winfelt manual version 1.1 - university of memphis

WinFElt Manual Version 1.1.3To demonstrate a simple FEM solution for CST we will use the FElt (Finite ELemenT) program.

FElt is a free system for introductory level finite element analysis.

It i i il i t d d t hi t l f i t d t t i fi itIt is primarily intended as a teaching tool for introductory type courses in finite elements - probably in the mechanical/structural/civil fields.

In a command line environment, FElt uses an intuitive, straightforward input syntax to describe problems.

It also includes a graphical user interface for workstations that allows the user to set-up, solve and post-process the problem in a single CAD-like environment.

The Windows interface, WinFElt, consists of an editor and an encapsulator for the command line applications. It has some graphical post-processing capabilities.

WinFElt Manual Version 1.1.3The current version of FElt knows how to solve linear static and dynamic structural and thermal analysis problems; it can also do modal and spectral analysis for dynamic problems.

FElt's element library currently contains fourteen elements.

FElt uses an intuitive, ASCII based syntax for problem definition.

This powerful syntax allows you to substitute analytic functions in place of numeric values (sin(60) instead of 0.866025) and even more importantly allows for time-dependent forcing and boundary conditions to be specified as analytic functions of time or in the more traditional fashion as a series of discrete time, magnitude pairs.

This feature makes it quite easy to specify a wide range of functionsThis feature makes it quite easy to specify a wide range of functions.

CIVL 8/7117 WinFElt Manual and Examples 1/19

WinFElt Manual Version 1.1.3We can generate a color plot of stress contours for the above wrench problem with one simple menu selection after we have solved the problem in velvet.

Displacement contours, and two- and three-dimensional wire frame plots of the displaced shape are also available post-processing options.

WinFElt Manual Version 1.1.3

Problem description

The problem description section is used to define the problem title and the number of nodes and elements in the problem. The problem description section is the only section which you cannot repeat within a given input file. The format for a problem-description is given belowdescription is given below.

problem description[ title = string ][ nodes = integer ][ elements = integer ][ analysis = static | transient | modal | static-thermal | transient-thermal | spectral]

nodes = integergelements = integer

These numbers will be used for error checking so the specifications given here must match the actual number of nodes and elements given in the definition sections. Note that the definitions for nodes and elements do not have to be given in numerical order, as long as nodes 1 ... m and elements 1 ... n (where m is the number of nodes and n is the number of elements) all get defined in one of the element and node definition sections in the file.



Problem description

The problem description section is used to define the problem title and the number of nodes and elements in the problem. The problem description section is the only section which you cannot repeat within a given input file. The format for a problem-description is given belowdescription is given below.

problem description[ title = string ][ nodes = integer ][ elements = integer ][ analysis = static | transient | modal | static-thermal | transient-thermal | spectral]

analysis = problem typey p yp

Defines the type of problem that you wish to solve. Currently it can either be static, transient, static-substitution, modal, static-thermal, transient-thermal, or spectral. If you do not specify anything, static analysis will be assumed.


Analysis parametersThe analysis parameters section is required only if you are doing some type of transient, modal, or spectral analysis (e.g., analysis=transient, analysis=spectral in the problem description section). For modal analysis it is simply used to set the type of element mass matrices that will be formed but for transient and spectral analyses

analysis parameters[ alpha = expression ][ beta = expression ][ gamma = expression ][ step = expression ][ stop = expression ]

of element mass matrices that will be formed, but for transient and spectral analyses it contains information that

[ stop expression ][ Rm = expression ][ Rk = expression ][ nodes = [ node-list] ][ dofs = [ dof-list] ][ mass-mode = lumped | consistent ]



Analysis parameters

The alpha, beta, and gamma parameters are used in numerical integration schemes (transient and transient-thermal analysis).

The start stop and step parameters define the range of time or frequency interestThe start, stop, and step parameters define the range of time or frequency interest for transient or spectral analyses.

In transient analyses, start is meaningless and duration and dt can be used as aliases for stop and step, respectively.

