摘要
在循环加载下壳体结构的安定分析,特别是对于具有应变强化的材料制成的壳体结构的安定分析具有很大的实际意义.文中对随动强化材料的安定定理有了进一步的认识并应用它去分析壳体结构的安定载荷.对于一个真实状态其残余应力与塑性应变之间是相关的.但我们在定理中所示的与时间无关的残余应力场(?)和与时间无关的几何容许的塑性应变场(?)可以是不相关的.明确指出这点对于工程应用带来很多方便,否则将是十分困难的.为此还给出了该定理的新的证明方法.我们还应用了上述定理对一个半球封头的圆柱壳体进行了安定分析.根据所求得的弹性解,各种可能的残余应力和塑性应变分布,结构的安定分析可归结为一个数学规划问题.计算结果表明应变强化材料的安定载荷要比理想塑性材料的安定载荷高出30～40％,这说明在安定分析中考虑材料强化是重要的,可使壳体结构的设计承载能力有相当大的提高,同时对改进目前壳体结构的设计提供了科学依据.
It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.
In this paper, some further understanding of the shakedown theorem for kinematic hardening materials has been made, and it is applied to analyze the shakedown of shell structures. Though the residual stress of a real state is related to plastic strain, the time-independent residual stress field a as we will show in the theorem may be unrelated to the time-independent kinematically admissible plastic strain field For the engineering application, it will be much more convenient to point this out clearly and definitely, otherwise it will be very difficult. Also, we have proposed a new method of proving this theorem.
The above theorem is applied to the shakedown analysis of a cylindrical shell with hemispherical ends. According to the elastic solution, various possible residual stress and plastic strain fields, the shakedown analysis of the structure can be reduced to a mathematical programming problem.
The results of calculation show that the shakedown load of strain hardening materials is about 30-40% higher than that of ideal plastic materials. So it is very important to consider the hardening of materials in the shakedown analysis, for it can greatly increase the structure design capacity, and meanwhile provide a scientific basis to improve the design of shell structures.
出处
《应用数学和力学》
EI
CSCD
北大核心
1989年第11期969-976,共8页
Applied Mathematics and Mechanics
