Adaptive hierarchical refinement of NURBS in cohesive fracture analysis

Lin Chen, Erik Jan Lingen and René de Borst
Int J Numer Meth Engng. 2017;112:2151–2173, DOI: 10.1002/nme.5600


Adaptive hierarchical refinement in isogeometric analysis is developed to model cohesive crack propagation along a prescribed interface. In the analysis, the crack is introduced by knot insertion in the NURBS basis, which yields C−1 continuous basis functions. To capture the stress state smoothly ahead of the crack tip, the hierarchical refinement of the spline basis functions is used starting from a coarse initial mesh. A multilevel mesh is constructed, with a fine mesh used for quantifying the stresses ahead of the crack tip, knot insertion to insert the crack, and coarsening in thewake of the crack tip, since a lower resolution suffices there. This technique can be interpreted as a moving mesh around the crack tip. To ensure compatibility with existing finite element programs, an element-wise point of view is adopted using Bézier extraction. A detailed description is given how the approach can be implemented in a finite element data structure. The accuracy of the approach to cohesive fracture modelling is demonstrated by several numerical examples, including a double cantilever beam, an L-shaped specimen, and a fibre embedded in an epoxy matrix.

The importance of designing for pressure surges in an LNG bunkering line

R.J. Fawcett
LNG Industry, February 2017


Pressure surge represents a real risk to a piping
system. Figure 1 shows two failures that have occurred due to surge and the accompanying unbalanced forces not being adequately accounted for at the design stage. Figure 1 (a) shows a case where the pipe shoe has fallen from the concrete supports, whilst Figure 1 (b) shows an extreme case where a pipe has been ruptured.
This article aims to explain the risks of surge for an LNG bunkering line.

In-field vibration assessment of the piping of a reciprocating compressor plant

R.J. Fawcett and E.J. Lingen
3rd International Rotating Equipment Conference (IREC), Düsseldorf, 14 – 15 Sept. 2016


For a number of years visible vibrations were noticeable in the process piping connected to a reciprocating compressor at a refinery, this was despite a pulsation analysis having been conducted at the design stage. The effects of these vibrations were also visible in the small-bore instrumentation pipes, even though they were braced back to the main run pipe. The operator of the plant was worried that fatigue cracks could occur, especially in the small bore lines, and therefore a study was conducted to determine how the vibration levels could be reduced and whether they were leading to stress levels exceeding the endurance limit.


To calculate the stress magnitudes arising in the piping, including those in the small bore connections, a forced mechanical response analysis was performed using a numerical computer model. As well as using the as-built technical drawings the behaviour of the model was tuned to replicate the findings of in-field vibration measurements taken upon both the piping and the bracing. Tuning a piping model to replicate the dynamic behaviour of an operating piping system is not a trivial undertaking. Within this paper the effect of various factors that were given special attention in tuning (matching) the computational model will be discussed.


Attention was given on how to ensure that the correct mechanical mode shapes were present in the model and that they were excited to the same level as in the field. These mode shapes were identified from the vibration measurements taken using a three-axis accelerometer. Factors such as equipment weights within the piping, and gaps and stiffnesses in the supporting deviate to varying degrees from those envisaged at the design stage in any piping system. Consequently the mechanical resonance modes predicted by the numerical model, initially based on the as-built technical drawings, exhibited some differences from those measured in the field. This was in terms of their shapes but also their response at a given excitation frequency.


In tuning the model the stiffness of the spring loaded guide supports, both laterally and axially had to be varied, as well as the stiffness of the bracing of the small bore branches. Only by modifying these values was it possible to match the vibration amplitudes seen in the field with the computational simulation of the piping system. It is impossible to include these factors at the design stage and they are addressed by the requirement that all mechanical resonance modes should be above 2.4 times the compressor rotational speed. However unintentional installation factors could result in this margin not being met in the field, and thus this additional modelling step with a tuned model is required for determining the stress level and the margin of safety.


