Analysis Of Thin-walled Composite Beams Research Articles

Comparison of various thin-walled composite beam models for thermally induced vibrations of spacecraft boom

A sufficiently accurate, yet computationally efficient prediction of thermomechanical behavior is essential for the structural design of spacecraft. This paper presents a novel modeling approach for thermally induced vibrations of thin-walled composite tubes in spacecraft, in which the generalized beam theory is employed, and meanwhile, the non-conventional shear and extension modes are introduced into it. Furthermore, a cross-sectional temperature model in terms of harmonic functions is developed to provide more accurate temperature field, which is performed by taking into account the strong couplings between average and perturbation temperatures and between perturbation temperatures. Combining the beam model and the temperature model, a thermal–structural finite element formulation for composite boom in space environment is established. By comparison to the finite shell element, the accuracy and characteristic feature of these new models are illustrated. The results show that the additional deformation modes may play a significant role in thermal–structural analysis of thin-walled composite beams.

Development of a cross-sectional finite element for the analysis of thin-walled composite beams like wind turbine blades

A method for structural analysis of thin-walled composite beams like wind turbine blades is presented. This method is based on the Nonhomogeneous Anisotropic Beam Section Analysis (NABSA) which consists in discretizing the beam cross section using finite elements. The proposed implementation uses 3-node line cross-sectional finite elements with nodes having rotational degrees of freedom to describe the cross-sectional warping displacements. Solutions obtained using this approach were verified against the corresponding analytical or numerical solutions. Agreement was very good to excellent for the computation of cross-sectional properties and distribution of stresses, strains and warping displacements for a broad range of possible composite beam behaviors including geometric and material couplings, open sections, multicell sections, and arbitrary laminates. For thin-walled layered structures, the proposed method provides models with fewer degrees of freedom than equivalent models based on a two-dimensional discretization of cross sections using triangular or quadrilateral elements such as conventional NABSA or VABS which suggests that computation time could be reduced.

Coupled flexural torsional analysis and buckling optimization of variable stiffness thin-walled composite beams

Present work examines flexural–torsional coupling for static and stability analysis of thin-walled composite beams having variable stiffness. Variable stiffness composites (VSCs), manufactured with curvilinear fibers, are considered in this work. Compared to straight fiber laminates, variable angle tow (VAT) sections may significantly improve structural response as they redistribute the in-plane stresses. A generalized beam kinematic model which considers the effect of flexural, torsional and, warping deformation is adopted and using the principle of minimum potential energy, governing equations are derived. The variable fiber angles can be defined using a general Lagrangian polynomial and as a particular case, the solution is presented for linearly varying fiber angles. Stability analysis considers geometric nonlinearity. The present model neglects transverse shear deformations, and governing equations are numerically solved using a set of C 1 continuous finite elements. Important observations are made on the coupled response of thin-walled VSCs for static and stability analysis, which indicates the necessity of optimization study. An efficient ‘Teaching Learning Based Optimization’ (TLBO) algorithm is applied to obtain the most efficient curvilinear fiber path. The results show that lateral torsional buckling load capacity can be increased by approximately 15% in optimized VSCs compared to unidirectional fiber composites. The present kinematic model and numerical scheme can be easily extended to the optimization studies considering manufacturing constraints, which may be further implemented in commercial designs.

Vibrations of composite thin-walled beams with arbitrary curvature – a unified approach

Abstract This paper presents a unified theory for the vibrational analysis of thin-walled composite beams (TWCB) with arbitrary planar axial curvature, variable cross section, and general composite material layup, allowing for the accurate modelling of a large class of composite beams with an accuracy normally achievable only through shell-type finite-element (FE) models, but at a fraction of the numerical cost. The kinematic description is based on the Frenet-Serret frame field, providing a transparent path for transforming the equations of motion from rectilinear to curved TWCB while fully accounting for curvature gradient terms, thereby allowing for the treatment of highly curved geometries. Additional innovations include the use of a novel formulation increasing the accuracy for cases with significant axial-bending-torsional structural coupling, as well as a computationally efficient Isogeometric Analysis (IGA) formulation. The new method has been applied to modal and transient analysis of several test cases where conventional TWCB models are found to yield limited accuracy. The results obtained are almost indistinguishable from those obtained with a full-sized shell-based FE model, at a computational cost which is about two orders-of-magnitude smaller.

