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A variationally consistent analytical beam model that describes the theory in a Timoshenko-Vlasov level is developed based on Reissner's mixed variational theorem. Starting from a shell theory, all the field-governing equations (equilibrium and continuity) and the boundary conditions of the shell wall are derived in closed form, and the mixed method enables finding the explicit forms of the reactive stresses and sectional warpings which are evaluated progressively depending on the level of beam model to be analyzed. The stress recovery part is incorporated in the post-stage of the analysis to compute the layer-wise distribution of stresses over the beam cross-section. The present analysis is validated against numerous benchmark examples available in the literature, including beams with multi-layered strip section, thin-walled anisotropic box sections with elastic couplings, and two-cell airfoil section. The comparison study demonstrates excellent correlations with the results from detailed three-dimensional finite element analysis and other up-to-date beam approaches. Also presented are symbolically expressed stiffness coefficients and the sectional warping modes of coupled composite beams to demonstrate the strength of the proposed beam model. [ABSTRACT FROM AUTHOR]

An analytical methodology is developed for thin-walled composite beams with arbitrary geometries and material distributions. The approach uses a mixed variational theorem which sets the shell displacements, and the shear stress resultants and hoop moments as the unknowns to obtain the stiffness constants at the level of Timoshenko–Vlasov beam. All the field equations and the continuity conditions that should be satisfied over the shell wall are derived in closed form as the part of the analysis. Numerical simulations are conducted to show the validity of the proposed analysis. The comparison of the predicted stresses and the stiffness constants indicates close correlation with those of the detailed finite element (FE)-based analysis and up-to-date beam approaches. Symbolically generated stiffness constants and the sectional warping deformation modes of coupled composite beams are presented explicitly to illustrate the strength of the proposed theory. [ABSTRACT FROM AUTHOR]

Classical finite element (FE) beam theories are based on displacement formulation requiring derivatives to obtain the stress components which leads to a large number of FEs and depend on nodal averaging techniques for achieving sufficient accuracy. In this work, a new multifield variational based FE formulation is proposed within the cross-sectional framework of multilayered composite beams for accurate and efficient predictions of sectional stiffness constants and stresses. The interlaminar stress continuity is not assumed a priori and inherently incorporated using the Hellinger-Reissner principle along with a global stress equilibrium constraint, directly computing the stresses at nodal locations. The three-dimensional (3D) stresses and warping deformations are considered as primary variables which inherently incorporate elastic coupling effects related to transverse shear and Poisson deformations. The formulation results in a generalized fully-coupled 6 × 6 sectional stiffness matrix considering elastic couplings. The efficacy of the present analysis is substantiated for thin-walled composite beams with elastic couplings. An excellent correlation is achieved for the elastostatic response as compared with the 3D FE and experimental results. The stresses obtained by the multifield analysis are in accord with detailed 3D FE solutions for various loading conditions while computed at a much reduced computational cost. Improved predictions of interlaminar stresses and stress concentrations are achieved compared to displacement-based approach along with the correct identification of continuity across layer interfaces. The effect of fiber orientation on the interlaminar stresses is also shown to be significant which can be useful for damage analysis of composite beams. Image 1 • A multifield variational finite element analysis developed for anisotropic beams. •3D stresses with interlaminar continuity modeled as unknowns without a priori assumptions or post-processing technique. •Excellent correlation obtained as compared with 3D finite element analysis while predicting interlaminar stresses and stress concentrations at corners correctly. •Influence of fiber angles on interlaminar stresses demonstrated for coupled beams. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to develop an analytical approach to evaluate the influence of material uncertainties on cross-sectional stiffness properties of thin walled composite beams. Design/methodology/approach – Fuzzy arithmetic operators are used to modify the thin-walled beam formulation, which was based on a mixed force and displacement method, and to obtain the uncertainty properties of the beam. The resulting model includes material uncertainties along with the effects of elastic couplings, shell wall thickness, torsion warping and constrained warping. The membership functions of material properties are introduced to model the uncertainties of material properties of composites and are determined based on the stochastic behaviors obtained from experimental studies. Findings – It is observed from the numerical studies that the fuzzy membership function approach results in reliable representation of uncertainty quantification of thin walled composite beams. The propagation of uncertainties is also demonstrated in the estimation of structural responses of composite beams. Originality/value – This work demonstrates the use of fuzzy approach to incorporate uncertainties in the responses analytically, in turn improving computational efficiency drastically as compared to the Monte-Carlo method. [ABSTRACT FROM AUTHOR]

Abstract: In the present work, a mixed beam approach that combines both the stiffness and the flexibility formulation in a unified manner has been performed to analyze the elastically-coupled composite beams with closed cross-sections. The analysis model includes the effects of elastic couplings, shell wall thickness, torsion warping, and constrained warping. The Reissner’s semi-complementary energy functional is used to derive the beam force–displacement relations. The theory is validated against detailed finite element analysis results for coupled composite beams with single and double-celled box sections. Various layup cases of box beams with bending–torsion or extension–torsion couplings are considered to evaluate whether all the significant non-classical structural effects of composites are captured in the beam theory. Good correlation of the present theory with the finite element analysis is obtained over the different cases. Numerical results showing the accuracy of the approach are demonstrated in the framework of the analysis. [Copyright &y& Elsevier]