The Rk and Rm parameters are global Rayleigh (stiffness and mass) damping proportionality constants.

The node-list is a comma or white space separated list of node numbers that are of interest in the analysis. Similarly, the dof-list is a list of the degrees of freedom (Tx, Ty, Tz, Rx, Ry, and Rz) that are of interest.

An object-definition 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 object-definition sections are allowed and the sections may occur in any order.


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:

nodesnode-definitions where a node-definition takes the following form:

node-number[ x = expression ][ y = expression ][ z = expression ][ constraint = constraint-name ][ ][ force = force-name ][ mass = expression ]

The node-number 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.



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:

nodesnode-definitions where a node-definition takes the following form:

node-number[ x = expression ][ y = expression ][ z = expression ][ constraint = constraint-name ][ ][ force = force-name ][ mass = expression ]

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.


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:natural number. Elements of specific type are defined with the following syntax:

element-type elementselement-definition

where an element-type is one of the following:

spring trussbeam beam3dCSTPlaneStrain CSTPlaneStressiso2d-PlaneStrain iso2d-PlaneStressquad-PlaneStrain quad-PlaneStresstimoshenko htkbrick ctgrod



Elements



An element-definition has the following form:

element-numbernodes = [ node-list ][ ][ material = material-name ][ load = load-name-list ]

The element-number 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 load-name-Iist is a list of up to three loads to apply to the element.


Elements



An element-definition has the following form:

element-numbernodes = [ node-list ][ ][ material = material-name ][ load = load-name-list ]

Each type of element requires a certain number 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.



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 anyone element.

The syntax for defining materials is as follows:The syntax for defining materials is as follows:

material propertiesmaterial-definitions

where material-definition has the following form:

material-name[ E = expression ] # Young's modulus[ Ix = expression ] # moment of inertia about x-x axis[ p ][ Iy = expression ] # moment of inertia about y-y axis[ Iz = expression ] # moment of inertia about z-z axis[ A = expression ] # cross-sectional area[ J = expression] # polar moment of inertia[ G = expression ] # bulk (shear) modulus[ t = expression ] # thickness[ rho = expression ] # density


Materials





material-name[ nu = expression ] # Poisson's ratio[ kappa = expression ] # shear force correction[ kappa expression ] # shear force correction[ Rk = expression ] # Rayleigh damping coefficient (K)[ Rm = expression ] # Rayleigh damping coefficient (M)[ Kx = expression ] # thermal conductivity in the x-direction[ Ky = expression ] # thermal conductivity in the y-direction[ Ky = expression ] # thermal conductivity in the z-direction



Materials





material-name[ nu = expression ] # Poisson's ratio[ kappa = expression ] # shear force correction[ Rk = expression ] # Rayleigh damping coefficient (K)[ Rm = expression ] # Rayleigh damping coefficient (M)[ Kx = expression ] # thermal conductivity in the x-direction[ Ky = expression ] # thermal conductivity in the y-direction[ Ky = expression ] # thermal conductivity in the z-direction

The material-name starts the definition. If an attribute of a material is not specified then that attribute is zero. The assignments may occur in any order.


Constraints

Constraints are applied to nodes to indicate about which axes a node can move. The syntax for defining a constraint is as follows:

constraintsconstraint –definitions

where constraint-definition has the following form:

constraint-name[ tx = c I u I expression ] # boundary translation along x axis[ ty = c I u I expression ] # boundary translation along y axis[ tz = c I u I expression ] # boundary translation along z axis[ rx = c I u I expression I h ] # boundary rotation about x axis[ I I i I h ] # b d t ti b t i[ ry = c I u I expression I h ] # boundary rotation about y axis[ rz = c I u I expression I h ] # boundary rotation about z axis[ itx = expression ] # initial displacement along x axis[ ity = expression ] # initial displacement along y axis[ itz = expression ] # initial displacement along z axis[ irx = expression ] # initial rotation about x axis[ iry = expression ] # initial rotation about y axis[ irz = expression ] # initial rotation about z axis



