Global Local Higher-order Theory Research Articles

Transverse stretching vibration analysis of cross-ply composite and sandwich beams by means of an equivalent single-layer theory

Due to largely different stiffness between the face sheets and the core, the vibration modes corresponding to the transverse stretching displacement will occur in the sandwich plates. The third-order models will encounter difficulty to reasonably produce these frequencies corresponding to transverse stretching displacement modes, which will influence engineering design. Therefore, a global-local higher-order theory including transverse stretching effect has been proposed to study transverse stretching vibration, which can meet in advance the continuity conditions and the free surface conditions of transverse shear stresses. In the light of Hamilton’s principle, the equation of motion is presented, and analytical solutions of the simply-supported beams can be acquired by using Navier’s technique. In order to verify the capability of the proposed model, free vibration of composite beams is firstly investigated and the results have been compared to two-dimensional elasticity solutions. After the proposed model is assessed by two-dimensional elasticity solutions, the proposed model is extended to study dynamic behaviors corresponding to the transverse stretching displacement vibration modes, which will be verified by utilizing the three-dimensional finite element (3 D-FEM). Furthermore, variation of natural frequencies of the sandwich beams is also investigated by altering the thickness of the face sheets, which can further illustrate the capability of the proposed model.

An alternative three-node triangular composite shell element in terms of Reddy-type higher-order theory

Composite curved shells are widely utilized as structural components in aerospace engineering. To inspire the potentiality of such structure, it is very necessary to well understand mechanical behaviors of composite curved shells. Compared to the composite plates, it is more difficult to predict accurately interlaminar stresses of composite curved shells. Therefore, this paper attempts to propose an alternative triangular composite shell element in terms of the Reddy-type global–local higher-order theory. In the present model, the continuity conditions of transverse shear stresses are enforced in advance to fulfill compatibility of transverse shear stresses at adjacent layers, which can improve precision of interlaminar stresses. In order to evaluate performance of the proposed shell element, several typical examples have been analyzed. Moreover, the results acquired from the present model are compared with the three-dimensional elasticity solutions and other published results. At the same time, a compression experiment of the thin-walled cylindrical grid structure is carried out to further verify the capability of the present model. These examples show that the proposed composite shell element can be used as an alternative method for static analysis of multi-layer thin and thick shell structures.

Parametric study of Sandwich Plates with Viscoelastic, Auxetic Viscoelastic and Orthotropic Viscoelastic Core Using a New Higher Order Global-Local Theory

In this paper, sandwich plates with flexible core and composite surfaces as well as viscoelastic and auxetic core is investigated under dynamic loading. A new higher order global-local theory is used for simulation of the dynamic behavior of sandwich plate. Ability of simulation the thickness changes of the plate and calculation of exact transverse stresses which are so crucial for studying of thick sandwich plate especially by soft core are some of the important features of the presented theory. Furthermore, in terms of solving equations, an iterative incremental method based on the formulation of transient nonlinear finite element as well as a real time algorithm was employed to simulate viscoelastic behavior accurately. The results indicate a significant increase in the stiffness of the sandwich plate due to the auxetic properties of the core materials, leading consequently to the reduction of the vibration amplitude and stresses level. Some of the innovations belonging to this paper are: 1) presenting a global-local higher-order theory while considering the changes in the thickness of the sandwich plates; 2) calculating transverse stresses using the three-dimensional elasticity method as well as modifying the results obtained from displacement and inertial effects based on this method; 3) simulating sandwich plate with viscoelastic and auxetic cores; 4) taking orthotropic properties for the viscoelastic core into account.

