Stress analysis of elliptical composite tubular beams using a meshless dimensional reduction method

Abstract In the present paper, a meshless dimensional reduction method is presented for the efficient stress analysis of composite tubular beams with elliptical cross-section. A polynomial based method in polar coordinates in conjunction with an asymptotic variational method were used to carry out cross-sectional analysis. The two-dimensional cross-section strain energy is perturbed by perturbing the warping field to obtain unknown warping of the cross-section. The transverse shear effect is taken into consideration using transformation to Timoshenko-Like beam model. Since the present approach does not use finite element mesh in two-dimensional analysis of the cross-section (such as that used in the software Variational Asymptotic Beam Sectional Analysis (VABS)), it is termed meshless method . The one-dimensional finite element analysis through the length is carried out to determine the transverse deflections and rotations of the beam. This procedure is much faster computationally as compared to the three-dimensional finite element method . It is simple-input, and needs less pre-processing time to prepare the model. The obtained results are compared with literature, strength of materials and VABS tool. In addition, the effect of ellipse diameter ratios and lay-up sequence on the mechanical behavior of elliptical tubular beams are investigated.