原文来自加拿大PVENG公司网站，这里翻译了一下，仅供参考。

报告编写风格是多样的，审查的要求也是多样的，确保本质安全，灵活处理。

有限元分析报告要求

FEA Submission Requirements

Last Updated: Aug 19 2015, By: LRB

CSA B51-14“锅炉，压力容器和压力管道”附录J“压力容器设计有限元分析要求”概述了有限元分析报告的要求。这些要求在附录J中是强制性的，但在整个加拿大并不被广泛接受。现在阿尔伯特省审查仍然要求按照ABSA AB-520，ABSA AB-520与CSA B51-14附录J 相似但是不完全相同。下面的斜体字部分是摘自B51的部分内容。

The requirements for FEA reports are outlined in CSA B51-14 annex J “Annex J (normative) Requirements regarding the use of finite element analysis (FEA) to support a pressure equipment design submission”. These requirements are mandatory to B51, but not universally accepted across Canada. At this date (Aug 2015) Alberta reviews are still done to ABSA AB-520, a similar but not identical document. Some extracts from the B51 standard are included in italics below.

J.1总则

J.1 General

分析设计需要具备压力容器设计、有限元基础以及有限元分析软件方面广博的知识和经验。设计者选择的有限元分析软件应可用于压力容器设计。

This analysis method requires extensive knowledge of, and experience with, pressure equipment design, FEA fundamentals, and the FEA software involved. The FEA software selected by the designer shall be applicable for pressure equipment design.

有限元程序是物理引擎。我们发现主流商业软件都适用于压力容器分析设计。虽然我们采用SolidWorks Simulation 和 ABAQUS，但其他的软件也是可以的。

FEA programs are physics engines. We have found that any of the main commercially available programs are suitable for pressure vessel analysis. In particular we use SolidWorks Simulation and ABAQUS, but others also work.

J.2 报告要求

J.2 Submission requirements

当结构形状在ASME规范中没有相应设计方法可采用有限元分析进行压力容器设计。设计人员应与监管机构确认有限元分析是可以被接受的。当分析设计被用来证明设计的合规性，应满足J.3和J.10的要求。

FEA may be used to support pressure equipment design where the configuration is not covered by the available rules in the ASME Code. The designer should check with the regulatory authority to confirm that use of FEA is acceptable. When this method is used to justify code compliance of the design, the requirements in Clauses J.3 to J.10 shall be met.

总体说来我们发现使用有限元分析进行非标项设计或者部分设计是可以被接受的。能用标准计算的要用标准进行计算，这一点在计算中很重要。在少数情况下，产品被要求进行重新设计，这样规则设计部分可以被使用。

In general we find it acceptable to use FEA for design of non code items or portions of items. It is important to include code calculations for those portions of the vessel that are code calculable. On rare occasions a product is forced to be re-designed so that regular code sections can be used.

J.3 专项设计要求

J.3 Special design requirement

有限元分析和报告应由熟悉有限元分析方法并具有丰富经验的人员完成。有限元分析报告应由专业工程师认证。

The FEA analysis and reports shall be completed by individuals knowledgeable in and experienced with FEA methods. The FEA report shall be certified by a professional engineer.

我们有时会被要求提供一份经验报告。请参阅我们的联系人页面，在那里我们为审查工程师贴出了资格简历。例如，Ben、Cameron和Matt的简历已被撰写，以展示执行有限元分析和审查有限元分析报告的资格。

We sometimes get asked to provide a report of our experience. See our Contacts page where we have posted qualification resumes for our review engineers. For example, the resumes of Ben, Cameron and Matt have been written to present qualifications for performing FEA and reviewing FEA reports.

对于J.4到J.10节的要求我们参考有限元分析样例报告章节。写这些样例报告是为了满足之前省里面这样或者那样的指导文件。除了CSA指导，我们的样例报告也被修改以回答CRN审查工程师和客户的常见问题。

For the sections J.4 through J.10 we refer to sample reports found in our FEA samples section. These reports are written to meet this or various previous provincial guidelines. Beyond this CSA guideline, our sample reports are also modified to answer common questions from CRN review engineers and customers.