Thermo-mechanical analysis of multilayered composite beams based on a new mixed global-local model

An accurate mixed-form global-local higher-order theory including transverse normal thermal deformation is developed for thermo-mechanical analysis of multilayered composite beams. Although transverse normal deformation is considered, the number of displacement parameters is not increased. The proposed mixed-form global-local higher-order theory is derived using the displacement assumptions of global-local higher-order theory in conjunction with the Reissner mixed variational theorem. Moreover, the mixed-form global-local higher-order theory retains a fixed number of displacement variables regardless of the number of layers. In order to obtain the improved transverse shear stresses, the three-dimensional equilibrium equation is used. It is significant that the second-order derivatives of in-plane displacement variables have been eliminated from the transverse shear stress field, such that the finite element implementation is greatly simplified. The benefit of the proposed mixed-form global-local higher-order theory is that no post-processing integration procedure is needed to accurately calculate the transverse shear stresses. The equilibrium equations and analytical solution of the proposed model can be obtained based on the Reissner mixed variational equation. The performance of the proposed model is assessed through different numerical examples, and the results show that the proposed model can better predict the thermo-mechanical responses of multilayered composite beams.

Efficient three-node triangular element based on a new mixed global-local higher-order theory for multilayered composite plates

An accurate and computationally attractive global-local higher-order theory (GLHT) is developed for the linearly elastic analysis of cross-ply multilayered composite plates. The theory is derived using the kinematic assumptions of GLHT in conjunction with the Reissner mixed variational principle. For a low-order linear element, it is difficult to accurately compute the transverse shear stresses even applying the three-dimensional equilibrium equation post-processing technique. The reason for this difficulty is that the higher-order derivatives of displacement variables are included in the transverse shear stress fields after using the post-processing technique. Thus, by employing the Reissner mixed variational principle, the higher-order derivatives of displacement variables have been removed from the transverse shear stress components before the finite element procedure is implemented. Based on the mixed GLHT, a computationally efficient C0-type three-node triangular plate element with linear interpolation function is proposed for the analysis of multilayered composite plates. The advantage of the present formulation is that no post-processing approach is needed to calculate the transverse shear stresses while maintaining the computational accuracy of a linear plate element. Performance of the proposed element is assessed by comparing with several benchmark solutions. Numerical results show that the present elements can robustly and accurately predict the displacements and stresses of multilayered composite plates.

Higher-order global-local theory with novel 3D-equilibrium-based corrections for static, frequency, and dynamic analysis of sandwich plates with flexible auxetic cores

ABSTRACTIn the present article, a high-order global-local theory with three-dimensional elasticity corrections is employed to trace the local and instantaneous variations of lateral deflections and stress components of sandwich plates with auxetic (negative Poisson ratio) cores under static and dynamic loads. Effects of the auxetecity of the core material on the natural frequencies are evaluated as well. The governing equations are extracted based on Hamilton's principle. The main novelties of the present research in comparison to the available literature and previous researches of the second author of the present paper are: (i) Presenting a higher-order global-local plate theory with a novel equilibrium-based three-dimensional elasticity corrections, (ii) Incorporation of the transverse flexibility of the core; a fact that is crucial when studying behaviors of thick or soft core sandwich plates, (iii) Frequency and dynamic behavior analyses (in addition to the traditional static analysis) of sandwich plates with soft cores by means of the presented accurate global-local theory, and (iv) Investigation of the negative Poisson ratio (auxeticity) effects of the core material on the static (stress) and dynamic responses and natural frequencies. All these items are accomplished here, for the first time. Since the transverse shear stresses are extracted based on the three-dimensional elasticity theory, in contract the traditional constitutive-based theories, the inter-laminar continuity condition of the transverse shear stresses is met. The verification results show that the presented finite element formulation leads to highly accurate results, even for thick or soft core sandwich plates. A comprehensive parametric study is accomplished to evaluate effects of the auxeticity of the core material and transverse compliance of the core on the resulting displacement and stress distributions, natural frequencies, and dynamic responses. Results reveal that auxeticity of the core material decreases the global and relative stresses and lateral deflections of the face sheets and the core compliance may lead to asynchronized movements of the face sheets and strengthen the local bending and extensions.

Efficient coupled refined finite element for dynamic analysis of sandwich beams containing embedded shear-mode piezoelectric layers

ABSTRACTAn efficient and computationally low cost finite element (FE) model is developed for dynamic free and forced response of sandwich beams with embedded shear piezoelectric layers based on a coupled refined high-order global-local theory. Contrary to most of the available models, all of the kinematic and stress boundary conditions are ensured at the interfaces of the shear piezoelectric layers. Moreover, both the electrical-induced strains components and transverse flexibility are taken into account for the first time in the present theory. For validation of the proposed model, various free and forced vibration tests for thin and thick sandwich beams are carried out. For various electrical and mechanical boundary conditions, excellent agreement has been found between the results obtained from the proposed formulation with previously published and the coupled two-dimensional (2D) FE results.

