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.

中文翻译：

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使用无网格分析降维方法对复合管进行结构分析

提出了一种基于多项式的模型结合降维方法进行横截面分析并确定复合管在弯曲载荷下的应变分布。对于管状横截面的梁结构，已采用变分渐近法 (VAM) 将三维 (3D) 弹性问题分解为二维横截面分析和沿长度方向的一维分析。与 3D 有限元方法 (FEM) 相比，这大大减少了计算时间。还存在公开可用的变分渐近梁截面分析 (VABS)，这是一种基于 VAM 的 FEM 截面分析工具。对于 VABS，需要生成梁截面的 FEM 网格。对于多层复合管的情况，网格生成很费力，没有必要。我们介绍了一种新的无网格降维方法，用于分析复合管。该方法利用极坐标中的帕斯卡多项式来模拟翘曲函数。使用它，可以获得复合管的刚度常数和 3D 应变。这种方法简单、无网格，计算时间与 VABS 相似，并且比传统的 3D FEM 高效得多。通过将获得的结果与 3D FE (ANSYS)、VABS、文献和实验进行比较，检验了所提出方法的准确性。可以得到复合管的刚度常数和 3D 应变。这种方法简单、无网格，计算时间与 VABS 相似，并且比传统的 3D FEM 高效得多。通过将获得的结果与 3D FE (ANSYS)、VABS、文献和实验进行比较，检验了所提出方法的准确性。可以得到复合管的刚度常数和 3D 应变。这种方法简单、无网格，计算时间与 VABS 相似，并且比传统的 3D FEM 高效得多。通过将获得的结果与 3D FE (ANSYS)、VABS、文献和实验进行比较，检验了所提出方法的准确性。