The Application of Finite Element Modelling to Pressure Vessel Design Codes

To ensure that a pressure vessel operates safely over its entire lifetimes it is designed to a nationally recognised design code. To date the most widely used codes are ASME VIII [1] and BS 5500 [2]. Within Europe, BS5500 has recently been reissued as a national standard, pd5500, and from May 2002, all vessels wil have to comply with the new draft European standard prEN 13442. These codes specify the minimum requirements for design, materials, fabrication and testing of pressure vessels. The design criteria are intended to guard against the following modes of failure:

  • Gross Plastic deformation
  • Incremental Collapse
  • Buckling
  • Fatigue
  • Creep

The main design section of the codes consists of a series of design rules based on strength of materials equations and empirical formulae. This method of design is commonly referred to as the ‘Design by Rule’ (or Design by Formula) approach. These equations and formulae cover the most common geometries found in vessel design such as flat plates, cylinders, spheres, etc. However, when designs are more complex it becomes difficult to apply Design by Rule without building in large factors of safety to cover for approximations made in representation of geometry.

To cover the design of more complex vessel geometries a separate section of the code was written to use the results from numerical analyses and is termed the ‘Design by Analysis’ approach. This section of the code was originally based on shell discontinuity analysis and the Tresca criterion and acceptable stress levels are prescribed in terms of membrane, bending and peak stress intensities. Engineers attempting to use FEA to design vessels to code are faced with the requirement to translate the stress results into a form that is compatible with these stress intensity levels, or with the inelastic limit load and shakedown analyses requirements that are included in the new prEN13445-3 (based on ASME inelastic Design by Analysis route).




List of Figures


Pressure Vessel Design codes 

  • Linear Elastic Analysis
  • Design by Rule
  • Design by Analysis
  • Applying Code Linear Elastic Criteria to FEA
  • Inelastic Analysis
  • Gross Plastic Deformation
  • Incremental Collapse

Case Study: GD Engineering Bandlock closure

Finite Element Modelling

  • Linear Elastic Analysis
  • Monotonic Elastic Plastic Analysis
  • Cyclic Elastic-Plastic Analysis
  • Linear Elastic Fracture Mechanics Analysis

Application of Design Code Criteria

  • Linear Elastic Results
  • Monotonic Elastic Plastic Results
  • Cyclic Elastic Plastic Results
  • Fracture Results

Review of Results of Bandlock Closure Analyses
Discussions on the Application of the Finite Element Method to Pressure Vessel Design Codes


Appendix: Visual Basic code for Kroenke’s method

Document Details

AuthorsWarrior. N Durrant. J
Date 1st January 2000


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