Optimal design of composite thin-walled beams using simulated annealing

In this paper, a problem formulation and solution methodology for optimal design of thin-walled composite beams is presented. The aim is to maximize the buckling load capacity and minimize the weight of the beam. For this purpose, a theoretical model is developed for the analysis of thin-walled composite beams under a state of arbitrary initial stresses. In order to find the optimal solution, Simulated Annealing method is implemented. Design variables are taken as the stacking sequences of laminate and the dimensions of the cross-section. The space of feasible solutions is constrained by strength, displacements, global and local buckling and geometric conditions.

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.

Coupled stability analysis of thin-walled composite beams with closed cross-section

For the coupled stability analysis of thin-walled composite beam with closed cross-section subjected to various forces such as eccentric constant axial force, end moments, and linearly varying axial force, the efficient numerical method to evaluate the element stiffness matrix is newly presented based on the homogeneous form of simultaneous ordinary differential equations. The general bifurcation type of buckling theory for thin-walled composite box beam is developed based on the energy functional corresponding to semitangential rotations and semitangential moments. The coupled stability equations including variable coefficients and the force–displacement relationships are derived from the energy principle and explicit expressions for displacement functions are presented based on power series expansions of displacement components. The element stiffness matrix is evaluated by applying member force–displacement relationships to these displacement functions. In addition, the finite element model based on the cubic Hermitian interpolation polynomial is presented. In order to verify the accuracy and validity of this study, numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the available results from other researchers. Particularly, the influence of the eccentricity and the force ratio of axial forces, the fiber orientation, and the boundary conditions on the buckling behavior of composite box beam are parametrically investigated. Also the emphasis is given in showing the phenomenon of buckling mode change.

Geometrical nonlinear analysis of thin-walled composite beams using finite element method based on first order shear deformation theory

Based on a seven-degree-of-freedom shear deformable beam model, a geometrical nonlinear analysis of thin-walled composite beams with arbitrary lay-ups under various types of loads is presented. This model accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The general nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Karman sense is developed to solve the problem. Numerical results are obtained for thin-walled composite beam under vertical load to investigate the effects of fiber orientation, geometric nonlinearity, and shear deformation on the axial–flexural–torsional response.

Stiffness matrices of thin-walled composite beam with mono-symmetric I- and channel-sections on two-parameter elastic foundation

For the coupled analysis of thin-walled composite beam under the initial axial force and on two-parameter elastic foundation with mono-symmetric I- and channel-sections, the stiffness matrices are derived. The stiffness matrices developed by this study are based on the homogeneous forms of simultaneous ordinary differential equations using the eigen-problem. For this, from the elastic strain energy, the potential energy due to the initial axial force and the strain energy considering the foundation effects, the equilibrium equations and force–displacement relationships are derived. The exact displacement functions for displacement parameters are evaluated by determining the eigenmodes corresponding to multiple non-zero and zero eigenvalues. Then the element stiffness matrix is determined using the force–displacement relationships. For the purpose of comparison, the finite element model based on the classical Hermitian interpolation polynomial is presented. In order to verify the accuracy and the superiority of the beam elements developed herein, the numerical solutions are presented and compared with results from the Hermitian beam elements and the ABAQUS’s shell elements. Particularly, the influence of the initial compressive and tensile forces, the fiber orientation, and the boundary conditions on the coupled behavior of composite beam with mono-symmetric I- and channel-sections is parametrically investigated.

Torsional analysis of thin-walled composite beams with single- and double-celled sections

The exact solutions for twist angle and fiber stresses of thin-walled composite box beams with single- and double-celled sections subjected to torsional moment are presented by introducing fourteen displacement parameters. For this, a general thin-walled composite box-beam theory including the effects of elastic couplings and restrained warping is developed based on the Vlasov’s assumptions. The equilibrium equations and the force–deformation relations are derived from the energy principle. A system of linear algebraic equations with non-symmetric matrices is constructed by introducing fourteen displacement parameters and by transforming the higher order simultaneous differential equations into first-order ones. This numerical technique determines eigenmodes corresponding to multiple zero and non-zero eigenvalues and derives exact displacement functions for displacement parameters based on the undetermined parameter method. Finally, the exact stiffness matrix is determined using the member force–deformation relations. The theory developed by this study is validated by comparing several torsional responses from the present approach with those from the finite element beam model that uses third-order Hermitian polynomials and detailed two-dimensional analysis results using the shell elements of ABAQUS for coupled composite beams with single- and double-celled sections.