Constraints




constraint-name[ vx = expression ] # initial velocity along x axis[ vy = expression ] # initial velocity along y axis[ vz = expression ] # initial velocity along z axis[ ax = expression ] # initial acceleration along x axis[ i ] # i iti l l ti l i[ ay = expression ] # initial acceleration along y axis[ az = expression ] # initial acceleration along z axis

The constraint-name starts the definition. A value of c for a boundary condition indicates that the axis is constrained; a value of u indicates that the axis is unconstrained. An expression indicates a displacement (non-zero) boundary condition and may contain the t variable for time varying boundary conditions in transient analysis problems.


Constraints




constraint-name[ vx = expression ] # initial velocity along x axis[ vy = expression ] # initial velocity along y axis[ vz = expression ] # initial velocity along z axis[ ax = expression ] # initial acceleration along x axis[ i ] # i iti l l ti l i[ ay = expression ] # initial acceleration along y axis[ az = expression ] # initial acceleration along z axis

The initial displacement, velocity and acceleration specifications are only used in transient problems. A value of h for a rotational boundary condition indicates a hinge. By default, all axes are unconstrained.



Forces

Forces, or point loads, may be applied to nodes. The syntax for a force definition is as follows:

forcesforce-definitions

where a force-definition has the following form:

force-name[ Fx = expression ] # force along x axis[ Fy = expression ] # force along y axis[ Fz = expression ] # force along z axis[ Mx = expression ] # moment about x axis[ M i ] # t b t i[ My = expression ] # moment about y axis[ Mz = expression ] # moment about z axis


Forces

Forces, or point loads, may be applied to nodes. The syntax for a force definition is as follows:

forcesforce-definitions

where a force-definition has the following form:

force-name[ Sfx = expression ] # frequency-domain spectra of force along x axis[ Sfy = expression ] # frequency-domain spectra of force along y axis[ Sfz = expression ] # frequency-domain spectra of force along z axis[ Smx = expression ] # frequency-domain spectra of moment about x axis[ S i ] # f d i t f t b t i[ Smy = expression ] # frequency-domain spectra of moment about y axis[ Smz = expression ] # frequency-domain spectra of moment about z axis

The force-name starts the definition. If the force or moment is not specified then it is assumed to be zero. The expressions for forces may be time-varying. Time-varying expressions include the single variable t 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 w to represent the independent variable (radial frequency).



Loads

Distributed loads, or loads for short, are applied to elements. The syntax for a defining a distributed load is as follows:

distributed loadsload-definitions

where a load-definition has the following form:

load-name[ direction = dir ] # direction[ values = pair-list ] # local nodes and magnitudes

The load-name starts the definition. The dir is one of LocalX, LocalY, LocalZ (local coordinate system), GlobalX, GlobalY, GlobalZ (global coordinate system), parallel, or perpendicular. The pair-list is a sequence of pairs. A pair 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.


Expressions

An expression can be either constant or time-varying. As discussed above, time-varying expressions contain the variable t 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 expression has one of the following forms, where all operators have the precedences and associativities given to them in the C programming language.



Expressionsexpression ? expression: expression # in-line conditionalexpression II expression # logical orexpression && expression # logical andexpression I expression # integer inclusive orexpression ^expression # integer exclusive orexpression ^expression # integer exclusive orexpression & expression # integer andexpression == expression # equalityexpression != expression # inequalityexpression < expression # less thanexpression > expression # greater thanexpression <= expression # less than or equalexpression >= expression # greater than or equalexpression << expression # integer shift leftexpression >> expression # integer shift rightexpression expression # integer shift rightexpression + expression # additionexpression -expression # subtractionexpression * expression # multiplicationexpression / expression # divisionexpression % expression # integer remainder-expression # arithmetic negation! expression # logical negation~ expression # integer bitwise negation( expression ) # enforce precedence


Expressionssin ( expression ) # sinecos ( expression ) # cosinetan ( expression ) # tangentpow ( expression, expression ) # power (exponentiation)exp ( expression ) # exponentialexp ( expression ) # exponentiallog ( expression ) # natural logarithmlog10 ( expression ) # base-IO logarithmsqrt ( expression ) # square roothypot ( expression, expression ) # Euclidean distancefloor ( expression ) # floorceil ( expression ) # ceilingCmod ( expression, expression ) # floating point remainderCabs ( expression ) # absolute valuenumber # literal valuenumber # literal valuet # current time

Finally, a discretely valued expression has the following syntax, where the optional +indicates that the list represents one cycle of an infinite waveform.

