Users:General FEM Analysis/Elements Reference/Beam1

Coded, still under development and testing. Missing:

• documentation in Carat++-Wiki
• benchmark-examples

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Contents 1 General Description 1.1 Element Type 1.2 Degrees of Freedom 2 Input Parameters 2.1 Parameter Description 2.2 Example of a Complete Input Block 3 Element Loading 3.1 Pressure 3.2 Dead Load 3.3 Snow Load 4 Theory 4.1 Material parameter 4.2 Thickness parameter 4.3 Prestress directions on the surface 4.4 Prestress state &sigma 4.5 Lagrange type 5 References

General Description

Element Type

• This beam element is a linear 3D-beam taking into account shear deformation (Timoshenko-beam element).
• This beam element has 6 DOFs per node (three translations and three rotations)

Degrees of Freedom

For the Beam1 element use the 3 translatoric degrees of freedom DISP_X, DISP_Y, DISP_Z and the 3 rotatoric degrees of freedom ROT_X, ROT_Y, ROT_Z.

Input Parameters

Parameter Description

Compulsory Parameters
Parameter	Values, Default(*)	Description
MAT	EL-MAT int	Number for the used Material e.g. MAT=EL-MAT 1
AREA		Definition of the cross-sectional area of the beam
IYY, IZZ		Definition of the moments of inertia
KY, KZ	0	Shear correction factor; if 0 or no value specified, shear is not taken into account
Optional Parameters

Example of a Complete Input Block

EL-PROP 1 : BEAM1
MAT= EL-MAT 1
AREA=5.555  IYY=1.222  IZZ=1.333
KY=1.4   KZ=1.5

Element Loading

Pressure

• not defined yet

Dead Load

• not defined yet

Snow Load

• not defined yet

Theory

The element implementation follows mainly the implementation of a linear 3D-beam element in FELyX ^[1], Schwarz ^[2] and Wunderlich ^[3].

For the correct use of the membrane element and the interpretation of related results, the following aspects should be considered:

Material parameter

With the parameter MAT the material, that would be used in the calculation, for the membrane element is defined. A very popular mistake is that a material number would be used, that isn't defined already. Please ensure that the material that you would like to use at this point are already exits. The following materials are testet for the membrane element:

• linear elastic isotropic
• linear elastic orthotropic (Münsch-Reinhardt)
• multilinear elastic isotropic
• elastoplastic isotropic
• material on the basis of response functions

Thickness parameter

The parameter THICKNESS defines the thickness of the membrane. The thickness should be constant over the element.

Prestress directions on the surface

The parameters A_X, A_Y, A_Z and B_X, B_Y, B_Z are used to define the prestress directions on the surface. In this approach the principle directions of the prestress are defined in a plane area (see figure below). The definition of the area is given by the two vectors f₁ and f₂. The normal vector of the area can be calculated with the cross product of the in plane vectors f₃=f₁ x f₂. Afterwards the line of intersection T₁ of the area which is given by f₁ and f₃ and the curved surface can be calculated. In this approach T₁ is interpreted as the first principle direction of the prestress on the curved surface. With the assumption that T₃ is equal to the surface normal vector G₃ (not uniformed), the second direction of the prestress is calculated as T₂=T₁ x T₃. W.r.t. the parameters for the input file, only the plane area with the vectors f₁ and f₂ have to be defined. Referring to the depict approach the vector A defines the vector f₁ and the vector B defines the vector f₂.

Prestress state &sigma

SIG11, SIG22, SIG12 describes the prestress of the membrane element. The element is based on the plane stress assuption. Due to that only normal and shear stresses in the midplane have to be defined. SIGG11 is the stress acting in T₁, SIG22 acting in T₂ and SIG12 is the in plane shear, whereas SIG12=SIG21 (see figure below).

Lagrange type

With the LARANGE parameter it is possible to switch between form finding and statical/dynamical analysis. For the value UPDATED the element is for form finding and for the value TOTAL the element is for statical/dynamical analysis. It is important that the LANGRANGE parameter match to the type of analysis.

References

1. ↑ https://www.rdb.ethz.ch/projects/project.php?proj_id=8314
2. ↑ Schwarz, H.: Methode der Finiten Elemente, Teubner, 1991
3. ↑ Wunderlich, W.: Statik der Stabtragwerke, Teubner, 2004

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