【摘要】 摄动法是解决非线性连续介质力学问题的一种有效方法.这种方法是建立在该问题的线性解析解的基础上的,因此,若得不到一个简单的解析解,应用这种方法去解决一些复杂的非线性问题将遇到困难.有限元法对解非线性问题也是一种十分有用的工具,然而一般来说,它需要相当长的计算时间. 本文介绍摄动有限元法.这种方法吸取上述两种方法的优点,能够解决更复杂的非线性问题,而且也能大量节省计算机的计算时间. 本文讨论了比例加载下的弹塑性力学问题,并提出一个带孔拉板的数值解.更多还原

【Abstract】 Perturbation method is one of the effective methods for solving problems in nonlinear continuum mechanics. It has been developed on the basis of the linear analytical solutions for the original problems. If a simple analytical solution can not be obtained, we would encounter difficulties in applying this method to solve some complicated nonlinear problems. The finite element method appears to be in its turn a very useful means for solving nonlinear problems, but generally it takes too much time in computation. In the present paper a mixed approach, namely the perturbation finite element method, is introduced, which incorporates the advantages of the above-mentioned two methods and enables us to solve more complicated nonlinear problems with great saving in computing time.Problems in the elastoplastic region have been discussed and a numerical solution for a plate with a central hole under tension is given in this paper.更多还原