.\"    This file is part of the FElt finite element analysis package.
.\"    Copyright (C) 1993-2000 Jason I. Gobat and Darren C. Atkinson
.\"
.\"    This program is free software; you can redistribute it and/or modify
.\"    it under the terms of the GNU General Public License as published by
.\"    the Free Software Foundation; either version 2 of the License, or
.\"    (at your option) any later version.
.\"
.\"    This program is distributed in the hope that it will be useful,
.\"    but WITHOUT ANY WARRANTY; without even the implied warranty of
.\"    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
.\"    GNU General Public License for more details.
.\"
.\"    You should have received a copy of the GNU General Public License
.\"    along with this program; if not, write to the Free Software
.\"    Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
.TH FELT 4fe "8/4/95" "Version 3.00" "Finite Element Package"
.SH NAME
felt \- finite element problem description file format
.SH DESCRIPTION
The \fIfelt\fR(4fe) file format is used by the programs of the finite element
package, \fIfelt\fR(1fe), \fIvelvet\fR(1fe), and \fIburlap\fR(1fe)
to describe a finite element problem.  The file is human
readable and consists of a friendly, intuitive syntax rather than a table of
numbers.  Syntactic and semantic errors are detected and reported assuring
that only valid problem descriptions are used.  In general white space is
unimportant, arbitrary numeric expressions may be used, and case of
keywords is unimportant.  As per standard convention, boldface items
represent keywords, italicized items represent the syntax of the grammar, and
items in brackets are optional.  The file syntax is shown below.
.PP
.RS
.RI [ " problem-description " ]
.br
.RI [ " analysis-parameters " ]
.br
.RI [ " object-definitions " ]
.br
.RI [ " appearance-description " ]
.br
.B "end"
.RE
.SS Problem description
The \fIproblem-description\fR section specifies the problem title and the
number of nodes and elements in the problem.  If this section is not
specified then the problem will be unnamed and is assumed to contain zero
nodes and zero elements.  This section may be absent for example in defaults
files which define objects but do not specify an actual problem instance.
The format for a \fIproblem-description\fR is given below.
.PP
.RS
.B "problem description"
.br
[
.BI "title = " string
]
.br
[
.BI "nodes = " integer
]
.br
[
.BI "elements = " integer
]
.br
[
\fBanalysis =\fB static \fR|\fB transient \fR|\fB modal\fR
|\fB static-thermal\fR|\fB transient-thermal\fR|\fB spectral\fR
]
.RE
.PP
If the \fBtitle\fR is missing then the problem is unnamed.  If \fBnodes\fR
or \fBelements\fR is missing then none of that type of object are expected.
The assignments can occur in any order and can even be repeated with the
last assignment being used.
.SS Analysis parameters
The \fIanalysis-parameters\fR section defines any parameters for a specific
type of analysis.  Currently, this section is used only if the analysis mode
is \fBtransient\fR.  The format of the \fIanalysis-parameters\fR section
is given below.
.PP
.RS
.B "analysis parameters"
.br
[
.BI "alpha = " expression
]
.br
[
.BI "beta = " expression
]
.br
[
.BI "gamma = " expression
]
.br
[
.BI "step = " expression
]
.br
[
.BI "start = " expression
]
.br
[
.BI "stop = " expression
]
.br
[
.BI "Rm = " expression
]
.br
[
.BI "Rk = " expression
]
.br
[
.BI "nodes = [ " node-list " ]"
]
.br
[
.BI "dofs = [ " dof-list " ]"
]
.br
[
\fBmass-mode =\fB lumped \fR|\fB consistent\fR
]
.RE
.PP
The \fBalpha\fR, \fBbeta\fR, and\fBgamma\fR parameters are used in numerical
integration schemes (transient and transient-thermal analysis).