Flexural–torsional buckling loads for spatially coupled stability analysis of thin-walled composite columns

For the spatially coupled stability analysis of thin-walled composite beam with symmetric and non-symmetric laminations, the element stiffness matrix is presented using the technical computing program Mathematica. For this, the bifurcation type buckling theory of thin-walled composite beam subjected to an axial compressive force is developed by extending the nonlinear anisotropic thin-walled beam theory proposed by Bauld and Tzeng. From the stability equations, the explicit expressions for displacements are derived based on the displacement state vector consisting of 14 displacements, and then the element stiffness matrix is determined using the force–deformation relations. In addition, as a special case, the analytical solutions for buckling loads of the orthotropically laminated composite beams with various boundary conditions are derived. To demonstrate the validity and the accuracy of this study, the numerical solutions are presented and compared with the analytical solutions and the finite element results using the Hermitian beam elements and ABAQUS’s shell elements.

A Series Solution for the Free Vibrations of Thin-Walled Composite Beams

Based on series solutions, the free vibration analysis of thin-walled composite beam with channel sections is performed. For this, the dynamic stiffness matrix is presented using the homogeneous form of the simultaneous ordinary differential equations. The 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 explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Then the exact dynamic stiffness matrix is determined using force-displacement relationships. In addition, the finite element model based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of this study, numerical solutions are presented and compared with the analytical solutions from other researchers and the finite element solutions using the Hermitian beam elements. Particularly, the effects of modulus orthotropy and boundary conditions on the vibrational behavior of thin-walled composite beam with various fiber orientations are investigated.

Improved flexural–torsional stability analysis of thin-walled composite beam and exact stiffness matrix

A simple but efficient method to evaluate the exact element stiffness matrix is newly presented in order to perform the spatially coupled stability analysis of thin-walled composite beams with symmetric and arbitrary laminations subjected to a compressive force. For this, the general bifurcation-type buckling theory of thin-walled composite beam is developed based on the energy functional, which is consistently obtained corresponding to semitangential rotations and semitangential moments. A numerical procedure is proposed by deriving a generalized eigenvalue problem associated with 14 displacement parameters, which produces both complex eigenvalues and multiple zero eigenvalues. Then the exact displacement functions are constructed by combining eigenvectors and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently exact element stiffness matrices are evaluated by applying member force–displacement relationships to these displacement functions. As a special case, the analytical solutions for buckling loads of unidirectional and cross-ply laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of this study, the numerical, analytical, and the finite element solutions using the Hermitian beam elements are presented and compared with those from ABAQUS's shell elements. The effects of fiber orientation and the Wagner effect on the coupled buckling loads are also investigated intensively.

Flexural analysis of thin-walled composite beams using shear-deformable beam theory

This paper presents a flexural analysis of I-shaped laminated composite beams. A general analytical model applicable to thin-walled I-section composite beams subjected to vertical load is developed. This model is based on the shear-deformable beam theory, and accounts for the flexural response of the thin-walled composites for arbitrary laminate stacking sequence configuration, i.e. unsymmetric as well as symmetric. Governing equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for thin-walled composites under vertical loading, addressing the effects of fiber angle and span-to-height ratio of the composite beam.

Analysis of Thin-Walled Composite Beams with Arbitrary Layup

A beam theory for open and closed section, thin-walled, composite beams is presented. The layup of each wall segment is arbitrary, the effects of shear deformation and restrained warping are neglected. Closed form expressions are developed for the calculation of the 4×4 stiffness matrix. It is also shown that the local bending stiffnesses of the wall segments may be neglected when the laminate is either symmetrical or orthotropic.

Higher-order shear deformation theory for thin-walled composite beams

A higher-order shear deformation theory for the static and dynamic analysis of thin-walled composite beams of arbitrary lay-ups and cross sections is presented. The method is applicable to beams of open as well as closed cross sections. The formulation includes Euler-Bernoulli and Timoshenko theories as subsets. The bendingand torsion-related warping functions are derived in closed form. The method is validated by comparison with experimental and analytical results for static deflections of composite beams with symmetric and antisymmetric lay-ups. Comparison with experimental results for the vibration of beams exhibiting bending torsion coupling shows that the present method gives better correlations. The significance of the higher-order theory is brought out by validating the results of the analyses against results from other theoretical methods. The results show the importance of the lay-up sequence on the shear lag in thin-walled composite beams.

Analysis of Thin-Walled Composite Beams by Energy Method

Utilization of fiber reinforced plastics in the aerospace structures has become commonplace recently. However, considerable amount of research work is needed to understand the various coupling phenomena that arise from the use of FRP materials, and in efficiently modelling the coupling behavior in analytical formulations. The present effort describes the formulation and solution of FRP box beam type of structures through the use of the total potential energy functional in conjunction with the Ritz method. Results obtained from the present effort are compared to those obtained from a finite ele ment formulation and also to those from experimental results available in the literature, and it is shown that the present procedure is accurate for beams of symmetric layups.