INTRODUCTION TO FINITE ELEMENTS ENGINEERING

CO? ROM Included

INTRODUCTION TO

FINITE ELEMENTS IN ENGINEERING

THIRD EDITION

Tirupathi R. Chandrupatla Ashok D. Belegundu

Programs Included in the CD-ROM

CH?1

CH?7

QUAD

QUADCG AXIQUAD

CH?l GAUSS caSOL SKYLINE

CH?8 BEAM FRAME2D FRAME3D

CH?J FEMlD

CH?9 TETRA3D HEXAFRQN

cn..

TRUSS2D TRUSSKY

CH?IO HEATlD HEAT2D TORSION

CH?5 CST

CH?ll INVITR JACOBI BEAMKM CSTKM GENEIGEN

cn..

AXISYM

CH?U MESHGEN PL0T20, BESTFIT BESTFITQ

CONTOURA

CONTOURB

CD-ROM Contents

Direetory

IQBASIC \FORTRAN

Ie

IVB IEXC'ELVB IMATLAB IEXAMPLES

Deseription

Programs in QBASIC Programs in Fortran Language Programs in C Programs in Visual Basic Programs in Excel Visual Basic Programs in MATLAB Example Data Files (.inp extension)

List of Key Symbols Used in the Text

Symbol

u(.t,y,:) "" [u(x,y, z), v(x, y, l,),

w(x,y,Z)]T

r, [[,,f,,a

T"= [T"T,,1~P i == [f.,ey,i"}""Y,,,Yq]T u =- {u"u"U"1',,,1',.. T.t,]T

n

?

Q

k K

r

T'

""(x,y, ~)

?

N, D,and B

Description

displacements along coordinate directions at point (x, y, zj

components of body force per unit volume, at point (x, y. z) components of traction force per unit area, at point (x, y,z) on the surface strain eomponents;t: are normal strains and}' are engineering shear strains stress components; u are normal stresses and T are engineering shear stresses

Potential energy = U + W P, where U == strain energy, W P = work potential

vector of displacements of the nodes (degrees of freedom or DOF) of an element, dimension (NDN?NEN,l)---see next Table for explanation of NDNand NEN

vector of displacements of ALL the nodes of an element, dimension (NN?NDN, I)-see next Table for explanation of NN and NDN element stiffne~ matrix: strain energy in element, U, == !qTkq

I glohal stiffness matrix for entire structure: n = Q1 KQ _ Q IF

body force in element e distributed to the nodes of the element traction fOfce in element e distributed to the nodes of the element virtual displacement variable: counterpart of the real displacement u(x, y, z) vector of vinual displacements of the nodes in an element; cOWlterpart of q shape functions in t1)( coordinates, material matrix, strain-displacement malril. respectively. u = Nq, = Bq and (J' = DBq

structure ofInpnt Files'

TITLE (*)

PROBLEM DESCRIPTION (*) NN NE NM NOIM NEN NON (*)

422 2 3 2

NO Nl NMPC (*) 5 2 0

1 Line of data, 6 entries per 1ine --- 1 Line of data, 3 entries

Node. Coordinate'! Coordinate#NDIH (*)

4~,

g;

O~2 } ---NN Lines of data, (NlJIM+l)entries

o.) of Eleml Nodell NodelNEN Mat' Element Characteristicstt (*)

1

4

1

2

1

0.5

---HE Lines data.

2

3

4

2

2

O.S

O. (NEN+2+#ofChar.)entries

OO~~F' speCggified}DiSPlacement (*)

---NO Llnes of data, 2 entries

8

0

DOF' Load (*)

4 -7500 ) ---NL Lines of data, 2 entries

3 3000

MAn Mat.erial Propertiestt (*)

1

30e6

0.25 12e-6 } --!.NM Lines of data, (1+ , of prop.)entries

2 20e6 81 i 82

0.3 O. j B3 (Multipoint constraint: Bl*Qi+B2*Qj=B3) (OJ

}

---NMPC Lines of data, 5 entries

tHEATlD and HEATID Programs need extra boundary data about flux and convection. (See Chapter 10.) (~) = DUMMY LINE - necessary No/eo' No Blank Lines must be present in the input file t'See below for desCription of element characteristics and material properties

Main Program Variables

NN = Number of Nodes; NE = Number of Elements; NM = Number of Different Materials NDIM = Number ofCoordinales per Node (e.g..NDlM = Uor 2?D.or = 3for3.D): NEN = Number of Nodes per

Element (e.g., NEN '" 3 for 3-noded trianguJar element, or = 4 for a 4-noded quadrilateral) NDN '" Number of Degrees of Freedom per Node (e.g., NDN '" 2 for a CiT element, or '" 6 for 3-D beam element)

ND = Number of Degrees of Freedom along which Displacement is Specified'" No. of Boundary Conditions

NL = Number of Applied Component Loads (along Degrees of Freedom)

NMPC = Number of Multipoint Constraints; NO '" Total Number of Degrees of Freedom = NN ~ NDN

..........

Element Cbancterisdcs

Mlterial PToperties

FEMlD, TRUSS, TRUSSKY CST,QUAD

AXISYM FRAME2D FRAME3D TETRA, HEXAFNT

HEATID BEAMKM

CSTKM

Area, Temperature Rise Thickness, Temperature Rise

Temperature Rise Area, Inertia, Distributed liJad Area, 3?ioertias, 2-Distr. Loads

Temperature Rise Element Heat Source

Inertia,Area Thickness

E E,II,a

E. ". Ct E E

E,II,a Thermal Conductivity, k

E,p E,I',a,p

1 I

Introduction to Finite Elements in Engineering

Introduction to Finite Elements in Engineering

T H I R D EDITION

TIRUPATHI R. CHANDRUPATLA

Rowan University Glassboro, New Jersey

ASHOK D. BELEGUNDU

The Pennsylvania State University University Park, Pennsylvania

Prentice Hall, Upper Saddle River, New Jersey 07458

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