1-D boundary value problem, diffeq,1,0
1-D boundary value problem,1,4
1-D Lagrangian shape functions,1,8
1-D ordinary differential equation,1,12
1-D, Effect of using a finer mesh,1,16
1-D, Series of elements,1,20
1-D, Single element,1,24
1-D, Differentiation,1,28
1-D, Shape functions,1,32
2-D circular domain,1,36
2-D code: Rectangular domain,1,40
2-D dimensions, Green's theorem,1,44
2-D Lagrange shape,1,48
2-D Laplace equation, diffeq,1,52
2-D Laplace, linear isoparametric elements,1,56
2-D Laplace, rectangular domain,1,60
2-D plane stress, isoparametric elements,1,64
2-D plane stress, triangular elements,1,68
2-D rectangular domain,1,72
2-D, Serendipity elements,1,76
2-D, Exact solution on rectangular domain,1,80
3-D body, general,1,84
7 steps of finite element method,1,88
algorithm assembly,1,92
algorithm, plotting,1,96
algorithms, Romberg,1,100
approximation of displacement,1,104
approximation, Rayleigh-Ritz method of,1,108
arbitrary shape, solid model of,1,112
arc length,1,116
area integral,1,120
assembled matrix equation,1,124
assembled stiffness matrix, properties of,1,128
assembled stiffness matrix,1,132
assembling the elements,1,136
automatic mesh generation,1,140
automatic solid mesh generation,1,144
axial deformation truss element,1,148
banded matrix,1,152
bandwidth, assembled stiffness matrix,1,156
block in constant stress field,1,160
bodies, homogeneous,1,164
body, 3-D,1,168
boundaries, derivative vectors,1,172
boundaries, node mapping along,1,176
boundaries,1,180
boundary condition, symmetric,1,184
boundary conditions, direct modification,1,188
boundary conditions, how to treat,1,192
boundary conditions,1,196
calculus, variational,1,200
chain rule,1,204
circular disk, Laplace, 2-D code,1,208
circular disk, Laplace's equation in,1,212
collocation, subdomain,1,216
comparison of meshes,1,220
comparison of the different methods,1,224
comparison of two mesh densities,1,228
comparison to direct method, elastic elements,1,232
compatibility rule, spring system,1,236
compatibility rule,1,240
completeness requirement,1,244
condensation of internal nodes,1,248
constant stress field for triangular elements,1,252
constant stress field, block in,1,256
constant stress field,1,260
constitutive equations,1,264
continuity of elements,1,268
continuity requirements,1,272
continuity, 1-D,1,276
continuous systems,1,280
continuous vs. discrete,1,284
continuum, potato,1,288
continuum, strain energy of a,1,292
contour plot of max. principal stress,1,296
contour plots,1,300
coordinate systems, local&global,1,304
coordinate transformations,1,308
coordinates, normalized,1,312
coordinates, transformation of,1,316
counterclockwise node numbering,1,320
cubic elements,1,324
cubic mapped elements,1,328
curved elements,1,332
derivation using inverse of coefficient matrix,1,336
derivative of linear approximation,1,340
derivative of quadratic approximation,1,344
derivatives of shape functions, 1-D,1,348
derivatives, transformation of,1,352
differential equation, 1-D ordinary,1,356
differential equation, ordinary,2,360
differential equations: 1-D boundary value problem,1,368
differential equations: 2-D Laplace equation,1,372
differential operators,1,376
differentiation and integration, 1-D,1,380
differentiation and integration, 2-D,1,384
differentiation, 1-D,1,388
direct method for plane stress,1,392
direct method, matrix equation for,1,396
direct method,1,400
direct modification, boundary conditions,1,404
direct modification,1,408
Dirichlet boundary condition,1,412
discrete approach,1,416
discrete systems,1,420
discrete vs. continuous,1,424
discretization using finite elements,1,428
discretization, process of,1,432
discretization,1,436
discretizations, irregularly shaped continuum,1,440
discretizing a rectangular area,1,444
displacement field,1,448
displacement function, exact,1,452
displacement, approximation of,1,456
displacement, interpolation of,1,460
distributed edge load,2,464
divergence of a vector,1,472
divergence theorem,1,476
domains, irregularly shaped,1,480
eigenvalue problems,1,484
eight-noded rectangular,1,488
elastic continua,1,492
elastic spring, simple,1,496
elastic, elements of,1,500
elasticity matrix, material,1,504
elasticity matrix,1,508
elasticity, modulus of,1,512
electrical networks,1,516
electrical potential,1,520
electrical resistors, network of,1,524
element boundaries, integration along,1,528