Efficient C0 Finite Element Formulation for Thermal Stress Analysis of Laminated Composite and Sandwich Plates

AbstractBy introducing thermal expansion coefficients in the transverse displacement field, this paper proposes an approach to improve the performance of the global-local higher-order theory for thermal stress analysis of laminated composite plates. Transverse normal deformation has been considered in the proposed model, whereas the additional displacement variables have not increased because thermal loads could be included in the generalized force vector. The proposed model a priori satisfies the continuity conditions of transverse shear stresses at interfaces, and the number of displacement variables involved in the present model is independent of the number of layers. The derivatives of transverse displacement have been eliminated from the displacement field so that the C0 interpolation functions are only required for the finite-element implementation. Based on the proposed model, a six-node triangular element is proposed for thermal expansion problems of laminated composite and sandwich plates. Numeri...

The Interlaminar Stresses Analysis of Composite Laminated Plates Based on the Generalized Higher-Order Global-Local Plate Theory

A generalized higher-order global-local theory was presented. The transverse shear stresses can be got directly through the constitutive equation without using the equilibrium equation. The second derivative of interpolation function was deduced. The hammer integration of triangular area coordinate method was applied to solve the multiple integration problem of the element stiffness matrix. The order choice of numerical integration was discussed and results obtained through two different integration orders were compared. The flow of how to compile a FORTRAN program was given. A moderately thick composite laminated plate was analyzed via finite element method (FEM) based on the theory and results were compared with that of Paganos three-dimensional elasticity. It shows that the interlaminar stresses are accurate for moderately thick laminated plates.

A finite element model based on coupled refined high-order global-local theory for static analysis of electromechanical embedded shear-mode piezoelectric sandwich composite beams with various widths

In this study, a new theory for the accurate simulation of the shear-mode behaviour of thin or thick piezoelectric sandwich composite beams is developed. The effects of transverse normal stress and transverse flexibility of layers are considered in the development of the proposed formulation. In order to increase the computational accuracy, all kinematic and stress continuity conditions are satisfied at layer interfaces. Moreover, for the first time, both the electrically induced strain components and the transverse flexibility are taken into account in the proposed formulation. Despite the fact that the number of unknown mechanical parameters in this theory is only one degree higher than the first order shear deformation theory, the accuracy is surprisingly more pronounced for the thicker beams.

A model of composite laminated beam based on the global–local theory and new modified couple-stress theory

In this paper, a model of composite laminated beam based on the global–local theory for new modified couple-stress theory is developed. For the modified couple-stress theory, an anisotropic constitutive relation is suggested. There is only one microlength-scale parameter in each ply of the composite laminated beam. The Reddy beam model of global–local higher-order theory proposed by Chen and Wu (2005) [1], which satisfies free surface conditions and the geometric and stresses continuity conditions at interfaces, and is adopted to formulate this model. On the model of laminated beam of modified couple stress theory, the transverse shear stress with scale effect is presented for the first time. Numerical results show that the proposed beam model can capture the scale effect at interfaces of the microstructure of the composite laminated beam.

C0-type global–local higher-order theory including transverse normal thermal strain for laminated composite plates under thermal loading

In order to consider the transverse normal strain for thermal expansion problems of laminated composites, the expansion order of the transverse displacement is generally increased, so additional displacement variables will be involved in the displacement fields. Differing from the previous methods, this paper proposes a global–local higher-order theory for thermal stress analysis of simply supported laminated composite plates by introducing transverse normal thermal deformation in transverse displacement field. Although transverse normal deformation is considered, the additional displacement variables have not increased in the proposed model since thermal loads could be included in the generalized force vector. The proposed model a priori satisfies the continuity conditions of transverse shear stresses at interfaces, and the number of displacement variables involved in the present model does not depend on the number of layers in laminates. The equilibrium equations are obtained by using the principle of virtual displacements, and results are computed by using Navier’s technique. Comparing to the three-dimensional theory, the proposed higher-order theory is acceptable even in the case of thick multilayerd composite plates subjected to thermal loads.

