This research focuses on generating the plastic collapse load boundaries of a cylindrical vessel with a radial nozzle via employing three different plastic collapse load techniques. The three plastic collapse load techniques employed are the plastic work curvature (PWC) criterion, the plastic work (PW) criterion, and the twice-elastic-slope (TES) method. Mathematical based determination of plastic collapse loads is presented and employed concerning both the PWC and the PW criteria. A validation study is initially conducted on a pressurized 90-degree pipe bend structure subjected to in-plane closing bending via finite element analyses along with an elaborate explanation of the mathematical approaches for determining the plastic collapse loads via the PWC and the PW criteria. Outcomes of the validation study revealed very good outcomes for the three techniques. Accordingly, the aforementioned three techniques are utilized to determine the plastic collapse load boundaries of a pressurized cylindrical vessel/nozzle structure subjected to in-plane (IP) and out-of-plane (OP) bending loadings applied on the nozzle one at a time. The TES method revealed considerate limitations when applied within the medium to the high internal pressure spectra. It is shown that both the PWC and the PW criteria outperform the TES method in computing the plastic collapse loads. The vessel/nozzle structure revealed relatively higher plastic collapse moment boundaries under IP bending as compared to OP bending. Conclusively, methodical steps are devised for determining the plastic collapse loads via the PWC and the PW criteria for the ease of systematic application on pressurized structures in general.

中文翻译：

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利用各种塑料塌陷载荷技术产生受喷嘴弯曲载荷的加压圆柱形容器/径向喷嘴结构的塑性塌陷载荷边界

本研究的重点是通过采用三种不同的塑性塌陷载荷技术来生成带有径向喷嘴的圆柱形容器的塑性塌陷载荷边界。采用的三种塑性塌陷载荷技术是塑性功曲率 (PWC) 准则、塑性功 (PW) 准则和两倍弹性斜率 (TES) 方法。提出并采用了关于 PWC 和 PW 标准的基于数学的塑性坍塌载荷测定。最初通过有限元分析对加压 90 度弯管结构进行了验证研究，并详细解释了通过 PWC 和 PW 标准确定塑性塌陷载荷的数学方法。验证研究的结果显示这三种技术的结果非常好。因此，上述三种技术用于确定加压圆柱形容器/喷嘴结构的塑性塌陷载荷边界，该结构受到一次一个施加在喷嘴上的平面内 (IP) 和平面外 (OP) 弯曲载荷. TES 方法在介质中应用于高内压光谱时显示出相当大的局限性。结果表明，PWC 和 PW 准则在计算塑性坍塌载荷方面都优于 TES 方法。与 OP 弯曲相比，IP 弯曲下的容器/喷嘴结构显示出相对较高的塑性塌陷力矩边界。最终，