\fBstart\fR, \fBstop\fR, and \fBstep\fR define the range of time or
frequency interest for transient or spectral analyses.  In transient
analyses, \fBstart\fR is meaningless and \fBduration\fR and \fBdt\fR can
be used as aliases for \fBstop\fR and \fBstep\fR, respectively.  \fBRk\fR
and \fBRm\fR are global Rayleigh (stiffness and mass) damping proportionality
constants.  The \fInode-list\fR is a comma or white space separated list of 
node numbers that are of interest in the analysis.  Similarly, the 
\fIdof-list\fR is a list of the degrees of freedom (\fBTx\fR, \fBTy\fR, 
\fBTz\fR, \fBRx\fR, \fBRy\fR, and \fBRz\fR) that are of interest.
.PP
An \fIobject-definition\fR section defines objects of a specified type.
Objects include nodes, elements, materials, constraints, forces, and
distributed loads.
Each of these types of objects is discussed below.  Multiple
\fIobject-definition\fR sections are allowed and the sections may occur in
any order.
.SS Nodes
Nodes are points in cartesian space to which elements are attached.  A
node must have a constraint and may have an optional force.  A node is
identified by a natural number.  The syntax is as follows:
.PP
.RS
\fBnodes\fR
.br
\fInode-definitions\fR
.RE
.PP
where a \fInode-definition\fR takes the following form:
.PP
.RS
.I node-number
.br
[
.BI "x = " expression
]
.br
[
.BI "y = " expression
]
.br
[
.BI "z = " expression
]
.br
[
.BI "constraint = " constraint-name
]
.br
[
.BI "force = " force-name
]
.br
[
.BI "mass = " expression
]
.RE
.PP
The \fInode-number\fR starts the definition.  Each node must have a unique
number.  If a cartesian coordinate is not given then the coordinate of the
previous node is used.  Similarly, if no constraint is given then the
constraint applied to the previous node is used.  As above, the assignments
can appear in any order and any number of times.  As indicated above, some
objects are identified by their name and some by their number.  Elements and
nodes have numbers while materials, forces, loads, and constraints have
names.
.SS Elements
Elements are linear, planar, or solid objects which are attached to nodes.
Each element must have a material and may have optional loads.  Furthermore,
each element has a type, or definition.  Like nodes, elements are identified
by a unique natural number.  Elements of specific type are defined with the
following syntax:
.PP
.RS
.IB "element-type " elements
.br
.I element-definition
.RE
.PP
where an \fIelement-type\fR is one of the following:
.PP
.RS
.B spring
.br
.B truss
.br
.B beam
.br
.B beam3d
.br
.B CSTPlaneStrain
.br
.B CSTPlaneStress
.br
.B iso2d_PlaneStrain
.br
.B iso2d_PlaneStress
.br
.B quad_PlaneStrain
.br
.B quad_PlaneStress
.br
.B timoshenko
.br
.B htk
.br
.B brick
.br
.B ctg
.br
.B rod
.RE
.PP
and an \fIelement-definition\fR has the following form:
.PP
.RS
.I element-number
.br
.BI "nodes = [ " node-list " ]"
.br
[
.BI "material = " material-name
]
.br
[
.BI "load = " load-name-list
]
.RE
.PP
The \fIelement-number\fR starts the definition.  Each element must have a
unique number.  If no material is given then the material applied to the
previous element is used.  The \fIload-name-list\fR is a list of up to three
loads to apply to the element.  The \fInode-list\fR is a comma or white space
separated list of node numbers.  Each type of element requires a certain of
nodes and in some cases a special "null node" which is numbered zero may be
used to indicate a gap or filler in the list.