element equations, evaluation of,1,532
element interpolation,1,536
element types,1,540
element, isoparametric,1,544
element, node rectangular,1,548
element, parent,1,552
element, subparametric,1,556
element, superparametric,1,560
element, triangular,1,564
elements, cubic,1,568
elements, curved,1,572
elements, linear,1,576
elements, rectangular,1,580
elements, triangular,1,584
energy method for plane stress,1,588
energy method,1,592
energy, minimization of total potential,1,596
energy, minimum potential,1,600
energy, strain,1,604
engineering design,1,608
equation, Laplace's,1,612
equation, strain-displacement,1,616
equations, global,1,620
equations, local,1,624
equilibrium problems,1,628
equilibrium, spring system,1,632
equivalent forces for stress field,1,636
equivalent forces,1,640
equivalent stiffness, spring system,1,644
evaluation of element equations,1,648
external work,2,652
field quantity,1,660
field variable, plot of over new mesh,1,664
field variable,1,668
field, displacement,1,672
field,1,676
finer mesh,1,680
finite difference method,1,684
finite element algorithm,1,688
finite element applications,1,692
finite element code, quadratic,1,696
finite element code,1,700
finite element mesh using tetrahedral elements,1,704
finite element mesh,2,708
finite element meshes, 2 correct,1,716
finite element method, 7 steps of,1,720
finite element method,1,724
finite element, triangular,1,728
finite element, truss analysis,1,732
finite elements of elastic continua,1,736
finite elements, discretization using,1,740
finite elements, Galerkin's method to,1,744
finite elements, history of,1,748
Fink truss,2,752
flow, heat,1,760
fluid flow networks,1,764
fluid networks,1,768
four-noded rectangular,1,772
function, exact displacement,1,776
function, shape,1,780
functions, interpolation,1,784
functions, serendipity,1,788
functions, shape,1,792
Galerkin's method to finite elements,1,796
Galerkin's method,1,800
Gaussian quadrature,1,804
Gaussian,1,808
Gauss-Legendre integration points,1,812
Gauss-Legendre quadrature, integration points,1,816
Gauss-Legendre quadrature,2,820
general assembly procedure,1,828
general form,1,832
generalization of 1-D shape functions,1,836
global coordinate system, truss elements,1,840
global coordinate systems,1,844
global equations,1,848
global force vector,1,852
global stiffness matrices,1,856
global vs. local approximation,1,860
gradient of a scalar,1,864
gravitational potential,1,868
Green's theorem, 2&3 dimensions,1,872
Green's theorem,1,876
half bandwidth,1,880
heat flow, details of,1,884
heat flow, steady-state,1,888
heat flow,1,892
higher-order polynomials, 1-D,1,896
history of finite elements,1,900
homogeneous bodies,1,904
Hooke's law,1,908
identical track link,1,912
incorrect mesh,1,916
integral, surface,1,920
integration along element boundaries,1,924
integration by parts, 1-D,1,928
integration by parts, 2-D,1,932
integration of mapped quadratic elements,1,936
integration points for Gauss-Legendre quadrature,1,940
integration points, Gauss-Legendre,1,944
integration points,1,948
integration, numerical,3,952
internal strain energy,1,964
interpolation - shape functions,1,968
interpolation functions,3,972
interpolation of displacement,1,984
interpolation of nodal values,1,988
interpolation, piecewise linear, 1-D,1,992
interpolations, piecewise quadratic, 1-D,1,996
irregularly shaped continuum, 3 discretizations,1,1000
irregularly shaped domains,1,1004
isoparametric element,2,1008
isoparametric plane stress elements, linear,1,1016
isoparametric plane stress elements, quadratic,1,1020
isoparametric plane,1,1024
isotropic materials,1,1028
Jacobian matrix, plot, cubic elements,1,1032
Jacobian matrix, plot, linear elements,1,1036
Jacobian matrix, plot, quadratic elements,1,1040
Jacobian matrix,1,1044
Jacobian plot, see plot of Jacobian matrix,1,1048
Jacobian, negative,1,1052
Lagrange element, rectangular,1,1056
Lagrange polynomials, 2-D,1,1060
Lagrange polynomials, limitations of,1,1064
Lagrange shape functions, 2-D,1,1068
Lagrange shape, 2-D,1,1072
Lagrange, 1-D,1,1076
Lagrange, 2-D,1,1080
Lagrange,1,1084
Laplace equation,1,1088
Laplace, 2-D code: circular disk,1,1092
Laplace, linear finite element code,1,1096
Laplace's equation in circular disk,1,1100
Laplace's equation,1,1104
law, Hooke's,1,1108
length of mapped line elements,1,1112
limitations of Lagrange polynomials,1,1116
