General descriptions of follower forces derived via a geometrically exact inverse contact algorithm
General descriptions of follower forces derived via a geometrically exact inverse contact algorithm
复制标题
DOI：
10.1002/nme.5253
复制
发表时间：
2016-12
影响因子：
2.9
通讯作者：
A. Konyukhov
中科院分区：
文献类型：
--
作者：
A. Konyukhov
几何精确接触理论的主要特征是，计算所需的所有对象、弱形式和残差、线性化弱形式和正切矩阵都在与接触对的几何形状相对应的局部坐标系中以协变封闭形式给出。这样可以轻松构建法向和切向从动力的计算算法作为逆接触算法。在这种情况下，按照给定的从动力的定义并且在局部坐标系中不改变，我们必须考虑从动力的定义而不是接触界面的本构关系来修改接触的所有对象。主要特征是法线部分和切线部分的切线矩阵被分成旋转部分和曲率部分，对于任何近似阶数都是对称的。本文选择以下数值示例来说明实现的有效性：（1）在 2D 和 3D 情况下对纯弯曲进行建模，其中力矩可以作为一对单力或分布式从动力（压力）施加； (2) 应用分布式随动件法向力（压力）对板的膨胀进行建模； (3) 应用切向从动力算法对矩形截面梁的扭转进行建模。版权所有 © 2016 约翰·威利父子有限公司
The main feature of the geometrically exact theory of contact is that all objects, which are necessary for computation, weak form and residual, linearized weak form, and tangent matrices are given in a covariant closed form in the local coordinate system corresponding to the geometry of contact pairs. This allows easily to construct computational algorithms for the normal and tangential follower forces as an inverse contact algorithm. In this case, following the definition of the follower forces as given and not changing in the local coordinate system, we have to modify all objects for the contact taking into account the definition of follower forces instead of constitutive relationships for the contact interfaces. The main feature is that the tangent matrices for both normal and tangential part being split into the rotational and the curvature parts are symmetric for any order of approximation. The following numerical examples are selected in the current article to illustrate the effectiveness of implementation: (1) the modeling of a pure bending with a moment applied either as a pair of single forces or a distributed follower forces (pressure) in both 2D and 3D cases; (2) modeling of inflation of a plate as application of the distributed follower normal forces (pressure); and (3) modeling of twisting of a beam with the rectangular cross‐section as application of the tangential follower forces algorithm. Copyright © 2016 John Wiley & Sons, Ltd.