J.4报告执行摘要

J.4 Report executive summary

有限元分析报告应包含执行摘要以简述有限元分析是如何被用于支持设计的，采用的有限元模型，有限元分析结果，结果的准确性，结果的验证，结论。

The FEA report shall contain an executive summary briefly describing how the FEA is being used to support the design, the FEA model used, the results of the FEA, the accuracy of the FEA results, the validation of the results, and the conclusions relating to the FEA results supporting the design submitted for registration.

J.5 报告引言

J.5 Report introduction

报告的引言应描述一下有限元分析与设计相关的内容，采用有限元分析支持设计计算的必要性判断，有限元分析采用的软件，有限元分析的类型（静力，动力，弹性，塑性，小变形，大变形等），分析所使用的材料特性完整描述，有限元分析所采用的模型假设。

The report introduction shall describe the scope of the FEA analysis relating to the design, the justification for using FEA to support the design calculations, the FEA software used for the analysis, the type of FEA analysis (static, dynamic, elastic, plastic, small deformations, large deformations, etc.), a complete description of the material properties used in the analysis, and the assumptions used for the FEA modelling.

J.5 有限元模型介绍

J.6 Model description

J.6.1

报告应包含一段内容用以介绍有限元分析所采用的模型。描述内容应包括实际承压设备几何尺寸信息和/或者图纸信息。应说明几何模型的简化及其合理性。网格和单元类型，形状，自由度，阶数。如果采用了不同类型的单元，应当说明不同单元是如何连接在一起的。当采用壳单元是应当给出单元顶面方向或者底面方向示图，应指明他们是厚壁还薄壁单元。

The report shall include a section describing the FEA model used for the analysis. The description shall include dimensional information and/or drawings relating the model geometry to the actual pressure equipment geometry. Simplification of geometry shall be explained and justified as appropriate. The mesh and type (h, p, 2D, 3D), shape, degrees of freedom, and order (2nd order or above) of the elements used shall be described. If different types of elements (mixed meshes) are used, a description of how the different elements were connected together shall be included. When shell elements are being used, a description of the top or bottom orientation with plots of the elements shall be included and shall indicate if they are thick or thin elements.

J.6.2

模型描述应列出所有假设。

The model description shall include a list of all assumptions.

J.6.3

应标明内圆角半径上每个单元的转角。

The turn angle of each element used on inside fillet radii shall be indicated.

转角只是绕一个圆所需的单元数。Inventor技术文件介绍了转角的使用。正常情况下，一个圆孔需要大约8个单元，每个单元会产生45度的转角。减小转角会增加单元的数量和提高有限元分析结果的准确性，但并非模型的所有区域都需要高精度。转角没有提供任何预测值，B51标准也没有提供验收标准。下面J.6.8中讨论的误差图是网格和结果质量的比较有用的判断依据。

The turn angle is simply the number of elements it takes to go around a circle. This Inventor support page explains the use of a turn angle. It is normal that a mesher needs around 8 elements to get around a circular hole which would produce a turn angle of 45 degrees per element. Decreasing the turn angle increases the number of elements and the accuracy of the FEA results, however not all areas of a model need to be highly accurate. The turn angle does not provide any predictive value, and the B51 standard provides no acceptance criteria. The use of an error plot as discussed in J.6.8 below is a much more useful measure of mesh and results quality.

J.6.4

单元整体尺寸的选择或者局部网格细化所采用的方法应当给与说明。

The method used to select the size of mesh elements with reference to global or local mesh refinement shall be indicated.

采用误差图来判断网格是否足够准确。标准里面没有说明的，但是很重要的一点，就是意识到压力容器结构不连续部位随着网格尺寸的减小应力会趋于无穷，容器应力超出了材料屈服强度。参考我们的线性化分析样例报告，应力线性化可以处理应力趋于无穷的情况。

We use the error plot to determine if the mesh is adequately refined. Beyond the scope of this standard, it is important to realize that pressure vessels have areas of discontinuity where in theory the stress approaches infinity as the mesh size is decreased. In practice the vessel experiences stresses above the yield point. Refer to our sample jobs for linearization analysis that can deal with stresses approaching infinity.

