Three-dimensional nonlinear displacement-based beam element for members with angle and tee sections
Three-dimensional nonlinear displacement-based beam element for members with angle and tee sections
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用于角钢和 T 形截面构件的基于三维非线性位移的梁单元
DOI：
10.1016/j.engstruct.2021.112239
复制
发表时间：
2021
影响因子：
5.5
通讯作者：
Hajjar, Jerome
中科院分区：
文献类型：
--
作者：
Du, Xinlong;Hajjar, Jerome
角钢、三通等非对称薄壁型材广泛应用于各种钢结构中。为了解决这些结构因飓风和地震等极端事件而遇到的极端极限状态，捕获由于静态或动态载荷引起的大变形而产生的响应非常重要。在非线性大变形状态下，由于所谓的瓦格纳效应以及不重合的剪切中心和质心，这些构件耦合了轴向-弯曲-扭转变形。在 OpenSees 共旋转框架中制定并实现了三维共旋转总拉格朗日梁单元，通过引用基本系统的格林-拉格朗日应变来解释这些耦合效应。在基本系统中，剪切力和扭矩是相对于剪切中心定义的，轴向力是相对于质心的，弯曲是围绕截面主轴但在包含剪切中心的平面中定义的。将虚功原理得到的控制方程线性化，得到单元切线刚度矩阵。开发中采用了横向位移的三次埃尔米特函数以及轴向和扭转变形的线性形状函数。在进行共旋转变换之前，所有单元端部力和位移都被变换为作用于剪切中心。为了纠正非拉伸弯曲模式下的膜锁定，轴向应变中的高阶弯曲项被恒定的有效应变所取代。通过将横截面离散成纤维网格，跟踪每根纤维处的钢单轴应力-应变本构，并对横截面进行数值积分以获得截面刚度矩阵，来考虑循环材料非线性。该公式与一组实验和数值结果进行比较，以验证该单元可以准确有效地模拟几何和材料非线性。
Asymmetric thin-walled sections such as steel angles and tees are widely used in a range of steel structures. To address extreme limit states that these structures encounter due to extreme events such as hurricanes and earthquakes, it is important to capture their response due to large deformations caused by static or dynamic loading. In the nonlinear large deformation regime, these members have coupled axial-flexural–torsional deformation due to the so-called Wagner effect and the noncoincident shear center and centroid. A three-dimensional corotational total Lagrangian beam element is formulated and implemented in the OpenSees corotational framework to account for these coupling effects by invoking Green-Lagrange strains referenced to a basic system. In the basic system, shear forces and torque are defined with respect to the shear center, axial force is referred to the centroid, and flexure is defined around the section principle axes but in the planes containing the shear center. The element tangent stiffness matrix is derived through linearization of the governing equation obtained from the principle of virtual work. Cubic Hermitian functions for the transverse displacements and a linear shape function for the axial and torsional deformation are adopted in the development. Before conducting the corotational transformation, all element end forces and displacements are transformed to act about the shear center. In order to remedy membrane locking in the inextensional bending mode, the high order bending terms in the axial strain are replaced by a constant effective strain. Cyclic material nonlinearity is considered by discretizing the cross section into a grid of fibers, tracking the steel uniaxial stress–strain constitutive at each fiber, and performing numerical integration over the cross section to obtain the section stiffness matrix. The formulation is compared against a set of experimental and numerical results to validate that the element can model geometric and material nonlinearities accurately and efficiently.
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非线性弹性非均匀扭转
DOI：
10.1061/(asce)0733-9445(2005)131:7(1135
发表时间：
2005
期刊：
Journal of Structural Engineering-asce
影响因子：
--
作者：
N. Trahair
通讯作者：
N. Trahair
影响因子：
5.5
作者：
Siu;S. Kitipornchai
通讯作者：
S. Kitipornchai
对局部和/或扭曲屈曲构件进行基于梁单元的分析：应用
影响因子：
6.4
作者：
Xi Zhang;K. Rasmussen;Hao Zhang
通讯作者：
Hao Zhang
DOI：
10.1061/(asce)0733-9445(1992)118:11(2949
发表时间：
1992-11
期刊：
Journal of Structural Engineering-asce
影响因子：
--
作者：
Y. Pi;N. Trahair
通讯作者：
Y. Pi;N. Trahair
影响因子：
6.4
作者：
Martins, Andre Dias;Camotim, Dinar;Dinis, Pedro Borges
通讯作者：
Dinis, Pedro Borges