LIMIT Sensoren

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Commonly, welded structures are composed of thin metal sheets where thicknesses are small compared to their other dimensions. These structures can be modeled accurately and efficiently with shell elements.

However, in many cases the model geometry is exported as a volume model by CAD systems, and building a shell model requires the extraction of mid-surfaces and merging of individual surfaces. These pre-processing steps can take a significant amount of time for complex structures.

Thus, many users prefer meshing the volume components directly with continuum Finite Elements. Automated meshing with tetrahedral continuum elements can be performed with particularly little effort. While modeling with continuum elements is straight-forward for static strength assessment, a fatigue assessment on the basis of the stress fields predicted by these models is difficult. Consequently, a lot of the benefits of the easier meshing procedure are lost. The stresses are a hybrid between local notch stresses and structural stresses and make a direct comparison to the admissible weld stresses defined in design codes difficult.

For the extraction of meaningful stress data from continuum FE models the structural hot spot stress concept was developed. In the literature different methods are proposed for defining structural stresses in the vicinity of notches. Generally speaking, the term structural stress implies a stress distribution which is linearized in thickness direction at the position of the notch. The linearized stress distribution gives the same effective membrane force and bending moment as the actual non-linear stress distribution. The next figure schematically shows different methods for defining linearized stress distributions:

  1. Extrapolation of linearized stresses (Hobbacher 2007)
  2. Linearization at the position of the notch
  3. Dong method (Dong,P., 2006, A Structural Stress Definition and Numerical Implementation for Fatigue Analysis of Welded Joints, International Journal of Fatigue, 25, pp 359–369), extrapolation based on local transverse forces

Methods determining Structural Stresses
Abb.: Methods for determining the Structural Stresses in Solid FE Models (Fricke, W. and Kahl, A., 2005, Comparison of Different Structural Stress Approaches for Fatigue Assessment of Welded Ship Structures, Marine Structures, 18, pp 473–488)

The actual numerical determination of the structural stresses at the notch position is difficult owing to local effects such as singularities. A frequently employed method is described in the recommendations of the IIW (Hobbacher 2007). Here, the linearized stress distributions are determined in well-defined distances from the notch, and then the stresses are extrapolated for calculating the actual structural stress. For obtaining meaningful results, fine meshes fulfilling strict requirements with regard to allowable element types and the necessary mesh refinement are necessary. In practice, this kind of meshing is not economically feasible for complex components. Using tetrahedral meshes in combination with the IIW structural stress concept is also an option, but only if the element size is approximately 0.3 times the component thickness. The first element row adjacent to the notch must be located distal of the reference points (Löffler, P., Modellstudien für die Entwicklung eines universellen Strukturspannungskonzepte (in german), Diploma Thesis, FH Oberösterreich).

In practice, traditionally used structural stress concepts prove to be ill-suited for the assessment of continuum element models.

CAE Simulation & Solutions has developed an innovative concept for translating the results obtained with continuum Finite Element models into a form which is suitable for efficient assessment.

The primary solution quantities of classical Finite Element methods are the displacements at the nodes of the structure (displacement-oriented formulation). By interpolating the nodal displacements using the shape functions of the element, the displacement field anywhere within the structure can be described. The displacement fields are continuous between adjacent elements. In contrast, the stress distributions are usually not continuous across element borders. This complicates the calculation of structural stresses from element stresses.

If the displacement field in the vicinity of a notch is resolved with sufficient accuracy, results will contain the information necessary for the calculation of structural stress. In an experimental investigation, strain gauges would be applied to the component’s surface and stresses at the assessment points would be calculated from measured strains. 

The extraction algorithm for structural stress in LIMIT works very similar to this experimental procedure. By means of so-called sensor elements the displacement data is extracted at selected points and transformed into structural stresses following linear stress-strain relationships. The sensor elements can be envisaged as virtual shell elements, which are embedded into the geometrical mid-surfaces of continuum element models during postprocessing and fit the deformation field of the continuum model to the shape functions of an equivalent shell element. The calculation of equivalent section forces and equivalent linearized stress distributions for the sensor element is then comparatively straight-forward.  The assessment points follow the specification of the IIW while the continuum element mesh does not have to obey these rules.

For two sensors, the next figure shows the sensor points at which the displacement fields of the FE model are probed.  A group of nine sensor points is located in the mid-surface and close to the two surfaces. From the displacements in these points LIMIT can calculate all necessary characteristic stress values in the sheet plane. In addition, the shear deformation distribution over the shell thickness is calculated and considered in the determination of structural stresses. The magenta points in the next figure indicate the locations of reference points, at which the linearized stress distributions over the shell thickness are assessed. The red dots show the location of the hot spots to which the stresses are extrapolated for subsequent assessment.

Fig.: Reference Points of Sensors

Besides the stress values in the red reference points, LIMIT can also calculate averaged stresses in the sensor centers. This stress value is comparable to the result given by a four-node shell element with only one integration point in the center of the element.

For the assessment of throat sections the section forces can also be determined from data provided by sensors.


The main advantages of this procedure are:

  • - The only requirement for the solid mesh is a sufficient resolution of the structural displacements.
  • - The sensors are independent of the underlying solid mesh and can be used for different meshes as long as the geometry is the same.
  • - The Methods also works in connection with TIE constraints.
  • - The size of the averaging zone for the results can be controlled via sensor dimensions.

Schweissnaht Sensoren
Fig.: Global weld assessment results visualized with sensors

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