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Table of Contents
                            Task Description
Theoretical Principles
	Systems of Coordinates
	Overview of the Element Types
	Mesh Partitioning
	Plane Elements
	Solid Elements
	Boundary Conditions
	Girders
	Literature
	Limitations
Input Description
	Nodes
	Elements
	Results
	Restart
	Input Records
	ECHO - Control of the Output
	SYST - Global System Parameters
	NODE - Nodal Coordinates and Constraints
	INTE - Intermediate Nodes
	KINE - Kinematic Dependencies
	MESH - Generation of Nodes and Quadrilateral Elements
	IMES - Generation of Irregular Nodes, Quadrilateral Elements
	CUBE - Nodes and Cubic Elements
	TRAN - Transformation of Nodes
	MIRR - Mirroring of Nodes
	ALIN - Node upon a Line (Projection to the Line)
	SECT - Node at Intersection of two Straight Lines
	Materials
	NORM - Default Design Code
	MAT - General Material Properties
	MATE - Material Properties
	MLAY - Layered Material
	BMAT - Elastic Support / Interface
	NMAT - Non-linear Material
	MEXT - Extra Materialconstants
	CONC - Properties of Concrete
	STEE - Properties of Metals
	TIMB - Properties of Timber
	MASO - Masonry / Brickwork
	SSLA - Stress-Strain Curves
	SVAL - Cross-section values
	SREC - Rectangle, T-beam, Plate
	SCIR - Circular and Annular Sections
	BORE - Bore Profile of a Sondation
	BLAY - Layer of the Soil Strata
	BBAX - Input of Axial Subgrade Parameters
	BBLA - Input of Lateral Subgrade Parameters
	HING - Hinged Connection Combinations for Beams
	GRP - Group Control
	TRUS - Truss-bar Elements
	CABL - Cable Elements
	BEAM - Beam Elements
	ADEF - Beginning of Beam Segment Definition
	BDIV - Input of Beam Segments
	BSEC - Beam Sections
	SUPP - Definition of Support Sections
	QUAD - Plane Elements (Disks / Plates / Shells)
	BRIC - Three-dimensional Solid Elements
	SPRI - Spring Elements
	BOUN - Distributed Elastic Support
	FLEX - General Elastic Element
	DAMP - Damping Elements
	MASS - Concentrated Masses
Output Description
	Nodal Values
	Material Values
	System Statistics
	Cross-sectional Overview
	Group Qualities
	Plane Elements (2-D, QUAD)
	Three-dimensional Solid Elements (3-D, BRIC)
	Boundary Elements
	Geometric Definitions (Bedding Profiles)
	Bending Beams and Piles
	Truss-bar Elements
	Cable Elements
	Springs
Examples
	Angle Plate
	Pointwise Supported Ceiling Plate
	Gridwork
	Plane Frame, Restrained in Space
	Shell Structure
	Reinforced Concrete Box
	Calotte Shell
	Examples in the Internet
                        
Document Text Contents
Page 195

GENFDefinition of Finite Elements

5−23Version 10.20

$ SUBPROGRAM FOR NODE GENERATION IN A COORDINATE THIRD
$ NODE COORDINATES WITH NONLINEAR INCREMENT ROTATION
$ #1,#2,#3 = NODE NUMBER ON AXIS + INCREMENTS
LET#10 0,45/#4 $ Starting value + Increment phi−Y
LOOP #4+1
LET#20 0,45/#4 $ Starting value + Increment phi−Z
LOOP #4+1
LET#90 SQR(TAN(#10)**2+TAN(#20)**2)
LET#91 ATN(#90)
LET#92 COS(#91),0.0
LOOP #91−0.001 ; LET#93 SIN(#91)/#90 ; ENDLOOP −1
$ nodes
#1 #9*#92 #9*TAN(#20)*#93 #9*TAN(#10)*#93
LET#20 #20+#21
LET#1 #1+#3
ENDLOOP
LET#10 #10+#11
LET#1 #1−#3*(#4+1)+#2
ENDLOOP
$BLOCK END1
LET#1 101,10,1 $ Node number + Increments of the X−Sector
NODE NO X Y Z
$BLOCK SET1
LET#1 101+#4*101,−100,10 $ Node number + Increments of the Y−Sector
NODE NO Y Z X
$BLOCK SET1
LET#1 101+#4*110,1,−100 $ Node number + Increments of the Z−Sector
NODE NO Z X Y
$BLOCK SET1
END

The following values were selected for a comparison of the two mesh parti�
tionings:

Radius R = 10.0 m
Thickness t = 5 mm
E−Modulus E = 2.1E8 kN/m2

Poisson’s ratio µ = 0.2
Loading p = 10 kN/m2 radial

n� �� p�R�2��� 50�kN�m

�R� �� n
�E� t�

� �1��� �R� �� 0.381�mm

In the case of the mixed mesh, the results at the QUAD−corners are u = 0.380
mm, n−xx = 49.83 kN/m2 and n−yy = 49.83 kN/m2. At the triangle’s corner

Page 196

GENF Definition of Finite Elements

Version 10.205−24

though one obtains u = 0.843 mm, n−xx = 43.22 kN/m2 and n−yy = 65.55 kN/
m2.

The present mesh results in the following values:

Partition 4 Partition 8
Axes of coordinates (Node 101) 0.133 mm 0.363 mm
Bisecting line of the angle (Node 109) 1.280 mm 0.458 mm
Space diagonal (Node 189) 4.806 mm 0.388 mm

The stress resultants in the elements fluctuate in partition 8 from 45.30 up
to 54.41 kN/m; the value on the axis of coordinates is 49.86 kN/m.

Opposite to the mixed mesh, the QUAD−elements generated in such manner
are unfortunately not perfectly plane any more, a fact that was neglected
earlier and led to excellent results. Starting from version 93 ASE takes this
effect into consideration by means of eccentricities. The entire structure be�
comes more flexible this way and a clear bulge is obtained along the space di�
agonals in cases of coarse partitioning. The influence of the eccentricities
diminishes very fast by refining the mesh.

5.8. Examples in the Internet

Different statics examples are to be found in the Internet at www.sofis�
tik.com/bibliothek.htm

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