J.6.5

当分析中涉及到接触，应当说明模型中两个分离体接触部位是如何连接的。应使用足够的网格尺寸，以确保单元足够小，以正确模拟接触应力分布。

When items in contact (e.g., flange joints, threaded joints) are modeled, the model shall describe how two separate areas in contact are linked. Adequate mesh size shall be used to ensure that the elements are small enough to model contact stress distribution properly.

J.6.6

边界条件，例如支撑，约束，载荷，接触单元和力，应描述清楚，在报告中图示出来。应对防止模型发生刚体位移的所施加的约束进行说明和判断。当使用部分模型时（通常基于对称性），应描述部分模型的基本原理，并说明对称截面的边界条件。

Boundary conditions, such as supports, restraints, loads, contact elements, and forces, shall be clearly described and shown in the report (present the figures). The method of restraining the model to prevent rigid body motion shall also be indicated and justified. When partial models are used (typically based on symmetry), the rationale for the partial model shall be described with an explanation of the boundary conditions used to compensate for the missing model sections.

J.6.7

有限元分析报告应包括有限元分析结果的验证和确认。验证应说明有限元分析结果正确描述了压力设备的实际行为，确认应说明提交给有限元分析解决方案的数学模型已正确求解。

The FEA report shall include validation and verification of FEA results. Validation should demonstrate that FEA results correctly describe the real-life behavior of the pressure equipment, and verification should demonstrate that a mathematical model, as submitted for solution with FEA, has been solved correctly.

验证很简单，只需将有限元分析运行的反作用力与边界条件下可计算的理论载荷进行比较。验证可接受的内容因审查者而异。很少必须提供预测爆裂试验结果的有限元分析。有时，必须提供应变计测试或位移测试，这些测试可以根据标准的无损水压测试进行。使用的其他方法是将Roark预测的壳体径向位移与模型运行结果进行比较。最常见的是，人们认识到，满足本标准其他要求的有限元分析比其他可用研究方法更准确，因此不需要进一步的物理测试证明。

Verification is as simple as comparing the reaction forces from the FEA run with the theoretical loads that can be calculated at the boundary conditions. What is acceptable for validation varies by reviewer. Rarely FEA runs must be provided that predict burst test results. Occasionally strain gauge testing or displacement testing must be provided that can be run against a standard non destructive hydrotest. Other methods used are comparing Roark’s predicted radial displacement of a shell with the results of a model run. Most commonly, it is recognized that a FEA run that meets the other requirements of this standard is far more accurate than other available methods of study so no further physical testing proof is required.

J.6.8

有限元分析结果的准确性分析应包括在有限元分析报告中，方法是进行收敛分析或与之前成功的内部模型的准确性进行比较。收敛研究的误差应小于等于5%。

The accuracy of the FEA results shall be included in the FEA report, either by the use of convergence studies or by comparison to the accuracy of previous successful in-house models. An error of 5% or less from the convergence study shall be acceptable.

注：有限元分析误差通常包括离散化误差和计算误差，离散化误差是由于单元的固有限制而导致的几何匹配和位移分布，计算误差是计算机浮点计算和数值积分方案公式的舍入误差。

Note: FEA inaccuracy usually consists of discretization errors, which result from matching geometry and displacement distribution due to the inherent limitation of elements, and computational errors, which are round-off errors from the computer floating-point calculation and the formulations of the numerical integration scheme.