.SS Materials
Elements are made of a type of material.  Each material has a name and
certain physical properties not all of which may be used by any one
element.  The syntax for defining materials is as follows:
.PP
.RS
.B "material properties"
.br
.I "material-definitions"
.RE
.PP
where \fImaterial-definition\fR has the following form:
.PP
.RS
.nf
.PD 0
.I material-name
.TP 25
[ \fBcolor =\fI string\fR ]
# color for \fIvelvet\fR
.TP
[ \fBE =\fI expression\fR ]
# Young's modulus
.TP
[ \fBIx =\fI expression\fR ]
# moment of inertia about x-x axis
.TP
[ \fBIy =\fI expression\fR ]
# moment of inertia about y-y axis
.TP
[ \fBIz =\fI expression\fR ]
# moment of inertia about z-z axis
.TP
[ \fBA =\fI expression\fR ]
# cross-sectional area
.TP
[ \fBJ =\fI expression\fR ]
# polar moment of inertia
.TP
[ \fBG =\fI expression\fR ]
# bulk (shear) modulus
.TP
[ \fBt =\fI expression\fR ]
# thickness
.TP
[ \fBrho =\fI expression\fR ]
# density
.TP
[ \fBnu =\fI expression\fR ]
# Poisson's ratio
.TP
[ \fBkappa =\fI expression\fR ]
# shear force correction
.TP
[ \fBRk =\fI expression\fR ]
# Rayleigh damping coefficient (K)
.TP
[ \fBRm =\fI expression\fR ]
# Rayleigh damping coefficient (M)
.TP
[ \fBKx =\fI expression\fR ]
# thermal conductivity in the x-direction
.TP
[ \fBKy =\fI expression\fR ]
# thermal conductivity in the y-direction
.TP
[ \fBKy =\fI expression\fR ]
# thermal conductivity in the z-direction
.TP
[ \fBc =\fI expression\fR ]
# heat capacitance
.PD
.fi
.RE
.PP
The \fImaterial-name\fR starts the definition.  If an attribute of a material
is not specified then that attribute is zero.  The assignments may occur in
any order.  The \fIcolor\fR specifies the color to use in drawing the
material within \fIvelvet\fR, and is ignored by other applications.
.SS Constraints
Constraints are applied to nodes to indicate about which axes a node can
move.  The syntax for defining a constraint is as follows:
.PP
.RS
.B "constraints"
.br
.I "constraint-definitions"
.RE
.PP
where \fIconstraint-definition\fR has the following form:
.PP
.RS
.PD 0
.I constraint-name
.TP 32
.nf
[ \fBcolor =\fI string\fR ]
# color for \fIvelvet\fR
.TP
[ \fBtx =\fB c \fR|\fB u \fR|\fI expression \fR]
# boundary translation along x axis
.TP
[ \fBty =\fB c \fR|\fB u \fR|\fI expression \fR]
# boundary translation along y axis
.TP
[ \fBtz =\fB c \fR|\fB u \fR|\fI expression \fR]
# boundary translation along z axis
.TP
[ \fBrx =\fB c \fR|\fB u \fR|\fI expression \fR|\fB h \fR]
# boundary rotation about x axis
.TP
[ \fBry =\fB c \fR|\fB u \fR|\fI expression \fR|\fB h \fR]
# boundary rotation about y axis
.TP
[ \fBrz =\fB c \fR|\fB u \fR|\fI expression \fR|\fB h \fR]
# boundary rotation about z axis
.TP
[ \fBitx =\fI expression\fR ]
# initial displacement along x axis
.TP
[ \fBity =\fI expression\fR ]
# initial displacement along y axis
.TP
[ \fBitz =\fI expression\fR ]
# initial displacement along z axis
.TP
[ \fBirx =\fI expression\fR ]
# initial rotation about x axis
.TP
[ \fBiry =\fI expression\fR ]
# initial rotation about y axis
.TP
[ \fBirz =\fI expression\fR ]
# initial rotation about z axis
.TP
[ \fBvx =\fI expression\fR ]
# initial velocity along x axis
.TP
[ \fBvy =\fI expression\fR ]
# initial velocity along y axis
.TP
[ \fBvz =\fI expression\fR ]
# initial velocity along z axis
.TP
[ \fBax =\fI expression\fR ]
# initial accel. along x axis
.TP
[ \fBay =\fI expression\fR ]
# initial accel. along y axis
.TP
[ \fBaz =\fI expression\fR ]
# initial accel. along z axis
.fi
.PD
.RE
.PP
The \fIconstraint-name\fR starts the definition.  A value of \fBc\fR
for a boundary condition indicates that the axis is constrained; a value 
of \fBu\fR indicates that the axis is unconstrained.  
