Users:General FEM Analysis/Elements Reference/Membrane NURBS

Contents 1 General Description 1.1 Element Type 2 Input Parameters 2.1 Parameter Description 2.2 Example of a Complete Input Block 3 Tests and Benchmarks 3.1 Benchmark examples 4 References

General Description

Element Type

• This membrane element is an isotropic plane stress element accounting for prestress
• The membrane element neglects bending stiffness
• The ratio of the thickness and the lengths in the other two directions is much smaller than one ( t/Lx << 1 and t/Ly << 1), the membrane is reduced to its mid-surface
• The thickness is constant over the element

An extensive description of the element can be found in ^[1]

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
THICKNESS	real	Thickness of the membrane
INT_TYPE_MEMBRANE_NURBS	FULL or USER	type of numerical integration. With FULL the integration rule is automatically chosen, with USER it can manually be defined. For USER also the parameters GAUSS_U and GAUSS_V have to be defined.
GAUSS_U, GAUSS_V	int	number of integration points in u and v-direction, respectively. In case of INT_TYPE_MEMBRANE_NURBS = FULL this specification is not required.
A_X, A_Y, A_Z B_X, B_Y, B_Z		Definition of the principal directions of the surface to define the prestress directions. (see description below)
SIG11 SIG22 SIG12	reals	Prestress state of the membrane. (see description below)
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 : MEMBRANE_NURBS
  MAT= EL-MAT 1
  THICKNESS= 1.0
  INT_TYPE_MEMBRANE_NURBS = FULL !or USER
  PROJECTED_PRESTRESS=1 SIG11=400.0     SIG22=400.0      SIG12=0.0
  A_X=1.0     A_Y=0.0    A_Z=0.0   !AREA FOR THE DEFINITION OF THE PRESTRESS
  B_X=0.0     B_Y=1.0    B_Z=0.0   !VECTOR A AND VECTOR B DEFINE THE AREA

The possibility for oriented anisotropic prestress fields is foreseen, yet no distortion control as for the classical FEM Membrane1-element is implemented.

Tests and Benchmarks

The element Membrane_NURBS has successfully been applied in 3D in various geometrically non-linear static applications, as well as in form-finding.

Benchmark examples

• form-finding of a four-point sail with with B-Rep edge cables and elastic columns as supports: ..\examples\benchmark_examples\isogeometric\iga_formfinding_4point_with_trusses\cbm_4PointSailwTrusses.txt
• static geometrically non-linear analysis of a prestressed single-patch membrane with fixed boundaries: ..\examples\benchmark_examples\isogeometric\iga_membrane_nln_1\cbm_iga_membrane_nln_1.txt

References

1. ↑ B. Philipp, M. Breitenberger, I. D’Auria, R.Wüchner, and K.-U. Bletzinger. "Integrated design and analysis of structural membranes using the Isogeometric B-Rep Analysis." In: Computer Methods in AppliedMechanics and Engineering 303 (May 2016), pp. 312–340. DOI: 10.1016/j.cma.2016.02.003.

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