直接基于单元平衡的梁非线性分析方法

Solution of the geometrical and material nonlinear beams by using direct element-based equilibrium framework

以单元力平衡条件为基础建立的梁单元在近年来受到广泛关注,与传统的以单元位移相容条件为基础建立的梁单元相比,基于平衡的梁单元可获得较高的精度。针对基于平衡的梁单元,给出了一种几何非线性分析方法,使用该方法进行几何非线性分析时不需进行单元内部位移场的构造,避免了使用现有位移场构造方法时可能引起的振荡问题,同时降低了有限元程序编制的难度,可实现几何非线性分析和材料非线性分析在程序代码层次上的"解耦"。当截面本构关系存在负刚度段时,基于平衡的梁单元出现变形集中而无法得到一致的负刚度段反应,给出了一种通过修正单元积分方案获得一致负刚度段反应的方法。编制了非线性有限元程序,数值算例验证了给出方法的可行性和有效性。

The development of beam elements based on the relationship of equilibrium has become a very active research field in recent years because the kind of elements is more accurate than elements developed based on the relationship of compatibility. A method for geometrical nonlinear analysis of the beam element developed based on relationship of equilibrium is proposed. The method has two superiorities than existing methods： （1） avoids the potential problem of oscillatory elemental displacement field; （2） simplifies the implementation of the finite element code by ＂decoupling＂ the codes of geometrical nonlinear analysis and material nonlinear analysis. The beam element developed based on relationship of equilibrium fail to present a consistent response in the case of section with negative stiffness because the localization of deformation. To resolve the problem, a modified numerical integration strategy is proposed. A nonlinear finite element code is then developed and numerical examples are provided in order to verify the feasibility and effectivity of the presented method.