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# 3.7.5: Principal Strains Approximation

Fig. 3.7.5.1: Approximation of principal strains in a grid of beams.

Karamba3D includes shell elements from which principal stress lines can be retrieved (see section 3.7.12). In case of single layer grid shells made up of beams the

**"Approximate Principal Strains"**-component can be used to determine the approximate principal strain directions of such structures (see fig. 3.7.5.1). It works on arbitrary sets of deformed points.The calculation of principal strains is based on the assumption of a continua. When applied to nodes connected with linear elements the result can thus only result in a qualitative picture -- therefore the term "Approximate".

The

**"Approximate Principal Strains"**-component expects as input a reference model (input-plug**"Model"**) and the same model in a deformed configuration (input-plug**"def.Model"**). The deformed model can be the output of a**"ModelView"**-component. Hand over a list of points to the input-plug**"Point"**where principal strain directions shall be computed. For each point in this list the following two steps are applied: First those three nodes of the reference model that do not lie on a line and have minimum distance to the given point are determined. Second the strains in the sides of the thus found triangle determine the principal strain directions -- plane stress is assumed. The conversion of first (output-plug**"VT1"**) and second principal strains (output-plug**"VT2"**) to vectors occurs in such a way that they align with the average displacement of the triangle that defines the corresponding strain-state. The size of the vectors emanating from**"VT1"**and**"VT2"**can be scaled by providing a factor in the input-plug**"Scale"**.The principal strains are tangents to the principal stress lines of a structure. Use e.g. Daniel Hambleton's

**"SPM Vector Components"**(see http://www.grasshopper3d.com/group/spmvectorcomponents) to retrieve these lines from the strain-vector-field.

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Principal_Strains_Approximation_SmallExample.gh

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