy after considering the transverse shear effect. Despite the global buckling mode is also involved in this unified solution, the emphasis of this study is on the wrinkling (short-wave) mode; the authors have shown that the transverse shear effect is particularly apparent in those short-wave modes. In the end, we determine a boundary where the shear effect will produce a non-negligible influence to the critical buckling of sandwich plates. [ABSTRACT FROM AUTHOR]

Problems related to mathematical modeling and active control of adaptive composite thin-walled beams incorporating lateral bending-extension elastic coupling and piezoelectrically induced transverse shear-extension actuation coupling are considered. The adaptive capabilities are provided by anisotropic piezo-actuators embedded into the host structure. Based on classical negative velocity feedback control and linear-quadratic regulator optimal control, the control authority played by the directionality property of piezo-actuators on vibration suppression is discussed, considering in conjunction with that of the structural tailoring. The results show that the control strategy based on the piezoelectrically induced transverse shear-extension coupling can be more efficient than that based on the piezoelectrically induced bending. In addition, the control effectiveness based on the piezoelectrically induced transverse shear is sensitive to the bending-extension elastic coupling. • Active control via piezoelectrically induced transverse shear is feasible. • Active control via transverse shear may make the system divergence. • Control effectiveness of transverse shear is sensitive to elastic coupling. • Piezo-actuator location has a significant effect on control authority. [ABSTRACT FROM AUTHOR]