Pressure Vessel Analysis is something that many engineers have spend (and made) their careers on- so you shouldn’t expect to find the answers overnight, or in a packaged piece of software. Nevertheless, the following important points will put you on the right track to become a pressure Vessel FEA Expert.

**1. In which case do I have to use FEA Analysis for Analysis of Pressure Vessels ?**

The codes do not specify to use of specific analysis methods in design, but Finite Element Analysis Now Predominates. The analysis capability has greatly outgrown the Pressure Vessel Design Code requirements, but problems may arise in interpreting code guidelines.

I’d suggest that you take a long, hard look at Part 5 of the 2007 edition of Div. 2. If you’re just getting into vessel FEA you might as well start with the latest, and the new Div. 2 was written to be much more “numerical analysis friendly” than the various variants of the 1968 version. The Div. 1 rules are along the same lines as the old (and parts of the new) Div. 2 with S (primary), 1.5*S (primary membrane & bending), and 3*S (primary & secondary) limits.

**2. Can I get ASME Code for Free ?**

The ASME and EN Codes are not free, and if you ever ask for them for free you will be kicked out. They are copyrighted material, and to ask for them to be given to you for free is highly unethical.

Why do you want to get into this industry? How do you expect to do that if you aren’t willing to “put a little skin in the game”? What do you think that you can offer competing against other engineers that have been doing this their entire careers?

**3. What is design by Analysis ?**

Before 1963, all Pressure Vessels were designed using a systematic Design by Formula Approach which was based on experience and simple mechanics. What was mostly described was how to keep hoop stress low with respect to yield and how to use ductile material to accommodate local peak stresses.

In the Design by formula, the vessel geometry and major dimensions such as radius, length, etc. are specified and the required thickness is then calculated for a given load using equations and graphical data. With the development of the nuclear technology in the 1950s, pressure vessel design requirements needed to be improved in order to permit the use of higher allowable stresses without reduction in Safety.

This required to change the philosophy of Code design by formula. It is also worth to note that advances in mechanics theory and analysis methods provided new and more scientific methods for the pressure vessel design.

In 1963, ASME published the B&PV Code Section III: Nuclear Vessels based on the principles of limit analysis (Shakedown analysis, Fatigue Analysis) and Stress Analysis was used to determine higher allowable loads and more consistent margins of safety.

This New code permitted two approaches for design:

- Improved design by formula, providing more accurate formula for sizing common components and higher allowable stresses, was intended for standard configurations
- Design by Analysis, in which designer performs stress analysis and evaluates results against code limits, was intended for configurations not covered by the Design By Formula

The main guidelines of the Design By Analysis are to prevent the gross plastic deformation or ductile burst under static load, the incremental plastic collapse under repeated or cyclic load and the fatigue under cyclic load. Elastic buckling, creep, brittle fracture, stress corrosion, etc. also have to be considered…

**4. What is Stress Categorization ?**

It is assumed (sensibly) that different types of loading, or different types of stress, require different allowable stress limits. Since terms like ‘membrane’ and ‘bending’, are often used rather loosely, ASME chose to strictly define different STRESS CATEGORIES to which different limits were to be applied.

Elastic stresses are categorized into three classes.

- Primary stress is associated with gross plastic deformation.
- Secondary stress (plus primary stress) is associated with incremental plastic collapse.
- Peak stress (plus primary, plus secondary) is associated with fatigue failure

Each “type” of stresses is limited to different allowable values specified in terms of a design stress

Additionally, a distinction has to be made between General Primary Membrane Stress and Local Membrane Stress.

**5. Should I mesh my model with Solid or Shell Elements ?**

Meshing with solid elements is typically easier, but membrane and bending can’t be separated out (as with shell elements). That’s where WRC 429 comes in handy with methods for linearizing the stresses in solid models.

**6. What is Stress Linearization ?**

In the finite element method, when structural elements are used in an analysis, the total stress distribution is obtained. Therefore, to produce membrane and bending stresses, the total stress distribution shall be linearized on a stress component basis and used to calculate the equivalent stresses.

If shell elements (shell theory) are used, then the membrane and bending stresses shall be obtained directly from shell stress resultants.

For starters, I would recommend obtaining and reading WRC Bulletin 429. I provides a good description of the linearization for 3D FEA. As far as classification goes, you are right – it is very subjective. Unfortunately, there is no way around that – I would recommend reading the “Criteria of the ASME Boiler and Pressure Vessel Code for Design by Analysis in Sections III and VIII, Division 2” document published by ASME

**7. What are the limitations of elastic analysis and the potential problems?**

The Major Problem is stress categorization because:

1) Stress distribution must be defined in terms of membrane, bending and peak stress.

2) Stress cannot be always linearized everywhere in a vessel

3)In practice, designers usually regard linearization as valid throughout the vessel for both 2D and 3D models

**8. What major problems lie in the interpretation of the finite element analysis results?**

Designers have to obtain linearized membrane and bending stresses first, then assign these to the appropriate stress category, so if the stress is assigned as a Primary Stress, yield will be limited, but the design may be over-conservative. If the stress is considered as a secondary stress, the yield limit will be multiplied by 2, which makes it possibly not conservative. Unfortunately, the code guidance is quite limited on this topic

**9. What is the current status of inelastic analysis in different codes ?**

The analysis is related directly to inelastic failure mechanisms (Gross plastic deformation and Ratchetting). Some routine inelastic FEA capabilities have now overtaken DBA guidelines and different types of inelastic analysis are included in the different codes.

PD5500 Inelastic DBA considers limit analysis for gross plastic deformation check. An elastic-perfect plastic material model is used and small deformation theory is used: The analysis is evaluating the limit load, then the allowable load is 2/3 of the limit load. This analysis is relatively simple to perform and requires only code material data. It may be applied also to non-standard configurations

EN13445 Inelastic DBA considers limit analysis but additional accounts for geometric weakening. No rules or procedures are given for including material strain hardening (enhances load carrying capacity). It may be applied to any configuration

ASME VIII Inelastic DBA uses limit analysis procedures similar to PD5500. Additionally, geometric non-linearity and strain hardening effects may be incorporated in a “plastic analysis”.

“Plastic Load” is defined by application of a “criterion of plastic collapse”. The allowable load is 2/3 the plastic load. This plastic load is plastic criterion dependent and leads often to a plastic load which is similar to a limit load. Shakedown analysis procedures are limited and not generally well understood. Inelastic shakedown analysis is permissible but not widely used (incremental and bounding theorem approaches).

**10. Is it possible to replace the physical tests of a pressure vessel by FE Analysis ?**

Not to throw cold water here, but MODELS NEVER PROVE ANYTHING. If you offered me an untested vessel that passed FEA I’d not only throw you out, I’d burn your business card.

Models are great for pointing out weaknesses that need to be beefed up prior to a physical test. They are really good for finding design bottlenecks that can be corrected prior to putting welder to metal. BUT, at the end of the day you have to build the vessel and break it.

I’m seeing a lot of areas where people are replacing testing with FEA and other computer simulations. Sometimes with disastrous results. When you call modeling “proof” you get bad engineering, bad science, and horrible regulations.