The output of the study was a robust set of conclusions to the operator of what changes should be made to ensure there was sufficient margin to prevent cracking in the line. The vibrations in the header lines were reduced using rigid supports where possible, given thermal expansion of the system, which have far fewer unknowns in their installation in the field than supports with pre-loaded springs. Additionally recommendations were given for the bracing and gussets on the small bore instrumentation lines so they were less sensitive to vibrations in the header.


In sharing this study though the intention is to increase the awareness of the factors that need to be considered when tuning a numerical piping model to replicate the field experience under a dynamic loading such as pressure pulsations. Thus improving the robustness of numerical simulations used for assessing potentially critical situations in the field. It is noted that the presented method is not as detailed as an Operating Deflection Shape (ODS) analysis of the system or an analysis in which the mechanical natural frequency and damping where de-termined directly. The method presented here though is easier to apply and is suitable for indicating relative im-provements to the system.

Comparison of initial accumulator design using analytical and numerical methods

C.W. Schoemakers and R.J. Fawcett
3rd International Rotating Equipment Conference (IREC), Düsseldorf, 14 – 15 Sept. 2016


Accumulators are used in order to reduce the pressure pulsations generated by reciprocating pumps. The design of such an accumulator is often done using an analytical sizing method at the start of the project. Depending on the system, the effectiveness of the accumulator on dampening the pulsations for a given system can be verified using an elaborate pulsation study according to the API 674 design code [3] in the later stages of the project. For other systems, the actual operation of the system is used to prove the correct accumulator design. This approach is almost trial-and-error as the analytical method used for the initial sizing of the accumulator can have significant short comings as will be shown in this paper. Improper accumulator design in the initial stages of a project can lead to costly system changes later on in the project, either by having to completely change the accumulator design, or in the adding and strengthening of pipe supports.


A comparison is made here between the analytical design method and a computational design method. The major characteristics of an accumulator are described using the computational meth-od. The results show that the analytical method should be used with caution when designing an accumulator and predicted pulsation levels can be significantly different from the actual pulsation levels. The results also verify an existing guideline of placing the accumulator as close to the pump as possible.


This study shows how the computational method can be used as an in-between method between the analytical sizing method and a full acoustical study of the complete study. The computational design method can be used by OEM’s of pumps and accumulators as an alternative to the analytical sizing method allowing for a more robust initial design of the pump and accumulator configuration at the start of a project, reducing cost at a later stage of the project by preventing last minute design changes.

A parallel linear solver exploiting the physical properties of the underlying mechanical problem

F.J. Lingen, P.G. Bonnier, R.B.J. Brinkgreve, M.B. Van Gijzen, C. Vuik
Comput Geosci (2014) 18:913–926, DOI 10.1007/s10596-014-9435-x


The iterative solution of large systems of equations may benefit from parallel processing. However, using a straightforward domain decomposition in “layered” geomechanical finite element models with
significantly different stiffnesses may lead to slow or non-converging solutions. Physics-based domain decomposition is the answer to such problems, as explained in this paper and demonstrated on the basis of a few examples. Together with a two-level preconditioner comprising an additive Schwarz preconditioner that operates on the sub-domain level, an algebraic coarse grid preconditioner that operates on the global level, and additional load balancing measures, the described solver provides an efficient and robust solution of large systems of equations. Although the solver has been developed primarily for geomechanical problems, the ideas are applicable to the solution of other physical problems involving large differences in material properties.

Nozzles – on external loads and internal pressure

C.J. Dekker, H.J. Bos
International Journal of Pressure Vessels and Piping, Volume 72, Issue 1, June 1997, Pages 1–18


Close comparison of local load stress calculation methods reveals considerable differences. To investigate we performed many finite element analyses of nozzles on cylinders concentrating not just on the shell stresses but also on the stresses in the nozzle wall. Local load stresses were sometimes found to be much higher in the nozzle than in the shell. This led us to formulate a ‘modified improved shrink ring method’ and to devise multiplication (contour-) charts for deriving local load nozzle stresses from local load shell stresses. Being important for a proper nozzle assessment, pressure induced stresses were investigated too. This resulted in non-dimensional parameter graphs to determine pressure induced stresses at nozzles. © 1997 Elsevier Science Ltd.