基于曲率插值的大变形梁单元

线性梁单元的形函数在单元大转动时会引起虚假应变，不适用于几何非线性分析．传统的几何非线性梁单元由于位移插值和转角插值的相干性，常常引起剪切闭锁等问题．该文 提出了一种平面大变形梁单元，通过单元域内的曲率插值以及曲率与节点位移之间的函数关系，将单元节点力和节点位移表示为节点曲率的函数．由于曲率插值本质上是对梁的应变进行插值，保证了单元任意刚体运动不会产生虚假的节点力；且将梁的截面形心位移表示为曲率的函数，避免了传统单元中的剪切闭锁问题．因而所提方法特别适用于梁的几何非线性分析．数值算例说明了所提方法的正确性和有效性.

Large Deformation Beam Element Based on Curvature Interpolation

The shape functions of linear beam element, which will cause the false strain when large rotation occurs, does not apply to geometric nonlinear analysis. Because of the coherence of the interpolation of the displacement and angle, traditional geometric nonlinear beam element is often caused by problems such as shear locking. A plane large deformation beam element was proposed, by use of the interpolation of curvature and the functional relationship between the curvature and nodal displacements . The element node forces and displacements were expressed as a function of the curvature. Essentially the interpolation of the beam curvature is strain interpolation，which ensures that the element rigid body motion does not produce false node force; the shear locking in traditional element is avoided because the beam centroid displacement is expressed as a function of curvature. Thus this method is especially suitable for geometry nonlinear analysis of the beam. The numerical examples show the truth and validity of the proposed method.