An expression indicates a displacement (non-zero) boundary condition and
may contain the \fBt\fR variable for time varying boundary conditions in 
transient analysis problems.  The initial dislacement, velocity and 
acceleration specifications are only used in transient problems.
A value of \fBh\fR for a rotational boundary condition indicates
a hinge.  By default, all axes are unconstrained.  The \fIcolor\fR specifies
the color to use in drawing the constraint within \fIvelvet\fR, and is
ignored by other applications.
.SS Forces
Forces, or point loads, may be applied to nodes.  The syntax for a force
definition is as follows:
.PP
.RS
.B "forces"
.br
.I "force-definitions"
.RE
.PP
where a \fIforce-definition\fR has the following form:
.PP
.RS
.PD 0
.I "force-name"
.TP 25
[ \fBcolor =\fI string\fR ]
# color for \fIvelvet\fR
.TP
[ \fBFx = \fIexpression\fR ]
# force along x axis
.TP
[ \fBFy = \fIexpression\fR ]
# force along y axis
.TP
[ \fBFz = \fIexpression\fR ]
# force along z axis
.TP
[ \fBMx = \fIexpression\fR ]
# moment about x axis
.TP
[ \fBMy = \fIexpression\fR ]
# moment about y axis
.TP
[ \fBMz = \fIexpression\fR ]
# moment about z axis
.TP
[ \fBSfx = \fIexpression\fR ]
# frequency-domain spectra of force along x axis
.TP
[ \fBSfy = \fIexpression\fR ]
# frequency-domain spectra of force along y axis
.TP
[ \fBSfz = \fIexpression\fR ]
# frequency-domain spectra of force along z axis
.TP
[ \fBSmx = \fIexpression\fR ]
# frequency-domain spectra of moment about x axis
.TP
[ \fBSmy = \fIexpression\fR ]
# frequency-domain spectra of moment about y axis
.TP
[ \fBSmz = \fIexpression\fR ]
# frequency-domain spectra of moment about z axis
.PD
.RE
.PP
The \fIforce-name\fR starts the definition.  If the force or moment is not
specified then it is assumed to be zero.  The
\fIexpressions\fR for forces may be time-varying.  Time-varying expressions
include the single variable \fBt\fR to represent the current time in the
solution of a dynamic problem or consist of a list of discrete (time, value)
pairs.  Frequency varying expressions for spectra can also use \fBw\fR to
represent the independent variable (radial frequency).
The \fIcolor\fR specifies the color to use in drawing the force
within \fIvelvet\fR, and is ignored by other applications.
.SS Loads
Distributed loads, or loads for short, are applied to elements.  The syntax
for a defining a distributed load is as follows:
.PP
.RS
.B "distributed loads"
.br
.I "load-definitions"
.RE
.PP
where a \fIload-definition\fR has the following form:
.PP
.RS
.nf
.I "load-name"
.PD 0
.TP 25
[ \fBcolor =\fI string\fR ]
# color for \fIvelvet\fR
.TP
[ \fBdirection = \fIdir\fR ]
# direction
.TP
[ \fBvalues = \fIpair-list\fR ]
# local nodes and magnitudes
.PD
.fi
.RE
.PP
The \fIload-name\fR starts the definition.  The \fIdir\fR is one of
\fBLocalX\fR, \fBLocalY\fR, \fBLocalZ\fR (local coordinate system),
\fBGlobalX\fR, \fBGlobalY\fR, \fBGlobalZ\fR (global coordinate system),
\fBparallel\fR, or \fBperpendicular\fR.  The \fIpair-list\fR is a sequence of
\fIpairs\fR.  A \fIpair\fR is a node number and an expression enclosed in
parentheses.  The node number refers to the position within the element
rather than referring to an actual node.  The \fIcolor\fR specifies the color
to use in drawing the load within \fIvelvet\fR, and is ignored by other
applications.
