Thin-walled Composite I-beams Research Articles

Buckling analysis of laminated composite thin-walled I-beam under mechanical and thermal loads

Despite the extensive use of thin-walled structures, the studies on their behaviours when exposed to extreme thermal environment are relatively scarce. Therefore, this paper aims to present the buckling analysis of thin-walled composite I-beams under thermo-mechanical loads. The thermal effects are investigated for the case of studied beams undergoing a uniform temperature rise through their thickness. The theory is based on the first-order shear deformation thin-walled beam theory with linear variation of displacements in the wall thickness. The governing equations of motion are derived from Hamilton's principle and are solved by series-type solutions with hybrid shape functions. Numerical results are presented to investigate the effects of fibre angle, material distribution, span-to-height's ratio and shear deformation on the critical buckling load and temperature rise. These results for several cases are verified with available references to demonstrate the present beam model’s accuracy.

A general higher-order shear deformation theory for buckling and free vibration analysis of laminated thin-walled composite I-beams

A general higher-order shear deformation theory for buckling and free vibration analysis of laminated thin-walled composite I-beams is proposed in this paper. It is based on a unified nonlinear variation of shear strains in the wall thickness and then theoretical formulation is derived in the general form which can recover the previous conventional theories such as classical and first-order thin-walled beam theory. Series-type solutions with hybrid shape functions are developed for different boundary conditions. Numerical examples are performed on laminated thin-walled composite I-beams with arbitrary lay-ups. Effects of transverse shear strains, fiber angles and slenderness ratio on the critical buckling loads and natural frequencies of the beams are reported.

Similitude analysis of thin-walled composite I-beams for subcomponent testing of wind turbine blades

In this study, the I-beam structure of a utility-scale blade is used as the basis for the design of a small-scale subcomponent emulating the same type of structural element of a utility-scale wind turbine blade. Governing equations for the bending of a shear deformable thin-walled composite I-beam are considered. Similitude theory is applied to derive the corresponding scaling laws. Accuracy of the derived scaling laws in predicting the strain and displacement fields of the full-scale I-beam is considered as a design criterion for small-scale I-beams. Both complete and partial similarity cases are discussed. A novel approach is proposed to design partially similar scaled I-beams with totally different layups from those of the full-scale I-beam. Using the proposed technique, scaled-down composite I-beams are designed that predict the strain and displacement fields of their full-scale parent I-beam with very good accuracy.

Vibration prediction of thin-walled composite I-beams using scaled models

Scaled models of large and expensive structures facilitate in understanding the physical behavior of the large structure during operation but on a smaller scale in both size and cost. These reduced-sized models also expedite in tuning designs and material properties, but also could be used for certification of the full-scale structure (referred to as the prototype). Within this study, the applicability of structural similitude theory in design of partially similar composite structures is demonstrated. Particular emphasis is placed on the design of scaled-down composite I-beams that can predict the fundamental frequency of their corresponding prototype. Composite I-beams are frequently used in the aerospace industry and are referred to as the back bone of large wind turbine blades. In this study, the governing equations of motion for free vibration of a shear deformable composite I-beam are analyzed using similarity transformation to derive scaling laws. Derived scaling laws are used as design criteria to develop scaled-down models. Both complete and partial similarity is discussed. A systematic approach is proposed to design partially similar scaled-down models with totally different layup from those of the full-scale I-beam. Based on the results, the designed scaled-down I-beams using the proposed technique show very good accuracy in predicting the fundamental frequency of their prototype.

Reducing shear-lag in thin-walled composite I-beam wing spars

Purpose – The purpose of this paper was to investigate and evaluate the influence of geometrical and structural design changes in order to reduce shear-lag and increase specific strength and stiffness of thin-walled composite I-beam wing spars. Design/methodology/approach – A detailed FEM model of a cantilevered I-beam spar was used to investigate the influence of increased transition fillet radius and increased web sandwich core thickness on the shear-lag effect at different width to thickness ratios of flanges. Evaluation functions were used to assess specific strength and stiffness of different spar configurations. Findings – Increased web core thickness has greater influence on normal stress distribution and the reduction of the shear-lag than fillet size. Additional weight of thicker core is not compensated enough through reduction of stress concentration. Increased transition fillet and web core thickness increase optimum flanges width to thickness ratio. Shear-lag reduces the strength of the spar m...

Vibration and Buckling of Thin-Walled Composite I-Beams with Arbitrary Lay-Ups under Axial Loads and End Moments

A finite element model with seven degrees of freedom per node is developed to study vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under constant axial loads and equal end moments. This model is based on the classical lamination theory, and accounts for all the structural coupling coming from material anisotropy. The governing differential equations are derived from the Hamilton’s principle. Numerical results are obtained for thin-walled composite I-beams to investigate the effects of axial force, bending moment and fiber orientation on the buckling moments, natural frequencies, and corresponding vibration mode shapes as well as axial-moment-frequency interaction curves.

Shear deformable doubly- and mono-symmetric composite I-beams

A shear deformable beam element is developed for the coupled flexural and torsional analyses of thin-walled composite I-beams with doubly- and mono-symmetric cross-sections. The present element includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Governing equations and force–displacement relations are derived from the principle of minimum total potential energy. Then the explicit expressions for displacement parameters are derived by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the element stiffness matrix is determined using the force–displacement relations. In order to verify the accuracy and the superiority of the beam element developed herein, the numerical solutions are presented and compared with the results obtained from the isoparametric beam elements based on the Lagrangian interpolation polynomial, the detailed three-dimensional analysis results using the shell elements of ABAQUS, and the solutions by other researchers.

