关键词: 解析解, 理想塑性, 平面问题, 轴对称

Abstract: Infinite exact analytical solutions are derived for 2-D generalized axisymmetrical (only the tangential derivative is zero but not the tangential stress) ideal plasticity case. The derivation method is inspired by the classical methods as well as trial and error method. A series of solutions are listed as typical solutions. For example, the solutions expressed by power functions, trigonometric functions, exponential functions, logarithm functions as well as hybrid functions and so forth. The solutions suitable for all axisymmetrical cases(disk and rings) and those only suitable for rings are pointed out. The essential condition of disk solution is no tangential stress(narrow sense axisymmetric). The discussion of ideal plasticity in Ref.[1] is continued. It is confirmed again that an ideal plasticity condition given by Ref.[8] is a little bit different from the original classical one, which used in Ref.[8] perhaps has to be called quasi-ideal-plasticity condition. For both ideal plasticity conditions and both axisymmetrical cases, their similarlities and differences are discussed. At last, an exact analytical solution of classical ideal plasticity condition is given for generalized axisymmetrical case.

Key words: Analytical solution, Axisymmetrical, Ideal plasticity, Plane stress