line integral from a surface integral,1,1120
linear elasticity theory,1,1124
linear elements,1,1128
linear finite element code, for Laplace,1,1132
linear interpolation,1,1136
linear isoparametric plane stress elements,1,1140
linear isoparametric plane stress,1,1144
linear mapped elements,1,1148
linear triangular element,1,1152
linear, 1-D,1,1156
linear,1,1160
local coordinate system, truss elements,1,1164
local coordinate systems,1,1168
local equations,1,1172
local stiffness matrices,1,1176
manual mesh generation,2,1180
mapped elements,2,1188
mapped rectangular,1,1196
mapping in one dimension,1,1200
material elasticity matrix,1,1204
matrices, global stiffness,1,1208
matrices, local stiffness,1,1212
matrix equation for direct method,1,1216
matrix equation, assembled,1,1220
matrix partitioning,2,1224
matrix, assembled stiffness,1,1232
matrix, banded,1,1236
matrix, Jacobian,1,1240
matrix, material elasticity,1,1244
matrix, stiffness,1,1248
maximum principal stress, contour plot,1,1252
mesh and tetrahedral elements,1,1256
mesh generation, automatic,1,1260
mesh generation, see discretization,1,1264
mesh, finer,1,1268
mesh, finite element,1,1272
mesh, plot finite element,1,1276
meshes, 2 correct finite element,1,1280
meshes, comparison of,1,1284
method of weighted residual,1,1288
method, direct,1,1292
minimization of total potential energy,1,1296
minimum potential energy principle,1,1300
modulus of elasticity,1,1304
negative Jacobian,1,1308
net stiffness, see equivalent stiffness,1,1312
network of electrical resistors,1,1316
network, electrical,1,1320
network, fluid,1,1324
networks, fluid flow,1,1328
Newton-Cotes quadrature,1,1332
nodal values, interpolation of,1,1336
node mapping along boundaries,1,1340
node numbering, counterclockwise,1,1344
node rectangular element,1,1348
nodes, restrained,1,1352
nodes,1,1356
normal strain,1,1360
normal stress,1,1364
normal vector,1,1368
normalized coordinates, transformation to,1,1372
normalized coordinates,2,1376
number of terms,1,1384
numerical integration ,1,1388
numerical integration,2,1392
one elastic spring,1,1400
operators, differential,1,1404
order of shape functions,1,1408
ordinary differential equation,2,1412
orthogonal transformations,1,1420
outline of Electronic Book,1,1424
overview,1,1428
parent element,1,1432
partitioned matrix,1,1436
partitioned system of equations,1,1440
partitioning, matrix,1,1444
parts, integration by, 1-D,1,1448
parts, integration by, 2-D,1,1452
Pascal's triangle,1,1456
Payne and Irons technique, boundary conditions,1,1460
Payne and Irons technique,1,1464
piecewise approximation, quadratic,1,1468
piecewise linear interpolation, 1-D,1,1472
piecewise quadratic interpolation, 1-D,1,1476
pin-jointed truss,1,1480
plane of symmetric, see symmetric boundary condition,1,1484
plane strain,1,1488
plane stress and strain,1,1492
plane stress elements,1,1496
plane stress, direct method for,1,1500
plane stress, energy method for,1,1504
plane stress, linear isoparametric,1,1508
plane stress,1,1512
plane, isoparametric,1,1516
plate in tension, analysis using,1,1520
plate with circular holes,1,1524
plot finite element mesh,1,1528
plot of a distributed load,1,1532
plot of an isoparametric element, 2-D,1,1536
plot of derivative vectors on element boundaries,1,1540
plot of field variable over new mesh,1,1544
plot of Jacobian matrix,1,1548
plot of principle stresses,1,1552
plotting algorithm,1,1556
polynomials, higher-order polynomials, 1-D,1,1560
point collocation,1,1564
point forces,1,1568
Poisson's ratio,1,1572
polynomials in 1-D: higher order,1,1576
polynomials in 1-D: Lagrange,1,1580
polynomials in 1-D,1,1584
polynomials in 2-D, Pascal's triangle,1,1588
polynomials in 2-D,1,1592
potato continuum,1,1596
potential energy, minimum,1,1600
potential, surface plot of,1,1604
potential,1,1608
principal stress, contour plot of,1,1612
principal stresses, in linear finite element code,1,1616
principal stresses, in quadratic finite element code,1,1620
principle of minimum potential energy,2,1624
propagation,1,1632
properties of shape functions,1,1636
quadratic elements, mapped, integration of,1,1640
quadratic elements,1,1644
quadratic finite element code,2,1648
quadratic interpolation,1,1656
quadratic isoparametric elements,2,1660
quadratic mapped elements,1,1668
quadratic piecewise approximation,1,1672
quadratic, 1-D,1,1676
quadratic,2,1680
