Structural analysis of composite tubes using a meshless analytical dimensional reduction method

A polynomial-based model in conjunction with dimensional reduction method are presented to perform cross-sectional analysis and to determine strain distribution in composite tubes under bending loading. For beam structures with tubular cross-section, the Variational Asymptotic Method (VAM) has been employed to decompose a three-dimensional (3D) elasticity problem into a two-dimensional cross-sectional analysis and a one-dimensional analysis along the length. This greatly reduces computational time as compared to 3D Finite Element Method (FEM). There also exists publically available Variational Asymptotic Beam Sectional Analysis (VABS), a FEM cross-sectional analysis tool based on VAM. For VABS, FEM mesh for the beam section needs to be generated. For the case of composite tubes with many layers, the mesh generation consumes efforts and is unnecessary. We introduce a new meshless dimensional reduction method for the analysis of composite tubes. This method utilizes Pascal polynomials in polar coordinates to model the warping functions. Using this, one can obtain stiffness constants and 3D strains of the composite tube. This method is straightforward, meshless, with similar computation time as VABS, and is much more efficient than conventional 3D FEM. The accuracy of the proposed method is examined by comparing the obtained results with 3D FE (ANSYS), VABS, literature, and experiment.