Interaction curves for vibration and buckling of thin-walled composite box beams under axial loads and end moments

Interaction curves for vibration and buckling of thin-walled composite box beams with arbitrary lay-ups under constant axial loads and equal end moments are presented. 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. The resulting coupling is referred to as triply flexural–torsional coupled vibration and buckling. A displacement-based one-dimensional finite element model with seven degrees of freedoms per node is developed to solve the problem. Numerical results are obtained for thin-walled composite box beams to investigate the effects of axial force, bending moment, fiber orientation on the buckling loads, buckling moments, natural frequencies and corresponding vibration mode shapes as well as axial-moment–frequency interaction curves

Free vibration of axially loaded thin-walled composite Timoshenko beams

Based on shear-deformable beam theory, free vibration of thin-walled composite Timoshenko beams with arbitrary layups under a constant axial force is presented. This model accounts for all the structural coupling coming from material anisotropy. Governing equations for flexural-torsional-shearing coupled vibrations are derived from Hamilton’s principle. The resulting coupling is referred to as sixfold coupled vibrations. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results are obtained for thin-walled composite beams to investigate the effects of shear deformation, axial force, fiber angle, modulus ratio on the natural frequencies, corresponding vibration mode shapes and load–frequency interaction curves

Geometrically nonlinear analysis of thin-walled open-section composite beams

A geometrically nonlinear model for general thin-walled open-section composite beams with arbitrary lay-ups under various types of loadings based on the classical lamination theory is presented. It accounts for all structural coupling coming from the material anisotropy and geometric nonlinearity. Nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. The finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed to solve the problem. Numerical results are obtained for thin-walled composite Z-beam and I-beam to investigate effects of geometric nonlinearity, fiber orientation and warping restraint on the flexural–torsional response

Flexural-torsional behavior of thin-walled closed-section composite box beams

This paper presents a flexural–torsional analysis of composite box beams. A general analytical model applicable to thin-walled box section composite beams subjected to vertical and torsional load is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional responses for arbitrary laminate stacking sequence configurations, 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 beams under vertical and torsional loading, addressing the effects of fiber angle and laminate stacking sequence

Free vibration of thin-walled composite box beams

Free vibration of a thin-walled laminated composite beam is studied. A general analytical model applicable to the dynamic behavior of a thin-walled composite box section is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes for arbitrary laminate stacking sequence configuration, i.e. unsymmetric as well as symmetric, and various boundary conditions. A displacement-based one-dimensional finite element model is developed to predict natural frequencies and corresponding vibration modes for a thin-walled composite beam. Equations of motion are derived from the Hamilton’s principle. Numerical results are obtained for thin-walled composites addressing the effects of fiber angle, modulus ratio, and boundary conditions on the vibration frequencies and mode shapes of the composites

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 Kármán 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

Vibration and buckling of cross-ply composite beams using refined shear deformation theory

Vibration and buckling analysis of cross-ply composite beams using refined shear deformation theory is presented. The theory accounts for the parabolical variation of shear strains through the depth of beam. Three governing equations of motion are derived from the Hamilton’s principle. The resulting coupling is referred to as triply coupled vibration and buckling. A two-noded C1 beam element with five degree-of-freedom per node is developed to solve the problem. Numerical results are obtained for composite beams to investigate modulus ratio on the natural frequencies, critical buckling loads and load-frequency interaction curves

Flexural–torsional buckling of thin-walled composite box beams

Buckling of an axially loaded thin-walled laminated composite is studied. A general analytical model applicable to the flexural, torsional and flexural–torsional buckling of a thin-walled composite box beam subjected to axial load is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes for arbitrary laminate stacking sequence configuration, i.e. unsymmetric as well as symmetric, and various boundary conditions. A displacement-based one-dimensional finite element model is developed to predict critical loads and corresponding buckling modes for a thin-walled composite bar. Governing buckling equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for axially loaded thin-walled composites addressing the effects of fiber angle, anisotropy and boundary conditions on the critical buckling loads and mode shapes of the composites

Flexural–torsional coupled vibration and buckling of thin-walled open section composite beams using shear-deformable beam theory

A general analytical model based on shear-deformable beam theory has been developed to study the flexural–torsional coupled vibration and buckling of thin-walled open section composite beams with arbitrary lay-ups. This model accounts for all the structural coupling coming from the material anisotropy. The seven governing differential equations for coupled flexural–torsional–shearing vibration are derived from Hamilton's principle. The resulting coupling is referred to as sixfold coupled vibration. Numerical results are obtained to investigate effects of shear deformation, fiber orientation and axial force on the natural frequencies, corresponding mode shapes as well as load–frequency interaction curves

Static behavior of composite beams using various refined shear deformation theories

Static behavior of composite beams with arbitrary lay-ups using various refined shear deformation theories is presented. The developed theories, which do not require shear correction factor, account for parabolical variation of shear strains and consequently shear stresses through the depth of the beam. In addition, they have strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. A two-noded C1 finite element with six degree-of-freedom per node which accounts for shear deformation effects and all coupling coming from the material anisotropy is developed to solve the problem. Numerical results are performed for symmetric and anti-symmetric cross-ply composite beams under the uniformly distributed load and concentrated load. The effects of fiber angle and lay-ups on the shear deformation parameter and extension-bending-shear-torsion response are investigated