Parametric Design of Shell Structures

Written and presented at the SOFiSTiK Seminar 2018 by:
Dipl.-Ing. (TH) Thomas Kamrad M.Sc.Eng. | Centerlöf & Holmberg
Dipl.-Ing. (TH) Stefan Fässler M.Sc.Eng. | Centerlöf & Holmberg


A complete workflow for parametric design of shell structures is presented. The key elements are modules for geometric modelling, load application, post-processing within SOFiSTiK and interfacing with external programs. The workflow is demonstrated using a simple portal frame bridge. Adaptation possibilities for more complex structures are shown using a concrete tunnel monolith.

1 Background

Since 2009 Swedish road administration guidelines demand the use of shell/plate elements to consider 3D effects of significant point loads, which increases the complexity of the structural models. (Often to the point of excess)

The negative side effects of increased complexity are:

  • Tedious modelling of structure (e.g. 3D drawing of the model)
  • Tedious & error-prone modelling of loads
  • Labour intensive post-processing, due to the need for sectional force distribution (averaging)
  • Inflexible and error-prone model updating w.r.t. external design change

Employing parametric design counterbalances, the issues above and enables the structural engineer to focus on the actual design. Potential work increase is negated by the ability to recycle previous projects (template creation).

The advantages of the parametric design are demonstrated by showcasing the workflow steps for a portal frame bridge (an inhouse template is used). Finally, the adaptation potential for non-standard structures is exemplified using a tunnel monolith.

2 From drawing to the structural model

Tender/measurement drawings are used directly to generate a simplified FE model, where the used input is related to “real measurements” (e.g. clearances rather than the distance between system lines).

The model is generated using sections that are “filled in” with shell elements, which are grouped into evaluation areas.

Parametrization advantages:

  • Optimization possibility (e.g. testing of thicknesses automatically adjusts system lines)
  • Ease of adaption w.r.t. external design change
  • Geometry parameters can be used in later workflow steps
  • Structures that are close to the template are gene­rated extremely efficiently
Fig. 1 Workflow for parametric design
Fig. 1: Workflow for parametric design
Fig. 2 Principle design flow – geometrical modelling
Fig. 2: Principle design flow – geometrical modelling

3 Stationary load application

Basic non-transient loads, such as self-weight, superimposed dead load and earth pressure, are automatically applied to the structural model:

  • User input is restricted to basic information, e.g. weight of backfill and thickness of surfacing
  • Loads are defined using geometry parameters (previously defined during geometric modelling)
  • Loading is always restricted to groups

This combination gives high accuracy and eliminates the risk of applying the load on wrong surfaces or with wrong coordinates.
Even slightly more complicated loads are fully automatically applied

Fig. 3 2-step process - earth pressure due to horizontal live load
Fig. 3: 2-step process – earth pressure due to horizontal live load

Earth pressure due to braking or acceleration is a classic example of soil-structure interaction and depends both on the structural stiffness and the soil bedding. The loading is determined in a 2-step procedure:

  1. The relevant braking load and a unit triangular earth pressure are applied to the system. These two loads create deformations in the superstructure which are read from the database by means of @key commands.
  2. Based on those deformations, a realistic earth pressure is determined by scaling and applied.

Another example is horizontal forces on the wing walls due to traffic and backfill. The earth pressure from backfill is computed with increased earth pressure coefficients due to the slope of the backfill. The traffic effects are determined based on the dispersal of the loads through the backfill. All relevant angles and measurements are automatically derived from the geometry model.

Restraint loads, i.e. temperature and shrinkage, are altered to give reasonable result (especially in the lateral direction). Expansion due to temperature, for example, is fully applied to the superstructure/carriageway, however, in the front walls, the same load is linearly decreased towards the foundation.

4 Live load application

Despite the Eurocode load models, Swedish Regulations demand the application of 14 additional vehicles with a rather advanced loading pattern including varying wheelbases (1,7m – 2,3m) and varying longitudinal offsets. Moreover, most of the vehicles are non-symmetrical resulting in approximately 50 load models needing to be applied. Figure 4 gives an example of such a load group. Finally, even the military loads acc. to STANAG are to be considered.

Fig. 4 Example of special vehicle
Fig. 4: Example of special vehicle

Dealing with these complicating load patterns can be done in two alternative ways:

  1. A front-end for ELLA which creates all necessary load definitions and the relevant geometry (GAX, POSL) and loading conditions (CASE)
  2. An automated brute-force approach with ASE and MAXIMA

The approach with ELLA creates automatically all necessary lane configurations (GAX and POSL), see Figure 5. As a default, the complete area between the edge beam is defined as the relevant traffic area. However, the use of multiple GAX is possible, e.g. when having bridges in roundabouts.

