Finite Element Analysis

Your partner for pressure vessel FEA

With Finite Element Analsysis, complex geometries and loading conditions can be modelled that cannot be analysed using the standard Design by Formula (DBF) rules of pressure vessel codes. Consider, for example, cyclic thermal loading, where the metal temperature distribution needs to be calculated, or the design of a nozzle with gussets or a nozzle close to a discontinuity in the shell geometry. These complex geometries and loading conditions can be modelled and analysed through Finite Element Analysis (FEA). At DRG, we regularly perform Finite Element Analyses (FEA) and assessments according to ASME VIII division 2 Part 5 or EN 13445-3. 
For these analyses we use the software packages Abaqus, CREO simulate, and FEPipe. Our knowledge in these areas also feeds through to our training courses in FEA software and pressure vessel design codes.
Our expertise with FEA includes:

Steps in an FEA assessment

An accurate 3D model of the relevant components needs to be constructed. If there is enough distance between components, isolated models can be constructed in order to reduce complexity and calculation time.

What is the temperature distribution within the vessel? Do significant local thermal gradients occur or are there large differences between components? Determining the (transient) heat transfer boundary conditions, and thereby the actual temperature distribution is a key part of most FEA analyses. Here we take care to ensure a conservative but credible case, which is either based on flow calculations with CFD, analytical formulas or HTRI results.

The calculated temperature distribution can be used as a boundary condition in the FEA model, together with the other loadings such as pressure and nozzle loads. With an elastic material model, the calculated stresses need to be categorized, it needs to be considered which load is primary (or weight driven) or secondary (displacement limited). It is important to consider which loads should be combined, for instance what is the range for the startup/shut down, or the operating cycle, or does the pressure load always act simultaneously with the thermal loading.

The results from a DRG analysis will always be documented in a detailed technical report. This will include all of the boundary conditions, details of the model setup and the analysis approach, and will be suitable for a rigorous review by a notified body. The report will also make sure that the results are explained to the client in a concise manner to build up to conclusions and practical recommendations.


1. Cyclic load assessment​

A cyclic loading assessment is required if the vessel does not conform to the fatigue screening criteria in ASME VIII-2 Part 5.5 or EN 13445-3 5.4. Cyclic loading can lead to the accumulation of micro strain, crack initiation and crack growth. A crack will typically reach macroscopic dimensions and cause failure after a high number of cycles (typically in the order of thousands, but there is no fixed limit).
On the other hand there is cyclic failure that can arise  due to a low number of cycles. This type of failure results from crack growth due to the build up of plastic strain, often called ratcheting.
FEA can be used to accurately calculate the stresses resulting from cyclic loading that can further be used to determine the fatigue damage to a vessel within its lifetime.

2. Non–standard geometry​

Not all geometries are covered by a standard design rule, think of the closure of a hairpin heat exchanger or a rectangular flange connection. One option is to expand the DBF approach to cover these geometries in a conservative manner. However, this most likely results in more material usage and the requirement to justify to the client or notified body why the method is conservative. With FEA, the geometry can be modelled in detail and stresses can be calculated. This provides a straightforward way to demonstrate code conformance. It also provides for the possibility to optimize the design, should the design not conform to the code specifications. 

3. Non-linear analyses​ 

When analyzing components under high tempe­ratures and stresses, the understanding of possi­ble creep deformations is of crucial importance. Creep is the tendency of a solid material to move slowly or deform permanently under the influ­ence of stresses well below the yield strength. It is a time-dependent deformation which does not occur suddenly under the application of stress. Rather, it is the accumulation of strain as a result of long-term stresses.
When a component deforms plastically, the stress in the component is redistributed. This behavior is not captured with a linear elastic material model. For some geometries the results of the stress assessment may be more optimistic when a plastic material model is used.

4. Nozzle flexibilities

FEA can be used to acurately determine flexibilities, Sustained Stress Indices (SSI) and Stress Intensification Factors (SIF) of nozzles on pressure vessels or Tee junctions in piping. Using this data helps in performing more accurate analyses of pipe stress, or allowable nozzle loads.