quadrature, Gaussian,1,1688
quadrature, Gauss-Legendre,1,1692
quadrature, Newton-Cotes,1,1696
quadrature,1,1700
Rayleigh-Ritz method of approximation,1,1704
rectangular area, discretizing of a,1,1708
rectangular domain,1,1712
rectangular elements,1,1716
rectangular Lagrange element,1,1720
rectangular region,1,1724
rectangular, eight-noded,1,1728
rectangular, four-noded,1,1732
rectangular, mapped,1,1736
rectangular, specialized,1,1740
rectangular, twelve-noded,1,1744
reduction to 1-D,1,1748
residual methods, overview of,1,1752
residuals, weighted,1,1756
restrained nodes,1,1760
retaining wall,1,1764
Romberg algorithm,1,1768
rule, Simpson's,1,1772
sampling points using Gauss-Legendre,1,1776
sampling points,1,1780
serendipity functions, rectangular elements,1,1784
serendipity functions,1,1788
serendipity shape functions,1,1792
serendipity, 2-D,1,1796
shape function,2,1800
shape functions, 1-D Lagrangian,1,1808
shape functions, derivatives of, 1-D,1,1812
shape functions, Lagrange, 2-D,1,1816
shape functions, order of,1,1820
shape functions, properties of,1,1824
shape functions, serendipity,1,1828
shape functions,2,1832
shape, arbitrary, solid model of,1,1840
shear strain,1,1844
shear stress,1,1848
simple elastic spring,1,1852
Simpson's rule,1,1856
solid mesh generation, automatic,1,1860
solid model of arbitrary shape,1,1864
solution, spring system,1,1868
specialized rectangular,2,1872
spring system, strain energy of a discrete,1,1880
spring system,2,1884
spring, elastic,1,1892
spring, one elastic,1,1896
spring, simple elastic,1,1900
spring, system,1,1904
springs, system of,1,1908
steady-state heat flow,1,1912
steady-state problems,1,1916
stiffness matrix: Properties,1,1920
stiffness matrix,2,1924
stiffness, equivalent,1,1932
strain components,1,1936
strain energy of a continuum,1,1940
strain energy of a discrete spring system,1,1944
strain energy, internal,1,1948
strain energy,1,1952
strain, normal,1,1956
strain,1,1960
strain-displacement equation,1,1964
stress components,1,1968
stress field, equivalent forces for,1,1972
stress, normal,1,1976
stress, Von Mises,1,1980
stress,1,1984
stress-strain relation,1,1988
stress-strain relationship,2,1992
subdomain collocation,1,2000
subparametric element,1,2004
substructuring,1,2008
surface integral, transformation,1,2012
surface integral,1,2016
surface plot of potential,1,2020
surface tractions, along an edge,1,2024
surface tractions, treating,1,2028
surface tractions,1,2032
symbolic form, 1-D,1,2036
symbolic form,1,2040
symmetric boundary conditions,1,2044
system of equations, partitioned,1,2048
system of springs,1,2052
system topology,1,2056
systems, continuous,1,2060
tangent vectors, curvilinear coordinates,1,2064
temperature distribution thru composite wall,1,2068
tension, plate in,1,2072
tetrahedral elements, finite element mesh using,1,2076
tetrahedral elements, mesh and,1,2080
theorem, divergence,1,2084
theorem, Green's,1,2088
theory of linear elasticity,1,2092
three famous princes,1,2096
three-noded triangular,1,2100
topology of system,1,2104
total potential energy,1,2108
track link,1,2112
traction, surface,1,2116
tractions, surface, treating of,1,2120
tractions,1,2124
transformation of coordinates,1,2128
transformation of derivatives,1,2132
transformation to normalized coordinates,1,2136
transformations, coordinate,1,2140
transformations, orthogonal,1,2144
transient problem,1,2148
transition elements,1,2152
treating surface tractions,1,2156
trial functions,1,2160
triangle, Pascal's,1,2164
triangular element, linear,1,2168
triangular element,1,2172
triangular elements, constant stress field for,1,2176
triangular elements,1,2180
triangular finite element,1,2184
triangular plane stress code,1,2188
triangular, three-noded,1,2192
truss analysis: Finite element,1,2196
truss analysis,1,2200
truss element, axial deformation,1,2204
truss structure,2,2208
truss, Fink,2,2216
truss, pin-jointed,1,2224
twelve-noded rectangular,1,2228
two dimensions,1,2232
variational calculus,1,2236
vector, global force,1,2240
vector, normal,1,2244
vectorize function, in linear finite element code,1,2248
vectorize function, in quadratic finite element code,1,2252
Von Mises stress,1,2256
wall, composite, temperature distribution thru,1,2260
wall, retaining,1,2264
warping,1,2268
weighted residual, method of,1,2272
weighted residuals, method of,1,2276
weighted residuals,1,2280
Zienkiewicz,1,2284