基于柔度的网格截面非线性梁单元

A FLEXIBILITY BASED BEAM ELEMENT WITH MESHED SECTIONS

梁单元材料非线性有限元求解时,材料进入非线性阶段后,难以通过梁理论准确描述截面的应力状态,该文据此提出了基于柔度法和分布式塑性理论的梁单元材料非线性方法-网格截面法,这种方法采用平面等参单元将梁单元网格化,由单元轴向积分点位置截面网格积分点的应力描述单元截面应力分布,并通过对截面网格材料的积分得到积分点位置的截面刚度,并运用基于柔度的有限元方法,通过力插值函数和能量原理得到梁单元的柔度矩阵,进而对柔度矩阵求逆以计算单元刚度矩阵。同时讨论了该方法在进行结构材料非线性有限元分析时的优越性。最后通过算例验证了上述结论。

A new beam element based on distributed plasticity and flexibility theory is presented for material nonlinear analysis of frame structures, In this formulation, the sections at the axial quadrature points of beam element are discretized into plane isotropic elements, and the stress distribution on the sections is described with the stresses at quadrature points in the mesh. The stiffness matrices of the sections are calculated by integration of the stress-strain relations of material on the meshes. The flexibility matrix of the element is also formed by integration of section flexibility matrices with force-interpolation functions, and then is inverted into the element stiffness matrix. The advantages of the flexibility method are discussed in the paper. Finally a numerical example is given for nonlinear analysis of a beam to illustrate the efficiency and accuracy of the method.