Vibration analysis of thin-walled composite beams with I-shaped cross-sections

A general analytical model applicable to the vibration analysis of thin-walled composite I-beams with arbitrary lay-ups is developed. Based on the classical lamination theory, this model has been applied to the investigation of load–frequency interaction curves of thin-walled composite beams under various loads. The governing differential equations are derived from the Hamilton’s principle. A finite element model with seven degrees of freedoms per node is developed to solve the problem. Numerical results are obtained for thin-walled composite I-beams under uniformly distributed load, combined axial force and bending loads. The effects of fiber orientation, location of applied load, and types of loads on the natural frequencies and load–frequency interaction curves as well as vibration mode shapes are parametrically studied.

Dynamic stiffness matrix of thin-walled composite I-beam with symmetric and arbitrary laminations

For the spatially coupled free vibration analysis of thin-walled composite I-beam with symmetric and arbitrary laminations, the exact dynamic stiffness matrix based on the solution of the simultaneous ordinary differential equations is presented. For this, a general theory for the vibration analysis of composite beam with arbitrary lamination including the restrained warping torsion is developed by introducing Vlasov's assumption. Next, the equations of motion and force–displacement relationships are derived from the energy principle and the first order of transformed simultaneous differential equations are constructed by using the displacement state vector consisting of 14 displacement parameters. Then explicit expressions for displacement parameters are derived and the exact dynamic stiffness matrix is determined using force–displacement relationships. In addition, the finite-element (FE) procedure based on Hermitian interpolation polynomials is developed. To verify the validity and the accuracy of this study, the numerical solutions are presented and compared with analytical solutions, the results from available references and the FE analysis using the thin-walled Hermitian beam elements. Particular emphasis is given in showing the phenomenon of vibrational mode change, the effects of increase of the modulus and the bending–twisting coupling stiffness for beams with various boundary conditions.

Shear-flexible thin-walled element for composite I-beams

A shear-flexible finite element based on an orthogonal Cartesian coordinate system is developed for the flexural and buckling analyses of thin-walled composite I-beams with both doubly and mono-symmetrical cross-sections. Using the first-order shear deformable beam theory, the derived element includes both the transverse shear and the restrained warping induced shear deformations. Governing equations are derived from the principle of minimum total potential energy. Three different types of finite elements, namely, linear, quadratic and cubic elements are developed to solve the governing equations. The geometric stiffness for the buckling analysis of axially loaded, thin-walled composite beams is developed. The resulting linearized buckling problem is solved using a shifted inverse iteration algorithm. A parametric study of the effects of the aspect ratio and the fibre orientation on the tip displacement is presented. The convergence of the elements is also investigated. The elastic buckling loads for mono- and doubly-symmetric I-beam cross-sections are compared with other results available in the literature and with solutions using shell elements in a commercially available finite element program.

Closed-form analysis of thin-walled composite I-beams considering non-classical effects

In this work, a closed-form analysis of thin-walled open profile composite beams such as I-beam has been performed. The analysis includes the effects of elastic couplings, shell wall thickness, transverse shear deformation, torsion warping, and constrained warping. A mixed beam approach based on Reissner’s semi-complementary energy functional is used to derive the beam force–displacement relations. A closed-form solution for the static response of both symmetric and anti-symmetric layup beams with transverse shear couplings is derived. The beams considered have the boundary condition of one end fixed and the other end warping restrained and are subjected to unit bending or torque load at the beam tip. The shear flow distribution related with the applied forces and moments along the contour of the beam is also identified. The static results of composite I-beams have been validated against those of detailed two-dimensional finite element analysis. The effects of warping restraint and transverse shear deformation on the static behavior of open-section composite beams are investigated in the analysis.

Static response of thin-walled composite I-beams loaded at their free-end cross-section: analytical solution

Analytical solutions for the static response of anisotropic composite I-beams loaded at their free end are presented. The analysis is accomplished within the framework of the theory of composite thin-walled beams featuring the two main coupling mechanisms, namely, circumferentially uniform stiffness (CUS) and circumferentially asymmetric stiffness (CAS) configurations. Within each of these two configurations, the implications of the directionality property of composite materials, of warping inhibition and transverse shear on the static response of I-beams are highlighted, and final conclusions are outlined.

Lateral-torsional buckling of thin-walled composite I-beams by the finite difference method

The finite difference method has been used to solve the differential equation for the critical loading associated with a specific lateral-torsional buckling test configuration. The linear elastic analysis is valid for thin-walled composite doubly symmetric I-beams made from mid-plane symmetric, fibre-reinforced laminated panels. Here, the test configuration has an I-beam with specially orthotropic panels. It is subjected to three-point bending, and supported at each end such that the only degree of freedom is rotation about the major axis of the beam. For the modelling case where the central load is applied at the shear centre (centroid) of the cross-section there is a favourable comparison between the finite difference results and those results presented by Timoshenko and Gere (1961, Theory of Elastic Stability 2nd edn, McGraw-Hill, New York), which were originally generated for isotropic beams. A favourable comparison has also been found between the finite difference analysis and experimental evidence using an E-glass fibre-reinforced polymeric pultruded I-beam, where the central load is now applied to the top compression flange. The various theoretical models presented in the paper are used to show that the critical loading for buckling in real composite I-beams will be strongly dependent on both the support boundary conditions and the height of the loading relative to the centroid (shear centre).