The plastic node method: A new method of plastic analysis
The plastic node method: A new method of plastic analysis
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塑性节点法：塑性分析的新方法
DOI：
10.1016/0045-7825(82)90103-7
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发表时间：
1982
影响因子：
7.2
通讯作者：
T. Yao
中科院分区：
文献类型：
--
作者：
Y. Ueda;T. Yao
1968年，上田和他的同事在塑性增量理论的基础上发展了新的塑性铰机构，并推导了一维杆件的弹塑性和塑性刚度矩阵。利用这种塑性铰链，发展了一种考虑大挠度影响的空间框架结构弹塑性分析方法，在此基础上，扩展了塑性铰方法的基本思想，提出了一种新的板体塑性分析方法。用普通有限元方法(刚度法)给出了新方法的基本理论，该理论将单元结点处的屈服条件描述为：“当结点处的综合应力满足适当的塑性条件时，该结点变为塑性，塑性变形仅在结点处发展”。在这个意义上，作者将这种方法命名为塑性节点法。对于有塑性节点的单元，节点力增量dx与节点位移du之间的关系导出如下：dx=kpDu。Kp这个方程是弹塑性或塑性刚度矩阵，并以显式表示。当单元承受恒定应变时，如果在任一点满足屈服条件，单元在整个体积内变成塑性的。同时，在单元的每个节点上形成塑性节点。无论是用普通有限元方法还是用塑性节点法，都可以得到完全相同的塑性刚度矩阵。当板单元受到均匀弯曲时，也可以观察到类似的事实。由此可知，当单元剖分增加时，该方法的解精度与普通有限元方法的精度相当。塑性节点法对于塑性分析是非常普遍的，因为它可以应用于任何几何形状的连续体，用该方法进行的实例分析证明了该方法的有效性和实用性。
In 1968, Ueda and his colleagues developed the new mechanism of plastic hinge based on the incremental theory of plasticity and derived the elastic-plastic and plastic stiffness matrices for one-dimensional members. Using this plastic hinge, a method of elastic-plastic analysis of space-framed structures was well developed including the effect of large deflection.In this paper, extending the basic idea of this plastic hinge method, a new method for plastic analysis of plates and solid bodies is developed. The basic theory of the new method is presented using the ordinary finite element method (the stiffness method).In this theory, the yield condition at theith node of an element is described as follows: “Theith node becomes plastic when the resultant stresses at this node satisfy the appropriate plasticity condition and the plastic deformation is developed only at the nodes”. In this sense, the authors named this method the ‘Plastic Node Method’.For the element withkplastic nodes, the relation between the increments of the nodal force, dx, and the nodal displacement, du, is derived in the following form:dx=Kpdu.Kpin this equation is either elastic-plastic or plastic stiffness matrix and is expressed in explicit form.When an element is subjected to constant strain, the element becomes plastic in the entire volume if the yield condition is satisfied at any point. Simultaneously, the plastic node is formed at every node of the element. Completely the same plastic stiffness matrix is obtained by either the ordinary finite element method or the present plastic node method. A similar fact is observed when a plate element is subjected to uniform bending. From these facts the accuracy of the solution by this method is anticipated to be the same order as that by the ordinary finite element method when the element division increases.The plastic node method is quite general for plastic analysis since this can be applied to a continuum of any geometrical shape, and example analyses by this method demonstrate the validity and usefulness of the method.