Formfinding and Membrane Analysis

This page descibes the simulation of prestressed membranes (isotropic and anisotropic) for analysis and formfinding which is implemented in the StructuralMechanicsApplication. The implentation is based on the following sources:

• Numerical Methods for the Design and Analysis of Tensile Structures, Falko Hartmut Dieringer
• Mechanik und Numerik der Formfindung und Fluid-Struktur-Interaktion von Membrantragwerken, Roland Wüchner

Prestressed Membrane Element

The prestressed membrane element (prestressed_membrane_element.h) is designed in such a way that it is suitable for both formfinding and membrane analysis. The prestress can either be read from a .mdpa file (which could for example result from a formfinding analysis, example see following code)

Begin ElementalData MEMBRANE_PRESTRESS
1	[3,1]((1.0),(1.0),(1.0))
2	[3,1]((2.0),(1.0),(-1.0))
3	[3,1]((3.0),(1.0),(6.0))
4	[3,1]((5.0),(2.0),(1.0))
5	[3,1]((6.0),(3.0),(-5.0))
End ElementalData 

or from a projection (planar or rotational, see picture). The prestress, the projection type and the projection direction(s) are defined in the material. In the rotational case the variable PRESTRESS_AXIS_1_GLOBAL defines the axis of rotation. The entries in the PRESTRESS_VECTOR define the components for ["radial prestress", "tangential prestress", 0]:

{
    "properties" : [{
        "Material"        : {
            "Variables"        : {
                "PRESTRESS_VECTOR": [6000,5000,0]
                "PROJECTION_TYPE_COMBO": "planar"
                "PRESTRESS_AXIS_1_GLOBAL: [1 0 0],
                "PRESTRESS_AXIS_2_GLOBAL: [0 1 0]
}}}]}

{
    "properties" : [{
        "Material"        : {
            "Variables"        : {
                "PRESTRESS_VECTOR"      : [100,0,0],
                "PROJECTION_TYPE_COMBO" : "radial",
                "PRESTRESS_AXIS_1_GLOBAL" : [0,0,1],
}}}]}

The projection of the prestress is executed by the method ProjectPrestress. The distinction between formfinding and membrane analysis is set by the value IS_FORMFINDING. If IS_FORMFINDING = True, the update reference strategy is applied where the base vectors are updated in each nonlinear iteration (Method: ComputeBaseVectors). In the case of prestress adaption, the prestress is updated in the method UpdatePrestress.

Formfinding Analysis

The formfinding analysis is executed in `formfinding_updated_reference_strategy.hpp<´. In order to use the formfinding strategy the following parameters have to be included in the parameter input file:

"solver_settings"          : {
        "solver_type"                        : "Static",
        "echo_level"                         : 2,
        "analysis_type"                      : "formfinding",
        "line_search"                        : false,
        "print_formfinding_iterations"       : true
    }

In order to use the result of a formfinding analysis for further simulations, the necessary information (whole modelpart or prestress data) can be printed in an output file using the formfinding_io_process. The same process can be used in subsequent simulations to read the prestress data.

"list_other_processes": [
        {
            "python_module": "formfinding_IO_process",
            "kratos_module": "KratosMultiphysics.StructuralMechanicsApplication",
            "help": "This process is for input and output of prestress data",
            "process_name": "FormfindingIOProcess",
            "Parameters": {
                "model_part_name": "Structure",
                "print_mdpa": true,
                "print_prestress": false,
                "read_prestress": false
            }}]

Formfinding example

The following pictures show an example where the formfinding is executed for a 4-point-sail. Isotropic prestress is applied by a planar projection. The first picture shows the original geometry and the second picture the formfinding result.