盘─鼓结构体─壳过渡元的“虚假应力”现象及改进方法

分析了体—壳过渡元中产生“虚假应力”现象的根本原因，给出了两种改进方法。方案一是在采用体元应力应变模型的基础上提出了一种单元内位移、应变及应力的直接修改方法；方案二是将采用壳体应变应力状态的三维体—壳过渡元推广到轴对称，给出了具体公式。通过几个算例将上述两种方法与改进前方法进行了比较，结果表明本文提出的两种方案均大大改善了轴对称问题体壳过渡元的“虚假应力”现象，相比之下，前者公式简单，更易于实现。

FALSE STRESS IN AN AXIASYMMETRIC TRANSITION ELEMENT AND ITS IMPROVEMENT

The reason for generating the false stress in a transition element connecting a solid element to a thin shell element for stress analysis is considered.Then two schemes are presented to reduce the false stress in a transition element connecting an axisymmetric solid element to an axisymmetric thin shell element for axisymmetric stress analysis.In the first scheme,such a three-dimensional model as one in an axisymmetric solid element is adopted to solve global nodal displacements.Then direct modifications of displacements,strains and stresses are performed in each transition element.In the second scheme,a formulation of a six-node axisymmetric transition element is presented in such a plane stress model as one in an axisymmetric shell element.At last,several numerical examples are given.The comparison of the results obtained with the analytic solutions indicates that the both schemes presented in this paper can considerably reduce the false stress in an axisymmetric transition element and the formulation of the first scheme is simpler and easier to be performed.