.SS Appearance Description
The \fIappearance-description\fR section is used by \fIvelvet\fR to
describe the appearance of a problem.  This section is currently not used by
\fIfelt\fR.  The appearance includes the state of the drawing area and
any tool figures.  This section consists of two subsections, the
\fIcanvas-configuration\fR section and the \fIfigure-list\fR section.  The
\fIcanvas-configuration\fR section has the following syntax.
.PP
.RS
.B "canvas configuration"
.br
.I "canvas-parameters"
.RE
.PP
where a \fIcanvas-parameter\fR has the following form:
.PP
.RS
.nf
.PD 0
.TP 35
[ \fBnode-numbers = \fIboolean \fR]
# node numbering
.TP
[ \fBelement-numbers = \fIboolean \fR]
# element numbering
.TP
[ \fBsnap = \fIboolean \fR]
# snap grid status
.TP
[ \fBgrid = \fIboolean \fR]
# visible grid status
.TP
[ \fBsnap-size = \fIexpression \fR]
# snap grid size
.TP
[ \fBgrid-size = \fIexpression \fR]
# visible grid size
.TP
[ \fBnode-color = \fIcolor-name \fR]
# node color
.TP
[ \fBelement-color = \fIcolor-name \fR]
# element color
.TP
[ \fBlabel-font = \fIfont-name \fR]
# labeling font
.TP
[ \fBtool-color = \fIcolor-name \fR]
# tool figure color
.TP
[ \fBtool-font = \fIfont-name \fR]
# text figure font
.TP
[ \fBx-min = \fIexpression \fR]
# x-axis minimum
.TP
[ \fBx-max = \fIexpression \fR]
# x-axis maximum
.TP
[ \fBy-min = \fIexpression \fR]
# y-axis minimum
.TP
[ \fBy-max = \fIexpression \fR]
# y-axis maximum
.TP
[ \fBx-pos = \fIexpression \fR]
# x position of drawing area
.TP
[ \fBy-pos = \fIexpression \fR]
# y position of drawing area
.TP
[ \fBwidth = \fIexpression \fR]
# width of viewport window
.TP
[ \fBheight = \fIexpression \fR]
# height of viewport window
.TP
[ \fBscale = \fIexpression \fR]
# scale of drawing area
.fi
.PD
.RE
.PP
A \fIboolean\fR is either \fBtrue\fR or \fBfalse\fR.  A \fIcolor-name\fR is
the name of a valid X11 color.  Similarly, a \fIfont-name\fR is the name of a
valid X11 font.  The last five parameters are probably not very meaningful to
the user.  The \fIfigure-list\fR section has the following syntax.
.PP
.RS
.B "figure list"
.br
.I "figure-definitions"
.RE
.PP
where a \fIfigure-definition\fR has the following form:
.PP
.RS
.PD 0
.TP 30
\fIfigure-type\fR
.TP
[ \fBx = \fIexpression \fR]
# x coordinate
.TP
[ \fBy = \fIexpression \fR]
# y coordinate
.TP
[ \fBwidth = \fIexpression \fR]
# width
.TP
[ \fBheight = \fIexpression \fR]
# height
.TP
[ \fBstart = \fIexpression \fR]
# starting angle
.TP
[ \fBlength = \fIexpression \fR]
# arc length
.TP
[ \fBtext = \fIname \fR]
# text string
.TP
[ \fBcolor = \fIname \fR]
# color
.TP
[ \fBfont = \fIname \fR]
# text font
.TP
[ \fBpoints = [ \fIpoint-list\fB ] \fR]
# line points
.PD
.RE
.PP
The \fIfigure-type\fR starts the definition and is one of \fBrectangle\fR,
\fBpolyline\fR, \fBtext\fR, or \fBarc\fR.  Note that not all properties
have meaning for all figures.  Any unneeded property is ignored.  If a color
or font property is not given then the previous property is used.  The
\fIpoint-list\fR is a list of (x-coordinate, y-coordinate) pairs.
