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, only applied with anisotropic prestress conditions. (see description of Membrane1-element)
SIG11 SIG22 SIG12	reals	Prestress state of the membrane. (see description of Membrane1-element)

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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