Users:General FEM Analysis/Elements Reference/Truss1

From Carat++ Public Wiki

< Users:General FEM Analysis | Elements Reference(Difference between revisions)

Jump to: navigation, search

Latest revision as of 07:35, 13 January 2017

General Description

Element Type

This TRUSS1 element is a truss element with 3 translational degrees of freedom per node
The truss element neglects bending and torsional stiffness
The ratio of the cross-sectional dimensions and the length is much smaller than 1( a/L << 1 and b/L << 1), the truss is reduced to its center-line
The cross-sectional area is constant over the element
The truss element is also used as a cable, as which it can also account for prestress

Degrees of Freedom

The membrane element uses the 3 translatoric degrees of freedom, DISP_X, DISP_Y, DISP_Z.

Input Parameters

Parameter Description

Parameter	Values, Default(*)	Description
Compulsory Parameters
MAT	EL-MAT int	Number for the used Material e.g. MAT=EL-MAT 1
AREA		cross-section area of the cable
SIG11		Prestress of the cable.
Optional Parameters
Parameter	Values, Default(*)	Description
LAGRANGE	TOTAL, UPDATED	Definition of lagrange type. UPDATED for form finding and TOTAL for statics or dynamics. (e.g. LAGRANGE=UPDATED)

Example of a Complete Input Block

EL-PROP 1 : TRUSS1
MAT= EL-MAT 1   AREA=1.0
PRESTRESS       SIG11=1.0

Element Loading

Being a line element not all general load cases are applicable.

Dead Load

implemented

Theory

The theory and finite element formulation is described in detail in ^[1] , ^[2] and ^[3].

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

Material parameter

With the parameter MAT the material that is used in the calculation is defined. Being a line element with constant, fixed cross-sectional area, only linear elastic isotropic is foreseen for now.

Cross-section area parameter

The parameter AREA defines the cross-section area of the truss. The area is assumed constant over the element and throughout the computation.

Lagrange type

With the (optional) 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.

Tests and Benchmarks

The element Truss1 has successfully been tested in 3D in various linear and geometrically non-linear static applications, as well as in dynamic analyses, be it as columns/trusses or as a (prestressed) cable.

Benchmark examples

cable under dead weight in a static geometrically non-linear analysis in a planar configuration: ..\examples\benchmark_examples\elements\truss1_dead_nln\cbm_trusss.dat
two-bar truss with arc-length path following: ..\examples\benchmark_examples\analyses\stanln_2bartruss_arclength_l\cbm_2bartruss_arclength_fixed.dat
dynamic eigenfrequency analysis of a prestressed string (modelled as a cable of trusses): ..\examples\benchmark_examples\analyses\eigenvalue_truss1_I\cbm_vib_row_50_elm.txt
form-finding of a four-point sail where the TRUSS1 is used as edge cable, column and retention cable: ..\examples\benchmark_examples\analyses\formfinding_membrane1_I\cbm_4_point_Fofi.txt
static geometrically non-linear analysis of a prestressed membrane under snow load: ..\examples\benchmark_examples\analyses\stanln_membrane1_I\cbm_4_point.txt

References

↑ Dieringer, F.: Implementierung eines geometrisch nichtlinearen Membranelements in einer objektorientierten Programmierumgebung, Master's Thesis, Lehrstuhl für Statik, Technische Universität München, 2009
↑ Linhard, J.: Numerisch-mechanische Betrachtung des Entwurfsprozesses von Membrantragwerken, Lehrstuhl für Statik, Technische Universität München, 2009
↑ Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Lehrstuhl für Statik, Technische Universität München, 2014

Whos here now: Members 0 Guests 0 Bots & Crawlers 1

[Die09-0] Dieringer, F.: Implementierung eines geometrisch nichtlinearen Membranelements in einer objektorientierten Programmierumgebung, Master's Thesis, Lehrstuhl für Statik, Technische Universität München, 2009

[1] Linhard, J.: Numerisch-mechanische Betrachtung des Entwurfsprozesses von Membrantragwerken, Lehrstuhl für Statik, Technische Universität München, 2009

[Die14-2] Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Lehrstuhl für Statik, Technische Universität München, 2014

[1]

[2]

[3]

