压力容器的应力分析有着悠久而活跃的历史。它的发展自然与壳理论的发展相联系，并与之同步。1888年，Love推导出了控制弹性壳（如压力容器及其封头）中应力的基本方程。这些方程的一些早期解，直接适用于压力容器分析，是在世纪之交由H.Ressiner、Meissner和他们的学生完成的。这涉及Dubois、Honegger、Bolle和Wissler对球形、锥形和环形旋转壳的研究。然而，就压力容器设计过程而言，这些非常详细的工作所涉及的艰苦手工计算过去是，现在仍然是令人望而却步的。因此，工程师们转向发展近似技术，从而减少分析和计算工作量。除其他方法外，这次搜寻还找到了那口井- 已知的薄膜近似法，其中忽略了壳体的弯曲阻力。这种分析方法大大简化了壳体应力的计算，并随着壳体变薄而提高了精度。它被纳入了美国机械工程师协会（ASME）非燃烧压力容器规范，直到最近才被牢固地纳入其中。该方法的主要缺点是，它引入了不一致性，从而错误地预测了匹配壳体之间连接处、支撑点和局部弯曲源处的应力。基于这些局限性，瓦茨和布伦斯敦促恢复使用1949年提出的抗弯理论。因此，压力容器研究委员会启动了一个项目，在洛夫最初的理论框架内对不同封头的圆柱形压力容器进行分析。

The analysis of stresses in pressure vessels has had a long and active history. Its development has, naturally, been tied to and kept pace with the advancement of the theory of shells. The basic equations which govern the stresses in an elastic shell, such as a pressure vessel and its heads, were derived in 1888 by Love. Some early solutions of these equations, which were directly applicable to pressure vessel analysis, were carried out by H. Ressiner, Meissner, and their students at the turn of the century. This involved studies of spherical, conical, and toroidal shells of revolution by Dubois, Honegger, Bolle, and Wissler. The arduous hand computations that were involved in these remarkably detailed efforts were, and still are, however, prohibitive as far as the pressure vessel design process is concerned. Engineers, therefore, turned to the development of approximate techniques in which the analytical and computational labor could be reduced. This search led, among other methods, to the well-known membrane approximation in which the resistance of the shell to bending is ignored. This method of analysis greatly simplifies the calculation of stresses in shells and improves in accuracy as the shell becomes thinner. It found its way into the ASME Code for Unfired Pressure Vessels and has been firmly lodged therein until recently. The chief shortcoming of the method is that it introduces inconsistencies and thereby incorrectly predicts the stresses at junctions between mating shells, at points of support and at local sources bending. On the basis of these limitations Watts and Burrows urged a return to the use of the original theory with bending resistance included in 1949. As a result the Pressure Vessel Research Committee embarked upon a program in which cylindrical pressure vessels with various heads were analyzed within the framework of Love's original theory.