收敛性分析仅说明模型的单个点已经收敛，而误差图证明了整个模型，不需要多次FEA运行。如J.6.4所述，我们使用误差图来证明收敛性。同样如上所述，并非压力容器模型的所有区域都收敛。没有收敛的部位需要进行的特殊分析，通常通过ASME VIII-2第5部分所述的线性化处理。

A convergence study only proves that a single point of a model has converged, whereas an error plot proves a whole model and does not required multiple FEA runs. As mentioned in J.6.4, we use error plots to prove convergence. Also mentioned above, not all areas of a pressure vessel model converge. The areas that do not converge require special study that cannot be handled by convergence studies. These areas are usually handled by Linearization as outlined by ASME VIII-2 part 5.

J.7 评定准则

J.7 Acceptance criteria

有限元分析结果的评定准则应基于建造规范和根据该规范建立的安全系数。FEA方法可基于另一规范。评定准则和规范应在报告中给出。

The criteria for acceptance of the FEA results shall be based on the code of construction and factor of safety established under that code. The FEA methodology may be based on another code. The acceptance criteria and code reference shall be presented in the report.

注：例如，如果建造规范为ASME规范VIII-1，则允许应力值来自ASME规范VIII-1，有限元分析方法可基于ASME规范VIII-2（图5.1）。

Note: For example, if the code of construction is Section VIII, Division 1, of the ASME Code, the allowable stress values are from Section VIII, Division 1, of the ASME Code. The FEA methodology could be based on Section VIII, Division 2, of the ASME Code (Figure 5.1).

J.8 结果的展示

J.8 Presentation of results

J.8.1

应提供以下信息和彩图：

（a） 总位移（图）；

（b） 变形形状与未变形形状叠加；

（c） 带网格的应力图

（c） （i）采用彩色条纹图例表示应力范围；

（c） （ii）允许在应力集中的大小和网格的大小之间进行比较；

（d） 单元应力云图，并比较节点（平均）应力与单元（非平均）应力；

（e） 反作用力与施加荷载的比较；

（f） 应力线性化方法和关注区域的应力值；

（g） 有限元分析结果的准确性。

应绘制结果，以图形方式验证收敛性。该图的x轴应显示感兴趣区域内网格密度的一些指示（曲线上的元素数量、单位长度的元素等）。这对于显示仅由于网格相对较小的变化而导致的真实收敛和明显收敛是必要的。

The following information and figures in colored prints shall be presented:

(a) resultant displacements (plot);

(b) deformed shape with undeformed shape superimposed;

(c) stress plot with mesh that

(c)(i) shows fringes using discrete color separation for stress ranges or plots; and

(c)(ii) allows comparison between the size of stress concentrations and the size of the mesh;

(d) plot with element stress and a comparison of nodal (average) stress vs. element (non-averaged) stress;

(e) reaction forces compared to applied loads (free-body diagrams);

(f) stress linearization methodology and the stress values in the area of interest; and

(g) accuracy of the FEA results.

The results shall be plotted to graphically verify convergence. The x axis of this plot shall show some indication of mesh density in the area of interest (number of elements on a curve, elements per unit length, etc.). This is necessary to show true convergence over apparent convergence that is due only to a relatively small change in the mesh.

J.8.2

当呈现图表或图形时，应包括与每个图形相关的说明，以说明图形的用途及其重要性。

When plots or figures are presented, an explanation relating to each figure shall be included to describe the purpose of the figure and its importance.

J.9 结果分析

J.9 Analysis of results

整体模型结果，包括高应力和变形区域，应与评定准则一起提交。分析应包括结果与评定准则的比较。

Overall model results, including areas of high stress and deformation, shall be presented with acceptance criteria. The analysis shall include a comparison of the results with acceptance criteria.

应确定要忽略的结果，并且应证明忽略这些结果的决定是合理的。

Results that are to be disregarded shall be identified, and the determination to disregard them shall be justified.

J. 10结论

结论至少应包括

（a） 支持设计的有限元分析结果总结；

（b） 结果与评定准则的比较；

（c） 总的建议

J.10 Conclusion

As a minimum, the conclusion shall include

(a) a summary of the FEA results in support of the design;

(b) a comparison of the results and the acceptance criteria; and

(c) overall recommendations.