Fig. 5 ELLA module, lane configuration
Fig. 5: ELLA module, lane configuration

A nominal lane is split it into two lanes representing each wheel. Since the lateral distance between two wheels can vary, this process must be repeated.

Finally, the worst load position for each vehicle is analysed by means of the COMB command.

The pros and cons of the ELLA approach are:


  • High probability of detecting the governing load situation
  • Input is rather straight forward, even for loads with varying distances
  • Output is restricted to the combined load cases
  • ELLA is a fast module in beam and small to midsize shell structures


  • Restriction to point or line loads. Modelling significant loads with point loads will r­sult in extreme values for sectional forces, especially shear
  • Unreasonable computational time for larger structures
  • Checking worst load placements is tedious

Modelling live loading with ASE is based on a brute-force approach. All load models are defined as discrete loads. The module considers the individual contact surfaces and dispersal through fill/asphalt and to the centreline of the structure. Thus, a set of area loads is created for each vehicle. These loads are then moved along a 3D-polyline. The 3D-polyline can be offset laterally to create multiple lanes. Varying longitudinal distances can be simulated by creating different load sets for each vehicle. Obviously, this will create a significant number of load cases.

The strengths and weaknesses using ASE/MAXIMA are:


  • Results are easily verifiable
  • Extreme values are heavily reduced resulting in a more economic design
  • Significantly faster in large FE-system


  • A large number of load cases
  • Higher computational cost in small and mid-size FE-systems
Fig. 6 Example of special vehicle G placed on a polyline. Isoline for principal shear force
Fig. 6: Example of special vehicle G placed on a polyline. Isoline for principal shear force

5 Postprocessing and Interfacing

Once a FE model is solved the eternal question is: What to do with the massive amount of results?

Common postprocessing approaches are:

  • Extracting numerical data directly (e.g. result viewer), which works well for beams due to a limited amount of data points
  • Analysing the data visually (e.g. WINGRAF), which works well for steel structure due to a minimal need for processing the results further

However, for concrete shell structures there exists a need of smoothing out sectional forces for reinforcement design and to export numerical data for external processing (e.g. excel). The data amounts are impractical for manual treatment; thus, a semi-automated workflow is required.

Smoothing can be performed by:

  • Utilizing WINGRAFs cuts function (preferably applied through TEDDY scripts)
  • “Manually” averaging the results for several elements (scripting by use of @key & element group numbers)

Data extraction routines can be scripted:

  • Internally, e.g. by using TEDDY’s @key functi­on in conjunction with text writing capabilities (Lower threshold for scripting)
  • Externally by accessing the database directly (Numerical speed advantage)
  • Results should be saved in text files for both approaches (broad combability)

Further external data treatment can be performed:

  • Completely detached from SOFiSTiK, e.g. in an environment of interlinked excel templates
  • External processing (e.g. C++ scripts), but with results written to CDB in order to piggyback the SOFiSTiK result tools (e.g. WINGRAF)

For the design of the portal frame bridge, all op­tions above are utilized:

The sectional forces in the longitudinal direction are transformed to dimensioning forces (e.g. mxx,d=mxx +  mue |mxy|) and even skew angles for reinforcement are considered.

The final forces are extracted to a central text document and all further design (Bending ULS, SLS, FLS and Shear ULS, FLS) is performed in an excel environment. All dimensions and forces in the various excel sheets are automatically fetched form the central document.

Design in the transversal direction is usually limited to bending ULS and SLS. This task is performed with a self-developed reinforcement tool. The resulting reinforcement amounts are saved in a CDB database and evaluated with WINGRAF.

Fig. 7 WINGRAF vs strip table
Fig. 7: WINGRAF vs strip table

6 Application for Advanced Structures

The presented approach steps for off-the-rack models can also be employed for bespoke structures.

Once a familiarity with the parametric workflow is established:

  • Initial geometric modelling (see Figure 8): Is performed with a limited time penalty, the crucial benefit consists of a greater control/certainty regarding dimensions. Furthermore, parametric variables can be employed in later steps (e.g. load application)
  • Stationary load application: Is always quicker and more controlled in a text-based environment.
  • Live load application: The presented tools are transferable to advanced models, with minimal input requirements
  • Postprocessing & interfacing (see Figure 9): The developed tools and approaches are especially valuable for advanced geometry
Fig. 8 Advanced structures - geometric modeling
Fig. 8: Advanced structures – geometric modeling
Fig. 9 Advanced structures - Postprocessing
Fig. 9: Advanced structures – Post-processing