本研究是旨在为成型压力容器封头制定合理设计规则的广泛调查的继续。该项目由压力容器研究委员会赞助和协调。这个问题是PVRC设计部门选择进行研究的首批研究项目之一，通过保持其兴趣，刺激了人们对看似相似的头部形状的不同行为进行越来越多的研究。在这项工作的过程中，不仅开发了新的分析技术，而且还发现了这些看似简单的几何形状特有的一些新的失效模式。这个问题的许多细节已经被研究过，尽管还有很多工作要做，但有足够的数据可以用来为更常见的碟形封头组装一套一致的设计规则。本报告旨在总结当前的最新技术，并为当前设计规则中的建议变更提供背景信息。 研究工作如下:首先讨论了复曲面球头的几何结构，描述了控制应力分布和失效模式的无量纲参数。接下来，总结了美国和国外设计规范的现状，并简要介绍了规范发展的历史背景。随后，给出了支持实验证据的可用分析结果，并描述了弹塑性和屈曲区域的结构行为和相应的失效概念。对分析方法进行了批判性评估，并针对理想几何形状提出了基于均匀安全裕度的设计标准。由此，确定了主要的几何参数，并评估了偏离完美形状的影响。最后，失效压力的数值以表格和图形形式组合，适用于规范设计规则。 总之，重新评估了设计程序拟议修订的可靠性，并讨论了未来工作的范围。

The present study is the continuation of an extensive investigation aimed at the development of rational design rules for formed pressure vessel heads. The program was sponsored and coordinated by the Pressure Vessel Research Committee. This problem was one of the first research projects the Design Division of PVRC selected for study and by maintaining its interest stimulated an increasing amount of work on the diverse behavior of seemingly similar head shapes. In the course of this work, not only new analysis techniques were developed but also a number of new failure modes unique to these deceivingly simple looking geometrical shapes were uncovered. Many of the details of the problem have been studied, and while much remains to be done, enough data became available to assemble a consistent set of design rules for the more common dished heads. This report is an attempt to summarize the present state-of-the-art and to provide the background information for the recommended changes in the present design rules. The study proceeds as follows: first the geometry of torispherical heads is discussed and the dimensionless parameters governing the stress distribution and failure modes are described. Next, the current status of the design codes in the U. S. and abroad is summarized and a brief historical background of the code development is presented. Following this, the available analysis results supporting experimental evidence are presented and the structural behavior and corresponding failure concepts for the elastoplastic and buckling regions are described. The analysis methods are critically evaluated and design criteria based on a uniform margin of safety are proposed for the ideal geometrical shapes. From this, the dominating geometry parameters are identified and the effects of deviations from the perfect shape are evaluated. Finally, the numerical values for the failure pressures are assembled in tabular and graphical forms which are adaptable for code design rules. In conclusion, the reliability of the proposed revisions of the design procedure is reassessed and the scope of future work is discussed.