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Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

机译:层次一维有限元分析梁结构的几何非线性

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摘要

The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.
机译:本文提出了一种用于梁状结构几何非线性静力分析的高级一维有限元的公式。通过统一配方(UF)沿厚度方向从运动学角度假定运动场。沿厚度方向的位移场的近似阶数是一个自由参数,导致几个高阶梁单元考虑了剪切变形和局部截面翘曲。每个元素的节点数也是一个自由参数。单元的切线刚度矩阵是通过虚拟位移原理获得的。为了解决非线性控制方程,使用了总拉格朗日方法,并采用了牛顿-拉夫森方法。锁定现象通过张量分量的混合插值(MITC)来解决,这也可以显着提高所提出元素的收敛性能。对不同边界条件和细长比的梁状结构进行大位移,大旋转和小应变分析的数值研究表明,基于超滤的高阶梁理论可以更有效地预测位移和与二维有限元解决方案相比时的应力场。

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