Geometrically exact hybrid beam element based on nonlinear programming
Geometrically exact hybrid beam element based on nonlinear programming
复制标题
基于非线性规划的几何精确混合梁单元
DOI：
10.1002/nme.6663
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发表时间：
2021
影响因子：
2.9
通讯作者：
Papakonstantinou, Konstantinos G.
中科院分区：
文献类型：
--
作者：
Lyritsakis, Charilaos M.;Andriotis, Charalampos P.;Papakonstantinou, Konstantinos G.
本文提出了一种剪切-柔性梁混合单元，每个单元只需一个单元，就能捕捉平面框架结构任意大的非弹性位移和转动。根据Reissner几何精确理论，本文采用非线性规划原理，以总势能为目标函数，以精确的应变-位移关系为运动约束，建立了有限元问题的数学模型。通过适当的求积对积分表达式进行逼近，通过引入拉格朗日乘子，形成极小化规划的拉格朗日算子，并在满足必要的最优性条件的基础上求解。除了两个单元边缘节点的位移自由度外，质心的应变测量在求积点处作为未知变量，而只对曲率场进行内插，以加强整个单元的协调性。弹塑性计算是通过在横截面水平上对材料应力-应变定律进行数值积分来进行的。给出并讨论了该单元的解锁行为，并通过一组著名的数值算例验证了其整体性能。将结果与解析解(如果有)以及基于柔度的梁单元和四边形单元的结果进行了比较，验证了公式的有效性。
This work presents a hybrid shear‐flexible beam‐element, capable of capturing arbitrarily large inelastic displacements and rotations of planar frame structures with just one element per member. Following Reissner's geometrically exact theory, the finite element problem is herein formulated within nonlinear programming principles, where the total potential energy is treated as the objective function and the exact strain‐displacement relations are imposed as kinematic constraints. The approximation of integral expressions is conducted by an appropriate quadrature, and by introducing Lagrange multipliers, the Lagrangian of the minimization program is formed and solutions are sought based on the satisfaction of necessary optimality conditions. In addition to displacement degrees of freedom at the two element edge nodes, strain measures of the centroid act as unknown variables at the quadrature points, while only the curvature field is interpolated, to enforce compatibility throughout the element. Inelastic calculations are carried out by numerical integration of the material stress‐strain law at the cross‐section level. The locking‐free behavior of the element is presented and discussed, and its overall performance is demonstrated on a set of well‐known numerical examples. Results are compared with analytical solutions, where available, and outcomes based on flexibility‐based beam elements and quadrilateral elements, verifying the efficiency of the formulation.
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具有不同应变测量的两种几何非线性梁模型的比较研究
影响因子：
3.2
作者：
A. Panteli;K. Spiliopoulos
通讯作者：
K. Spiliopoulos
影响因子：
0.8
作者：
M. Lucchesi
通讯作者：
M. Lucchesi
DOI：
10.1016/0045-7825(95)00724-f
发表时间：
1995-04-01
影响因子：
7.2
作者：
IBRAHIMBEGOVIC, A
通讯作者：
IBRAHIMBEGOVIC, A
平面框架的弹塑性破坏载荷
DOI：
--
发表时间：
1963
期刊：
Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
影响因子：
--
作者：
M. Horne
通讯作者：
M. Horne
影响因子：
2.2
作者：
I. Planinc;M. Saje;Bojan Cas
通讯作者：
Bojan Cas