A coupled refined high-order global-local theory and finite element model for static electromechanical response of smart multilayered/sandwich beams

In the present study, a coupled refined high-order global-local theory is developed for predicting fully coupled behavior of smart multilayered/sandwich beams under electromechanical conditions. The proposed theory considers effects of transverse normal stress and transverse flexibility which is important for beams including soft cores or beams with drastic material properties changes through depth. Effects of induced transverse normal strains through the piezoelectric layers are also included in this study. In the presence of non-zero in-plane electric field component, all the kinematic and stress continuity conditions are satisfied at layer interfaces. In addition, for the first time, conditions of non-zero shear and normal tractions are satisfied even while the bottom or the top layer of the beam is piezoelectric. A combination of polynomial and exponential expressions with a layerwise term containing first order differentiation of electrical unknowns is used to introduce the in-plane displacement field. Also, the transverse displacement field is formulated utilizing a combination of continuous piecewise fourth-order polynomial with a layerwise representation of electrical unknowns. Finally, a quadratic electric potential is used across the thickness of each piezoelectric layer. It is worthy to note that in the proposed shear locking-free finite element formulation, the number of mechanical unknowns is independent of the number of layers. Excellent correlation has been found between the results obtained from the proposed formulation for thin and thick piezoelectric beams with those resulted from the three-dimensional theory of piezoelasticity. Moreover, the proposed finite element model is computationally economic.

A nonlinear double-superposition global–local theory for dynamic buckling of imperfect viscoelastic composite/sandwich plates: A hierarchical constitutive model

Abstract Nonlinear dynamic thermo-mechanical buckling and postbuckling analyses of imperfect viscoelastic composite laminated/sandwich plates are performed by a proposed theory that takes into account all the interlaminar kinematic and transverse stress continuity conditions, for the first time. Even the dynamic buckling analysis of the multi-layered/sandwich plates employing the hierarchical constitutive model has not been performed before. The proposed theory is a double-superposition high-order global–local theory that is calibrated based on the nonlinear strain–displacement expressions for the thermoelastic loadings taking into account the structural damping. The buckling loads are determined based on a criterion previously published by the author. Various complex sensitivity analyses evaluating effects of the relaxation parameters, rate of the loading, sudden heating, and pre-stress on thermo-mechanical buckling of the viscoelatic multi-layered/sandwich plates are performed. Results show that the viscoelastic behavior may decrease the buckling load. Sudden dynamic buckling loads are higher due to the reflected stress waves.

An improved in-plane displacement model for the stability analysis of laminated composites with general lamination configurations

Abstract This paper describes how the derivatives of lateral displacement are eliminated in the general displacement field of the global–local higher-order theory for stability analysis of laminated composite and sandwich plates with general lamination configurations. In contrast to previous models, the present model is applicable not only to the cross-ply but also to the angle-ply laminated composite and sandwich plates. Based on known traction forces on the surface boundaries, the derivatives of transverse displacement have been taken out from the general displacement field, so that C 0 interpolation functions are only required for the finite element implementation. To verify the proposed theory, the classical quadratic six-node C 0 triangular element is employed for the interpolation of all the displacement parameters defined at each nodal point on the composite plate. Numerical results show that following the proposed theory simple C 0 finite elements could accurately predict the critical loads of sandwich plate with soft core, which has long been a difficult case for the other global higher-order theories.

A double-superposition global–local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach

A higher-order global–local theory is proposed based on the double-superposition concept for free vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied. Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account. Some dynamic buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time. Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm.