@@ Line 61: / Line 61: @@
 == Element Loading ==
+Being a line element not all general load cases are applicable.
-=== Pressure ===
-Pressure load -- characterized by its application in the current configuration, including direction and application area -- is implemented for the Membrane1 element. Note that it may also be included in the form-finding in order to define pressurized cushions, etc.
 === Dead Load ===
-Dead load is implemented. It takes the thickness of the element and the density of the material which is then multiplied by the assigned acceleration value in the proposed direction.
+*implemented
-=== Snow Load ===
-Snow load is implemented. It considers the projected surface area of the element w.r.t. the load direction that is applied.
 == Theory ==
@@ Line 78: / Line 73: @@
 and <ref name="Die14">Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Lehrstuhl für Statik, Technische Universität München, 2014</ref>.
-For the correct use of the membrane element and the interpretation of related results, the following aspects should be considered:
+For the correct use of the truss 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. The following materials are tested for the membrane element:
+With the parameter MAT the material that is used in the calculation is defined. Being a line element with constant, fixed cross-sectional area, only linear elastic isotropic is foreseen for now.
-* 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 is assumed constant over the element.
-=== Prestress directions on the surface ===
+=== Cross-section area parameter ===
-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, which is necessary in case of anisotropic prestress conditions. In this approach the principal directions of the prestress are defined in a plane area (see figure below). The definition of the area is given by the two vectors '''f'''<sub>1</sub> and '''f'''<sub>2</sub>. The normal vector of the area can be calculated with the cross product of the in plane vectors '''f'''<sub>3</sub>='''f'''<sub>1</sub> x '''f'''<sub>2</sub>. Afterwards the line of intersection '''T'''<sub>1</sub> of the area which is given by '''f'''<sub>1</sub> and '''f'''<sub>3</sub> and the curved surface can be calculated. In this approach '''T'''<sub>1</sub> is interpreted as the first principal direction of the prestress on the curved surface. With the assumption that '''T'''<sub>3</sub> is equal to the surface normal vector '''A'''<sub>3</sub> (not normalized), the second direction of the prestress is calculated as '''T'''<sub>2</sub>='''T'''<sub>1</sub> x '''T'''<sub>3</sub>. W.r.t. the parameters for the input file, only the plane area with the vectors '''f'''<sub>1</sub> and '''f'''<sub>2</sub> has to be defined. Referring to the depicted approach the vector '''A''' defines the vector '''f'''<sub>1</sub> and the vector '''B''' defines the vector '''f'''<sub>2</sub>.
+The parameter AREA defines the cross-section area of the truss. The area is assumed constant over the element and throughout the computation.
-[[File:MembraneElement PrestressDirectionDefinition.jpg|600px|up|Definition of the prestress directions for the membrane element]]
-=== Prestress state ===
-SIG11, SIG22, SIG12 describes the prestress of the membrane element. The element is based on the plane stress assumption. Due to that only normal and shear stresses in the midplane have to be defined. SIG11 is the stress acting in '''T'''<sub>1</sub>, SIG22 acting in '''T'''<sub>2</sub> and SIG12 is the in-plane shear, whereas SIG12=SIG21 (see figure below).
-[[File:Stress_state_for_membranes.jpg|600px|up|Stress state for Membranes]]
 === Lagrange type ===
 With the (optional) 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.
+== Tests and Benchmarks ==
+The element Truss1 has successfully been tested in 3D in various linear and geometrically non-linear static applications, as well as in dynamic analyses, be it as columns/trusses or as a (prestressed) cable.
+=== Benchmark examples ===
+* cable under dead weight in a static geometrically non-linear analysis in a planar configuration: ..\examples\benchmark_examples\elements\truss1_dead_nln\cbm_trusss.dat
+* two-bar truss with arc-length path following: ..\examples\benchmark_examples\analyses\stanln_2bartruss_arclength_l\cbm_2bartruss_arclength_fixed.dat
+* dynamic eigenfrequency analysis of a prestressed string (modelled as a cable of trusses): ..\examples\benchmark_examples\analyses\eigenvalue_truss1_I\cbm_vib_row_50_elm.txt
+* form-finding of a four-point sail where the TRUSS1 is used as edge cable, column and retention cable: ..\examples\benchmark_examples\analyses\formfinding_membrane1_I\cbm_4_point_Fofi.txt
+* static geometrically non-linear analysis of a prestressed membrane under snow load: ..\examples\benchmark_examples\analyses\stanln_membrane1_I\cbm_4_point.txt