Users:General FEM Analysis/BCs Reference/Neumann

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Some general remarks concerning Neumann conditions:

  • The parameter LD-CURVE is an optional input. It is only used in dynamic analyses. For non-linear statics the load curve has to be defined in the analysis block.


Contents

Node Loads (LD-NODE)

A node load is the most simple kind of Neumann boundary condition. A force or a bending moment is directly applied to a finite element node, whereat the load is defined by its direction and its value. The length of the direction defining vector [D1, D2, D3] does not play any role.

LD-NODE 1  TYPE = FORCE    LD-CURVE = LD-CURVE 1
  NODE 1   D1 = 1.0   D2 = 0.0   D3 = 0.0   VAL = 10
  NODE 2   D1 = 0.0   D2 = 0.0   D3 = 1.0   VAL = 20


If several nodes should be assigned the same load value and direction, this can be done by using a node set, too.

ND-SET 1  NAME = LOADED_NODES
NODE  1  2  3  4

LD-NODE 1  TYPE = FORCE
  ND-SET 1   D1 = 1.0   D2 = 0.0   D3 = 0.0   VAL = 10

Element Loads (LD-ELEM)

A more complex way of defining Dirichlet conditions is to apply a constraint not to a node but to an element, so the element itsself has to determine its equivalent nodal forces. Depending on the direction and the influenced area one can distinguish between snow load, dead load and pressure load.

PRES

Pressure is an element load acting on an element surface. It is usually acting normal to the element surface, so defining a direction is not necessary. If a different acting direction is desired it can be defined via the direction vector in local element coordinates. The load value is equal to the value entered in the load definition.

outline pressure load


LD-ELEM 1 PART=1
 LD-CURVE = LD-CURVE 1
 TYPE=PRES       VAL=10            ! input using default direction D1=0  D2=0  D3=1

! alternative input for pressure parallel to the element surface acting parallel to the element's 1st local coordinate
 TYPE=PRES D1=1.0  D2=0.0  D3=0.0   VAL=10   

SNOW

Snow load is also an element surface related load. In contrast to pressure load it is defined by a direction and it is not acting onto the complete element surface but on its projection into the plane normal to the direction of action. The picture below shows snow load acting into z-direction onto an inclined element.

LD-ELEM 1 PART=1
 LD-CURVE = LD-CURVE 1
 TYPE=SNOW  D1 = 0.0  D2 = 0.0  D3 = 1.0   VAL=10
outline snow load


DEAD

Dead load is acting onto the whole volume of an element. It is computed by multiplying material's density times the load value, which should be equal to gravity's acceleration. Gravity's direction can be defined by the direction vector [D1, D2, D3]. The following input block represents material and load parameters for concrete material and gravity acting in z-direction.

EL-MAT 1 : LIN_ELAST_ISOTROPIC
 EMOD=3.5e10  ALPHAT=1e-5  DENS=2.5e3  NUE=0.2
 
LD-ELEM 1 PART=1
 LD-CURVE = LD-CURVE 1
 TYPE=DEAD      D1=0.0   D2=0.0   D3=1.0  VAL=9.81
outline deadload

TEMPERATURE

(This part is currently under development. Author: Helmut. Date: 08/2010.)
The second kind of volume load is the temperature load object. In contrast to the loads mentioned above it is not defined by elements but by nodes, as the underlying temperature field is defined by nodal values. To this purpose it is possible to define multiple temperature layers at one node, for example top and bottom layer of a shell.

As an example we consider a U-shaped cantilever, where we describe a temperature of +10 over reference temperature at the lower edge and -10 below reference temperature at the top edge.

LD-ELEM 1
 TYPE = TEMPERATURE
 INTERPOLATE_PART = 1
 ND-SET = 30         LAYER = 1  VAL =  10
 ND-SET = 23         LAYER = 1  VAL = -10
geometry of temperature example

Although we only prescribed the temprature at the upper and lower edge we receive a temperature filed which is linear over the height. This is due to the fact that we inputed INTERPOLATE_PART = 1 which forces to interpolate the temperature field for all nodes belomging to part 1. If one omited this input flag all nodes offside the defined edges would be assigned reference temperature and so the displacement would differ significantly.



Load curve

A load curve is used to define time depending load factors for non-linear static analysis or dynamics.

The concept is quite simple: The user specifies a discrete load factor-time-function and values in between are interpolated linearly.

LD-CURVE 1  TYPE=DISCRETE
TIME = 0.000    VAL = 0.0000
TIME = 1.000    VAL = 1.0000
TIME = 10.000   VAL = 2.0000
TIME = 12.000   VAL = 0.0000
Hints:
  • In non-linear static analysis pseudo time is used with Δt=1, so pseudo time steps take on growing integer values 1,2,3,etc only.




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