.SS Expressions
An \fIexpression\fR can be either constant or time-varying.  As discussed
above, time-varying expressions contain the variable \fBt\fR or consist of a
list of discrete (time, value) pairs.  If a time-varying expression is given
where a constant expression is expected, the expression is evaluated at time
zero.  An \fIexpression\fR has one of the following forms, where all
operators have the precedences and associativities given to them in the C
programming language.
.PP
.RS
.PD 0
.nf
.TP 37
\fIexpression\fB ? \fIexpression\fB : \fIexpression\fR
# in-line conditional
.TP
\fIexpression\fB || \fIexpression\fR
# logical or
.TP
\fIexpression\fB && \fIexpression\fR
# logical and
.TP
\fIexpression\fB | \fIexpression\fR
# integer inclusive or
.TP
\fIexpression\fB ^ \fIexpression\fR
# integer exclusive or
.TP
\fIexpression\fB & \fIexpression\fR
# integer and
.TP
\fIexpression\fB == \fIexpression\fR
# equality
.TP
\fIexpression\fB != \fIexpression\fR
# inequality
.TP
\fIexpression\fB < \fIexpression\fR
# less than
.TP
\fIexpression\fB > \fIexpression\fR
# greater than
.TP
\fIexpression\fB <= \fIexpression\fR
# less than or equal
.TP
\fIexpression\fB >= \fIexpression\fR
# greater than or equal
.TP
\fIexpression\fB << \fIexpression\fR
# integer shift left
.TP
\fIexpression\fB >> \fIexpression\fR
# integer shift right
.TP
\fIexpression\fB + \fIexpression\fR
# addition
.TP
\fIexpression\fB - \fIexpression\fR
# subtraction
.TP
\fIexpression\fB * \fIexpression\fR
# multiplication
.TP
\fIexpression\fB / \fIexpression\fR
# division
.TP
\fIexpression\fB % \fIexpression\fR
# integer remainder
.TP
\fB- \fIexpression\fR
# arithmetic negation
.TP
\fB! \fIexpression\fR
# logical negation
.TP
\fB~ \fIexpression\fR
# integer bitwise negation
.TP
\fB( \fIexpression\fB )\fR
# enforce precedence
.TP
\fBsin (\fI expression\fB )\fR
# sine
.TP
\fBcos (\fI expression\fB )\fR
# cosine
.TP
\fBtan (\fI expression\fB )\fR
# tangent
.TP
\fBpow (\fI expression\fB , \fIexpression \fB)\fR
# power (exponentiation)
.TP
\fBexp (\fI expression\fB )\fR
# exponential
.TP
\fBlog (\fI expression\fB )\fR
# natural logarithm
.TP
\fBlog10 (\fI expression\fB )\fR
# base-10 logarithm
.TP
\fBsqrt (\fI expression\fB )\fR
# square root
.TP
\fBhypot (\fI expression\fB , \fIexpression \fB)\fR
# Euclidean distance
.TP
\fBfloor (\fI expression\fB )\fR
# floor
.TP
\fBceil (\fI expression\fB )\fR
# ceiling
.TP
\fBfmod (\fI expression\fB , \fIexpression \fB)\fR
# floating point remainder
.TP
\fBfabs (\fI expression\fB )\fR
# absolute value
.TP
\fBnumber\fR
# literal value
.TP
\fBt\fR
# current time
.fi
.PD
.RE
.PP
Finally, a discretely valued expression has the following syntax, where the
optional \fB+\fR indicates that the list represents one cycle of an infinite
waveform.
.PP
.RS
\fB( \fIexpression \fB',' \fIexpression \fB) \fR... [ \fB+ \fR]
.RE
.SH AUTHOR
The \fIfelt\fR file format was developed by Jason I. Gobat (jgobat@mit.edu)
and Darren C. Atkinson (atkinson@ucsd.edu).
.SH SEE ALSO
corduroy(1fe), felt(1fe), velvet(1fe), xfelt(1fe), corduroy(4fe).