( expression ',' expression ) ...[ + ]



Expressions

Below are a few examples of loading expressions:

5 10 15 20

t(s)

500

F (lbs)

F 100 * fmod( ,5.0)t

1 2

t(s)

1500

F (lbs)

F (fmod( ,1.0) 0.5 ? 3000 * fmod( ,0.5) :

3000 * (0.5 - fmod( ,0.5)))

t t

t

F (0,0.0) (4.99,500.0) F (0,0.0) (0.5,1500.0)(1,0)


Expressions

Below are a few examples of loading expressions:

2 4 6 8

t(s)

2000

F (lbs)

F (0,2000) (1.99,2000) (2,0) (3.99,0)

10 12

t(s)

1500

F (lbs)

F 3 ? 650 / 3* :

( 9 ? 650 : ( 12 ? 650 / 3*(12 ) : 0))

t t

t t t

93

F (fmod( ,4.0) 2.0 ? 2000 : 0)t F (0,0.0) (3,650) (9,650) (12,0) (13,0)



WinFElt Example 1

Use WinFElt to determine the nodal displacements and the element stresses.

Assume plane stress conditions. Let E = 30 x 106 psi, = 0.30, and t = 1 in. Consider the following discretization of two plane stress CSTthe following discretization of two plane stress CST.


WinFElt Example 1

WinFElt input file:

problem descriptionproblem descriptiontitle="CST Sample Problem (Logan 6.2, p.356)" nodes=4 elements=2

nodes1 x=0 y=0.0 constraint=pin2 x=0 y=10.0 constraint=pin3 x=20.0 y=10.0 constraint=free force=point4 x=20.0 y=0.0 constraint=free force=point

CSTPlaneStress elements1 nodes=[1,3,2] material=steel2 nodes=[1,4,3] material=steel

material propertiessteel e=30e06 nu=0.30 t=1.0

forcespoint fx=5000

constraintspin tx=c ty=c free tx=u ty=uend



WinFElt Example 1

WinFElt output file:

** CST Sample Problem (Logan 6 2 p 356) **** CST Sample Problem (Logan 6.2, p.356) **

Nodal Displacements-----------------------------------------------------------------------------Node # DOF 1 DOF 2 DOF 3 DOF 4 DOF 5 DOF 6-----------------------------------------------------------------------------1 0 0 0 0 0 02 0 0 0 0 0 03 0.00060958 4.1633e-06 0 0 0 04 0.0006637 0.00010408 0 0 0 0

Element Stresses-------------------------------------------------------------------------------1: 1004.8 301.44 2.4019 1004.8 301.43 0.195662: 995.2 -1.201 -2.4019 995.2 -1.2068 -0.13812

Reaction Forces-----------------------------------Node # DOF Reaction Force-----------------------------------1 Tx -50001 Ty -3002.42 Tx -50002 Ty 3002.4


WinFElt Example 1

The results are similar to those presented in the textbook on page 356.

In addition, WinFElt has some graphical visualization capabilities. By selecting the appropriate options on the Controls menu, a color contour of the displacements can be plotted.



WinFElt Example 1

The results are similar to those presented in the textbook on page 356.

If more elements are utilized it may be possible to visualize the smoothed stress contours.


WinFElt Example 2

Use WinFElt to determine the nodal displacements and the element stresses for the thin plate shown below.

Assume plane stress conditions. Let E = 210 GPa, = 0.30, and t = 5 mm. Consider the following discretization of four plane stress CST.



