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针对剪式铰单元的单肢,建立了平面3节点梁单元模型。首先根据Lagrange插值理论建立了3节点梁单元的位移场,其中用二阶多项式表示梁单元的轴向位移场,五次多项式表示梁单元的横向位移场,然后根据有限元理论推导出了3节点梁单元的线性刚度矩阵。通过改变剪式铰单元中间节点的位置,可以得到不同情况下的单元线性刚度矩阵。最后通过算例验证了3节点梁单元的计算正确性,为更复杂剪式可展结构的有限元计算提供了理论基础。
For single limbs of scissor-hinge unit, a planar 3-node beam element model is established. Firstly, according to Lagrange interpolation theory, the displacement field of 3-beam element is established. The second-order polynomial is used to represent the axial displacement field of the beam element. The fifth-order polynomial is used to represent the lateral displacement field of the beam element. According to the finite element theory, Linear stiffness matrix of beam elements. By changing the position of the middle node of the shear hinge unit, the linear stiffness matrix of the unit under different conditions can be obtained. Finally, an example is given to verify the correctness of the calculation of the 3-node beam element, which provides a theoretical basis for the finite element calculation of the more complex scissor-like structure.