叶片有限元分析中弹塑性过渡区应力奇异产生原因及解决方法

Origin and Elimination of Stress Singularity in Blade Elasto-Plastic Transition Region in Finite Element Analysis

采用弹塑性有限元法、借助大型商业有限元软件对汽轮机叶片进行应力分析时,弹塑性过渡区应力的计算值有时会高于塑性区应力的计算值,即会产生应力奇异现象。为分析产生这一现象的原因,以8节点六面体单元为例,研究了有限元法计算应力的过程,并在理想弹塑性的条件下,采用有限元法和解析法计算了弹塑性过渡区单元节点应力。研究发现,有限元法通常采用高斯积分点应力值外推插值法得到单元节点应力,当单元一部分位于弹性区、另一部分位于塑性区时,这种外插算法会导致节点应力计算值高于结构的实际应力,甚至超出理想弹塑性材料的屈服极限,从而造成应力奇异。研究表明,在叶片弹塑性的有限元分析中,采用相邻高斯积分点应力加权平均的方法计算单元节点应力,可有效避免弹塑性过渡区应力产生奇异的现象。

When stresses of steam turbine blades are computed with the finite element method, sometimes the calculated stress in elasto-plastic transition region gets higher than the calculated stress in plastic region, namely there exits stress singularity. To explain this fact, the calculation process of nodal stress with finite element method is discussed in detail, where a kind of 8-node hexahedron element and an ideal elasto-plastic material model are chosen as the example. Nodal stresses of the elements in elasto-plastic transition region are comparatively calculated. It is found that in the finite element method the nodal stress is calculated via extrapolation of stresses at Gauss integration point in an element, and the calculated nodal stress maybe exceed the actual stress even the yield limit of ideal elasto-plastic material when one part of an element is located in elastic zone and the other part remains in plastic zone, thus stress singularity is brought out by the extrapolation algorithm. It is suggested that the nodal stresses are calculated in terms of weighted average stress at Gauss integration points of neighboring elements to effectively eliminate stress singularity.