WinFElt Example 2

WinFElt input file

title="CST Sample Problem (Logan 6.14, p.381)" nodes=5 elements=4

nodesnodes1 x= 0.0 y= 0.0 constraint=free2 x=400.0 y= 0.0 constraint=free3 x=400.0 y=400.0 constraint=pin4 x= 0.0 y=400.0 constraint=pin5 x=200.0 y=200.0 constraint=free force=point

CSTPlaneStress elements1 nodes=[1,2,5] material=steel2 nodes=[2,3,5]3 nodes=[3,4,5]4 nodes=[1,5,4] material=steel

material propertiessteel e=210 nu=0.30 t=5.0

forcespoint fy=-30

constraintspin tx=c ty=c free tx=u ty=u

end


WinFElt Example 2

WinFElt output file** CST Sample Problem (Logan 6.14, p.381) **

Nodal Displacements----------------------------------------------------------------------------------------------------------------------------------------------------------Node # DOF 1 DOF 2 DOF 3 DOF 4 DOF 5 DOF 6-----------------------------------------------------------------------------1 -0.0016515 -0.012505 0 0 0 02 0.0016515 -0.012505 0 0 0 03 0 0 0 0 0 04 0 0 0 0 0 05 4.9049e-19 -0.016279 0 0 0 0

Element Stresses-------------------------------------------------------------------------------1: 0.00059891 -0.003784 -1.0875e-19 0.00059891 -0.003784 -1.4217e-152: 0.0031171 0.0075 0.003716 0.0096226 0.00099449 -29.7353: 0.0056352 0.018784 -1.9808e-19 0.018784 0.0056352 04: 0.0031171 0.0075 -0.003716 0.0096226 0.00099449 29.735

Reaction Forces-----------------------------------Node # DOF Reaction Force-----------------------------------3 Tx 6.23413 Ty 154 Tx -6.23414 Ty 15



WinFElt Example 3

Use WinFElt to determine the nodal displacements and rotations, element forces, and the reactions for the rigid frame shown below

Assume E = 3 x 106 psi, A = 15 in2, and I = 250 in4


WinFElt Example 3

WinFElt input file

problem descriptiontitle="Simple Frame Problem (Logan 5.8 p.302)" nodes=4 elements=3

nodes1 x= 0.0 y= 0.0 constraint=fixed2 x= 0.0 y=240.0 constraint=free3 x=240.0 y=240.0 constraint=free4 x=240.0 y= 0.0 constraint=fixed

beam elements1 nodes=[1,2] material=steel load=uni2 nodes=[2,3]3 nodes=[3,4] material=steel

material propertiessteel E=30e06 A=15 Ix=250

distributed loadsuni direction=perpendicular values=(1,-20.833) (2,-20.833)

constraintsfixed tx=c ty=c rz=c free tx=u ty=u rz=u

end



WinFElt Example 3

WinFElt output file

** Simple Frame Problem (Logan 5.8 p.302) **

Nodal DisplacementsNodal Displacements-----------------------------------------------------------------------------Node # DOF 1 DOF 2 DOF 3 DOF 4 DOF 5 DOF 6-----------------------------------------------------------------------------1 0 0 0 0 0 02 0.24746 0.00038057 0 0 0 -0.000194353 0.2469 -0.00038057 0 0 0 -0.000725364 0 0 0 0 0 0

Element Stresses-------------------------------------------------------------------------------1: -713.57 3959.2 2.8118e+05 713.57 1040.7 690342: 1040.7 -713.57 -69034 -1040.7 713.57 -1.0222e+053: 713.57 1040.7 1.0222e+05 -713.57 -1040.7 1.4756e+05

Reaction Forces-----------------------------------Node # DOF Reaction Force-----------------------------------1 Tx -3959.21 Ty -713.571 Rz 2.8118e+054 Tx -1040.74 Ty 713.574 Rz 1.4756e+05


winfelt manual version 1.1 - university of memphis

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