Abstract The present work outlines a computational approach, based on the so-called Finite Analytic Method (FAM), to deal with second-order effects in the structural analysis of tapered members accounting for geometrical nonlinearity by using only one element per physical member. The proposed modelization considers the equilibrium in the deformed configuration of a “beam-column” element, by addressing the resulting mechanical coupling between bending moment and axial force (M-N interaction). A flexibility-based method is developed, to derive the force-displacement relations of the finite element, by obtaining its flexibility and stiffness matrices. Through Gauss-Lobatto integration, the stiffness coefficients capturing second-order geometrical effects are consistently evaluated, to achieve the complete stiffness matrix. Examples and comparisons with reference studies are provided, in order to prove the effectiveness of the proposed methodology. Results on the critical load evaluation of sample tapered members are delivered.

中文翻译：

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锥形梁柱单元中二阶 MN 耦合和几何刚度自适应的实现

摘要 目前的工作概述了一种基于所谓的有限分析方法 (FAM) 的计算方法，通过每个物理构件仅使用一个元素来处理锥形构件结构分析中的二阶效应，其中考虑了几何非线性。建议的建模通过解决弯矩和轴向力（MN 相互作用）之间产生的机械耦合来考虑“梁柱”单元变形配置中的平衡。开发了一种基于柔度的方法，通过获得其柔度和刚度矩阵来推导有限元的力-位移关系。通过 Gauss-Lobatto 积分，可以一致地评估捕捉二阶几何效应的刚度系数，以实现完整的刚度矩阵。提供了与参考研究的示例和比较，以证明所提出方法的有效性。提供了样品锥形构件的临界载荷评估结果。