Fast Processing of Bending Deflection for Euler–Bernoulli Beam Under Different Boundary Constraints Based on a Semi-Analytical Null Space Method
Fast Processing of Bending Deflection for Euler–Bernoulli Beam Under Different Boundary Constraints Based on a Semi-Analytical Null Space Method
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DOI：
10.1007/s44198-023-00155-z
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发表时间：
2023-12
影响因子：
0.7
通讯作者：
W. J. Luo;T. Y. Liu;T. J. Chai;J. W. Yan;W. J. Guo
中科院分区：
文献类型：
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作者：
W. J. Luo;T. Y. Liu;T. J. Chai;J. W. Yan;W. J. Guo
本文提出了一种半解析的零空间法，实现了各种边界约束下欧拉-伯努利梁弯曲挠度的快速计算。零空间方法采用诸如具有未知权系数的三角函数的基函数来近似场函数。未知权系数可由边界约束矩阵独立求解，从而避免了对场函数匹配给定边界约束的高要求，并可在各种边界约束之间快速切换。通过与解析解的比较，确定了基函数对最终结果的影响，并将零空间法应用于新盾构施工引起的既有隧道沉降预测。零空间法的计算结果与有限元和现场试验结果吻合较好。
In this paper, a semi-analytical method called null space method is proposed to realize fast processing of bending deflection for Euler–Bernoulli beam among various types of boundary constraints. The null space method employs a basis function such as trigonometric function with unknown weight coefficients to approximate the field function. The unknown weight coefficients can be independently solved by the boundary constraint matrix, thus this method can easily keep away from the high demanding of field function to match the given boundary constraint and fastly switch among various types of boundary constraints. The effect of basis function on the final results are first confirmed as compared with the analytical solutions, and the null space method is then applied to predict the settlement of the existing tunnel due to new shield tunneling. The calculated results by null space method gives a good prediction of FEM and in-situ test results.