Information Technology Reference
In-Depth Information
TABLE 2.4
The Generalized Variational Principles in Matrix Form
Form AB:
z
T
0
E
−
1
z
p
V
0
dV
z
T
0A
T
00
z
−
dS
S
p
δ
p
0
−
D
T
σ
V
δ
−
+
+
D
u
−
S
u
δ
z
T
00
−
z
0
Au
dS
+
+
=
0
A0
Form CD:
z
T
0
E
−
1
z
p
V
0
dV
z
T
00
A0
z
−
dS
p
0
u
D
T
V
δ
−
+
S
p
δ
+
−
σ
D
−
S
u
δ
z
T
0
z
+
0
Au
dS
A
T
00
−
+
=
0
Form CB:
z
T
0
−
E
−
1
z
p
V
0
dV
z
T
−
dS
p
u
D
T
V
δ
−
+
S
p
δ
D
u
0
z
T
0
z
0
Au
dS
S
u
δ
−
A
T
+
+
=
0
−
A0
Form AD:
z
T
0
E
−
1
z
p
V
0
dV
z
T
0A
T
A0
z
p
0
dS
−
D
T
σ
V
δ
−
+
S
p
δ
−
−
σ
D
−
S
u
δ
z
T
0
Au
dS
+
=
0
is often referred to as the
Hellinger
7
-Reissner
8
functional
[Hellinger, 1914 and Reissner, 1950].
It commonly forms the basis of the so-called
mixed methods
of analysis.
7
Ernst Hellinger (1883-1950) was a German pioneer in operator theory. He attended the same high school (gym-
nasium) in Breslau as Richard Courant and Max Born and then became Hilbert's student in G ottingen, as did
Courant and Born. Born is sometimes also given credit in the development of the fundamentals of the mixed
variational theorems. Hellinger was a long-term champion of Hilbert's philosophies. After some time in Marburg,
Hellinger in 1914 received a professorship at what is now the Johann Wolfgang Goethe Universit at Frankfurt am
Main. After a brief 1938 stay in Dachau he departed from Germany. In 1939 a temporary position, involving no
university financial support, was created at Northwestern University. His position was continued for a second
year with private support, and, finally, he was funded as a lecturer in mathematics by Northwestern. He retired
from Northwestern in 1949 at the mandatory retirement age of 65 and, because of financial difficulties, took a
temporary position at the Illinois Institute of Technology.
8
Max Erich Reissner (1913-1996) was born in Aachen, Germany, and educated primarily in Germany, receiving
his Dipl. Ing. (1935) and Dr. Ing. (1936) from the Technische Hochschule, Berlin and his Ph.D. (1938) from MIT.
He began to publish technical papers as a student in 1934. Because of the political developments in Germany he
departed for the United States in 1936. His professional career was spent at MIT in the Department of Mathematics
and as a Professor of Applied Mechanics and Mathematics at the University of California at San Diego. He and his
father as well as his son have worked in similar areas of solid mechanics. Reissner contributions to the literature
on thin-walled beams, plates, and shells, the theory of elasticity, and structural mechanics were immense. Some of
the ideas he proposed have become familiar theories, e.g., Reissner's plate theory and his variational theorem. His
work with thin-walled structures has been influential in design. For example his shear lag theory for box beams
has been important in the design of the wing-body intersection of jet aircraft.
Search WWH ::
Custom Search