Gap

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*****************************************************************
Copyright @ 1988 by Algor Interactive Systems, Inc.
All rights reserved. No part of this manual may be reproduced, stored
in a retrieval system, or transmitted in any form by any means without
permission in writing from Algor Interactive systems, Inc.
Published by Algor Interactive Systems, Inc.
Printed in the United States of America.
1-st edition: Febrary 1988
2-nd edition: May 1988
*****************************************************************
SECTION IV.14
-------------
IV.14 Gap elements
Gap elements are identified by the number 14.

Gap elements are defined by two end nodes specified in three-
dimensional space. Only the element axial forces are calculated for
each element. No element based loading is defined for gap elements.
In general, there are 3 kinds of application for gap elements. Each
has its own characteristics in terms of element data input. They are
briefly summarized as follows.
---------------------- ----------------- -------------------------
Application type Element direction Input element stiffness
---------------------- ----------------- -------------------------
1) Rigid support at Element must be 3 or 4 orders of magnitude
structure boundary aligned with larger than the other
to calculate the global X, Y or Z normal stiffness in the
support reactions axis structure
2) Interface element Element may be Same order of magnitude of
between two faces defined in any the other normal stiffness
of structure direction in the structure
in space
3) Elastic spring Element may be Actual spring constant
between the base defined in any calculated from the
of structure and direction foundation soil
foundation
Excessively stiff gap elements (i.e. with very large spring stiff-
ness) that are not aligned with the global coordinate system should be
avoided. Such elements introduce large off-diagonal values into
structural stiffness matrix and cause solution difficulties. The
resulting solution may be inaccurate. The provided spring stiffness
with about 3 or 4 orders of magnitude larger than the other normal
stiffness in the structure is usually sufficient for rigid gap element
used in application type (1).
There are four types of gap elements:

Gap type Description Gap space
-------- ---------------- -------------------------------
0 Compression gap Distance between two end points
1 Tension gap Distance between two end points
2 Compression gap Zero gap
3 Tension gap Zero gap

The compression gap is not activated until the gap is closed; the
tension gap is not activated until the gap is open. Therefore, the
structural behavior of a finite element model associated with gap
element is always nonlinear because of its indeterminate boundary
condition, i.e., whether the gaps are closed or open is not known in
advance.
In this analysis, the material of structures used in the finite
element model is assumed to be linear and elastic and to have small
deformation. The geometric stiffness, nonlinear strain of element and
the friction force between two surfaces due to sliding are not consi-
dered. Therefore, the loading and unloading do not dissipate the
energy. The stress and strain of structure are completely defined by
the final deformed geometry which is independent of the loading
history.
The nonlinear structural analysis with gap elements is linearized
into many piecewise linear calculation steps. At the beginning of each
load increment, it is assumed that there is no additional closing or
opening gap. Then, during the loading process, when any gaps are
closed (compression gap) or open (tension gap) over the specified gap
space, the structural global stiffness is reformulated to include the
stiffness from gap element and the load vector is scaled down to the
value that just makes the gap closed or open precisely. The deforma-
tions of structure are updated for each load increment. This process
continues until the full loading is completely applied.
Some other restrictions are:
1) Currently gap element is NOT available for dynamic analysis.
2) Only ONE load case is allowed in the static analysis.
IV.14.A Element Control Card
Fixed Format (3I5)
Free Format (N/A)
Notes Columns Variables Description
----- ------- --------- -----------------------------------
1 - 5 NPAR(1) The number 14
6 - 10 NPAR(2) Number of elements in group
11 - 15 NAPR(3) Number of element stiffness sets
(1) 16 - 20 NAPR(4) Number of maximum calculation steps
Notes:
(1) The default value for calculation step is set to 200 if the
input value is zero. If the number of total calculation steps
performed by the program exceeds this value, the program stops.

IV.14.B Material Property Data
Fixed Format (I5,5F10.0)
Free Format (N/A)
The following set of data must be supplied for each different
spring stiffness in the model.
Notes Columns Variables Description
----- ------- --------- --------------------------------------
(1) 1 - 5 N Stiffness identification number
(2) 6 - 15 SPS Spring stiffness
Notes:
(1) Stiffness identification numbers must be in ascending order.
The highest number cannot exceed NAPR(3) (See Section IV.14.A,
above)
(2) The input spring stiffness shall satisfy the following
condition:
Used as Input stiffness
-------------------- -------------------------
.. Rigid support 3 or 4 orders of magnitude
at boundary larger than the other
to calculate the normal stiffness in the
support reactions structure
.. Interface element Same order of magnitude of
between two faces the other normal stiffness
of structure in the structure
in space
The default value is the maximum diagonal stiffness in the
global stiffness matrix when the assembling of element
stiffness is completed. This value is only good for the
second type of application above.
IV.14.C Dummy Element Load Factors
Fixed Format (4(4F10.0))
Free Format (N/A)
Supply four dummy element load factor cards here.
IV.14.D Element Data Cards
Fixed format (4I5,F10.0,I5)
Free format (6 Items)
Notes Columns Variables Description
----- ------- --------- -----------------------------------
(1) 1 - 5 M Element number
6 - 10 II Node I (1-st Node)
11 - 15 JJ Node J (2-nd Node)
(2) 16 - 20 MTYP Spring Stiffness index
(3) 21 - 30 TEM (Dummy variable)
(4) 31 - 35 ICODE Gap element type
Notes:
(1) Element number shall be in an ascending sequence.
(2) The spring stiffness index cannot exceed NAPR(3) (See Section
IV.14.A, above)
(3) This is a dummy variable reserved for future use.
(4) There are four gap element types:
Gap type Description Gap space
-------- ---------------- -------------------------------
0 Compression gap Distance between two end points
1 Tension gap Distance between two end points
2 Compression gap Zero gap
3 Tension gap Zero gap
The default value is 0.

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