基于网格截面法的非线性梁单元

Nonlinear Beam Element with Meshed Sections

为准确描述材料进入非线性阶段后的应力状态,针对采用梁单元时框架结构材料非线性的有限元分析问题,提出了基于分布式塑性理论的三维材料非线性梁单元分析方法——网格截面梁单元法,并通过算例对其有效性和准确性进行了验证.这种方法采用平面等参单元将梁单元截面网格化,通过引入材料本构模型,由截面网格材料的应力-应变关系和应力分别积分得到梁单元的截面刚度矩阵和截面抗力,再通过位移插值函数计算梁单元在材料进入非线性阶段时的单元刚度矩阵和节点抗力.

Based on the distributed plasticity approach, a new kind of beam element, 3-D materially nonlinear beam element with meshed sections, was presented to analyze the materially nonlinear behaviour of frame structures accurately, and a numerical example for the elasto-plastic analysis of a cantilever beam was given to illustrate the accuracy and efficiency of this approach. With this approach, beam sections are discretized into planar isoparametric elements at the integral points along the longitudinal direction of beam element, the stiffness matrices and resistant forces of sections are calculated by introducing the nonlinear stress-strain relations of materials and respectively integrating the stress-strain relations and stresses of sections, and the element stiffness and nodal resistant forces can also be evaluated with displacement interpolation functions when materials are in a nonlinear state.