A refined high-order global-local theory for finite element bending and vibration analyses of laminated composite beams

A refined high-order global-local laminated/sandwich beam theory is developed that satisfies all the kinematic and stress continuity conditions at the layer interfaces and considers effects of the transverse normal stress and transverse flexibility, e.g. for beams with soft cores or drastic material properties changes. The global displacement components, described by polynomial or combinations of polynomial and exponential expressions, are superposed on local ones chosen based on the layerwise or discrete-layer concepts. Furthermore, the non-zero conditions of the shear and normal tractions of the upper and lower surfaces of the beam may also be enforced. In the present C1-continuous shear locking-free finite element model, the number of unknowns is independent of the number of layers. Comparison of present bending and vibration results for thin and thick beams with results of the three-dimensional theory of elasticity reveals efficiency of the present method. Moreover, the proposed model is computationally economic and has a high convergence rate.

Non-linear dynamic thermo-mechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a global-local theory inherently suitable for non-linear analyses

The available accurate shell theories satisfy the interlaminar transverse stress continuity conditions based on linear strain–displacement relations. Furthermore, in majority of these theories, either influence of the transverse normal stress and strain or the transverse flexibility of the shell has been ignored. These effects remarkably influence the non-linear behavior of the shells especially in the postbuckling region. Furthermore, majority of the buckling analyses performed so far for the laminated composite and sandwich shells have been restricted to linear, static analysis of the perfect shells. Moreover, almost all the available shell theories have employed the Love–Timoshenko assumption, which may lead to remarkable errors for thick and relatively thick shells. In the present paper, a novel three-dimensional high-order global-local theory that satisfies all the kinematic and the interlaminar stress continuity conditions at the layer interfaces is developed for imperfect cylindrical shells subjected to thermo-mechanical loads.In comparison with the layerwise, mixed, and available global-local theories, the present theory has the advantages of: (1) suitability for non-linear analyses, (2) higher accuracy due to satisfying the complete interlaminar kinematic and transverse stress continuity conditions, considering the transverse flexibility, and releasing the Love–Timoshenko assumption, (3) less required computational time due to using the global-local technique and matrix formulations, and (4) capability of investigating the local phenomena. To enhance the accuracy of the results, compatible Hermitian quadrilateral elements are employed. The buckling loads are determined based on a criterion previously published by the author.

Hygrothermal effects on multilayered composite plates using a refined higher order theory

A four-node quadrilateral plate element based on the global–local higher order theory (GLHOT) is proposed to study the response of laminated composite plates due to a variation in temperature and moisture concentrations. C0 and C1 continuities are required in the transverse displacement functions as the first and the second derivatives are involved in the computation of the strain components in GLHOT [Int J Mech Sci, 2007; 49:1276–1288]. In this paper, a displacement function satisfying C0 continuity is constructed by using the refined element method, and the discrete Kirchhoff quadrilateral thin plate element DKQ is employed for satisfying the requirement of C1 continuity. The effects of temperature and moisture concentrations on the material properties and the hygrothermal response of multilayered plates are studied, in contrast to most of the previous investigations in which the material properties are assumed to be independent of temperature. Hygrothermal response due to a variation in temperature and moisture concentrations has been studied for different material types sensitive to changing hygrothermal environment conditions. Numerical results suggest that temperature-dependent material properties ought to be used in the analysis of laminated plates subjected to hygrothermal loads.

Refined global–local higher-order theory for angle-ply laminated plates under thermo-mechanical loads and finite element model

To analyze angle-ply laminated composite and sandwich plates coupled bending and extension under thermo-mechanical loading, a refined global–local higher-order theory considering transverse normal strain is presented in this work. Hitherto, present theory for angle-ply laminates has never been reported in the literature, and this theory can satisfy continuity of transverse shear stresses at interfaces. In addition, the number of unknowns in present model is independent of layer numbers of the laminate. Based on this theory as well as methodology of the refined triangular discrete Kirchhoff plate element, a triangular laminated plate element satisfying the requirement of C1 continuity is presented. Numerical results show that the present refined theory can accurately analyze the bending problems of angle-ply composite and sandwich plates as well as thermal expansion problem of cross-ply plates, and the present refined theory is obviously superior to the existing global–local higher-order theory proposed by Li and Liu [Li XY, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 1997;40:1197–212]. After ascertaining the accuracy of present model, the distributions of displacements and stresses for angle-ply laminated plates under temperature loads are also given in present work. These results can serve as a reference for future investigations.