# Discrete Beam

## Preface

A discrete beam (beam formulation 6) has up to 6 degrees-of-freedom (DOF) whereas a spring (`*ELEMENT_DISCRETE`

) has only one DOF. Resultant forces and moments of a discrete beam are output in the local (r,s,t) coordinate system. This is true of the `d3plot`

, `d3thdt`

, and `elout`

databases.

The length of a discrete beam may be zero or nonzero. A nonzero value of volume (`VOL`

in `*SECTION_BEAM`

) must be provided. The mass of the discrete beam is not related to its length but is the product of the material density and `VOL`

. `INER`

is the mass moment of inertia of the beam about each of its three axes. A nonzero value of `INER`

is required if any of the rotational DOF of the beam are activated. The values `CA`

and `OFFSET`

apply only to cables (`*MAT_CABLE_DISCRETE_BEAM`

). Using 970/rev6763 (and later releases of the code), the cable volume is automatically calculated as length `*CABLE`

area when `VOL`

is set to zero.

## Materials that apply to discrete beams are (see subroutine mvalid):

`*MAT_USER_DEFINED_MATERIAL_MODELS`

`*MAT_66 (*MAT_LINEAR_ELASTIC_DISCRETE_BEAM)`

`*MAT_67 (*MAT_NONLINEAR_ELASTIC_DISCRETE_BEAM)`

`*MAT_68 (*MAT_NONLINEAR_PLASTIC_DISCRETE_BEAM)`

`*MAT_69 (*MAT_SID_DAMPER_DISCRETE_BEAM)`

`*MAT_70 (*MAT_HYDRAULIC_GAS_DAMPER_DISCRETE_BEAM)`

`*MAT_71 (*MAT_CABLE_DISCRETE_BEAM`

)

### Some recent additions are:

`*MAT_74 (*MAT_ELASTIC_SPRING_DISCRETE_BEAM)`

**

`*MAT_93 (*MAT_ELASTIC_6DOF_SPRING_DISCRETE_BEAM)`

<< requires also`*MAT_74`

`*MAT_94 (*MAT_INELASTIC_SPRING_DISCRETE_BEAM)`

`*MAT_95 (*MAT_INELASTIC_6DOF_SPRING_DISCRETE_BEAM)`

<< requires also`*MAT_94`

`*MAT_97 (*MAT_GENERAL_JOINT_DISCRETE_BEAM)`

<< couples any of 6 DOF

`*MAT_119 (*MAT_GENERAL_NONLINEAR_6DOF_DISCRETE_BEAM)`

`*MAT_121 (*MAT_GENERAL_NONLINEAR_1DOF_DISCRETE_BEAM)`

`*MAT_146 (*MAT_1DOF_GENERALIZED_SPRING)`

<< takes SCALAR or SCALR option in`*ELEMENT_BEAM`

`*MAT_196 (*MAT_general_spring_discrete_beam)`

<< alternative to`*MAT_74,93,94,95`

Includes separate tensile and compressive failure criterion.**

`*MAT_197 (*MAT_SEISMIC_ISOLATOR)`

** `*MAT_074`

and `*MAT_196`

include a default damping term `damp=1.5*dtmax*stiffness`

which is probably to enhance stability. `*Mat_066`

, by comparision, does not include any default damping.

## Orientation of a discrete beam is controlled by the values of `SCOOR`

, `CID`

, `RRCON`

, `SRCON`

, and `TRCON`

provided in `*section_beam`

.

If the discrete beam is initially of zero length, permissible values of `SCOOR`

are -3, -1, 0, 1, or 3. If `SCOOR`

is -3 or 3, a shear force developed by the finite beams as a result of shear stiffness will produce a beam torque contribution equal to `(shear force * beam length)/2`

which is not accounted for by the beam rotational stiffness alone. This torque contribution is necessary to give realistic beam-like behavior. If `SCOOR`

is -1, 0, or 1, equilibrating torques are NOT developed. Thus, to avoid nonphysical rotational constraints on the structure, `SCOOR`

= -3 or 3 is generally recommended. In rare instances, `SCOOR`

= -1, 0, or 1 may be preferred for discrete beams which otherwise become unstable or which remain very close to zero length throughout the simulation. `CID`

defines the initial orientation of the local (r,s,t) system. If `CID`

= 0, the initial r,s,t directions are aligned with the global X,Y,Z directions, respectively.

If the discrete beam is of finite length, `SCOOR`

should be set to -3, -2, 2, or 3 so that torque contributions develop due to shear forces as in a real beam (see explanation in above paragraph). `CID`

defines the initial orientation of the local (r,s,t) system. If `CID`

= 0, the initial r,s,t directions are aligned with the global X,Y,Z directions, respectively, unless a third node N3 is defined in the beam connectivity in which case the three beam nodes N1, N2, and N3 determine the initial orientation of the beam local system (if and only if `SCOOR`

= 2 or -2). See the example discrete.beams.finite.k for an illustration of the effect of `SCOOR`

on finite length discrete beams.

### Discrete Beam Local System Update:

`RRCON`

, `SRCON`

, and `TRCON`

may be used to fix any or all of the 3 local directions. The default is that the local directions are updated, not fixed.

If `RRCON`

, `SRCON`

, and `TRCON`

are zero (not fixed), the local system is updated based on the angular velocity of node1, node2, or the average of the two (`SCOOR`

says which). The exception is if the coordinate system identified by `CID`

uses `*DEFINE_COORDINATE_NODES`

with `FLAG`

= 1. In that case, the beam local system is updated based on the current orientation of the three nodes identified in `*DEFINE_COORDINATE_NODES`

. If `SCOOR`

is set to -2 or 2, a final adjustment is made to the local system so that the r-axis lies along the axis of the beam (node1 to node2).

What is difficult to understand about a discrete beam is that the N1-to-N2 axis of the beam does not have to move along with the material (local) coordinate system. This is so because the relative deformation between the nodes is incrementally calculated based on the instantaneous values of incremental force and the current orientation of the material coordinate system.

## Orientation of `*ELEMENT_DISCRETE`

Orientation of `*ELEMENT_DISCRETE`

(not to be confused with a discrete beam) is controlled by the parameter `VID`

.

If `VID`

= 0 (preferred), the line-of-action of an `*ELEMENT_DISCRETE`

remains along the node1 to node2 direction throughout the calculation. If a different orientation is desired, we recommend using a discrete beam with `SCOOR`

set to -3,-2, 2, or 3. A spring using an orientation vector (`VID`

> 0) is NOT recommended owing to the likelihood of developing unwanted rotational constraint. We suggest that you use a discrete beam with `SCOOR`

=2 (see `*SECTION_SHELL`

) in place of finite-length springs whose line-of-action is not along N1-to-N2. A transverse force developed by finite length discrete beams as a result of transverse stiffness will produce a beam torque contribution equal to `(shear force * beam length)/2`

. This torque contribution is necessary for physical behavior. In contrast, a finite-length spring whose line-of-action is not along its N1-to-N2 axis does not produce an equilibrating torque to accompany transverse force. This omission can result in a nonphysical resistance to body rotation.

If `VID`

> 0 (NOT recommended owing to the likelihood of developing unwanted rotational constraint), IOP in `*DEFINE_SD_ORIENTATION`

determines the method by which the element orientation is determined. If `IOP`

=0 or 1, the orientation is permanently fixed in space. If `IOP`

=2 or 3, the orientation is updated as the two elements nodes move in space. Further details of `*DEFINE_SD_ORIENTATION`

are provided in the User's Manual.