ANALYSIS
METHODS
ENUIRONMENTRL RNO
CONDITIONS
OPERRTI ONRL
+
32
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+
OUERRLL STRRINS
RSSUMPTIONS
GOUERNING
RNO
EQURTIONS
OISPLRCEMENTS
b
AN0 MOOELS
*
A
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Vasiliev
32.1 INTRODUCTION
A detailed analysis of composite structures can
provide information about the stressstrain
state, strength, stiffness, stability and vibra
tional behaviour of structural elements. The
analytic methods are those used in solid
mechanics; the equations are modified to
reflect the structural behaviour of composite
structures. These equations are based on a sys
tem of assumptions that take into account the
key features of a structure and establish the
appropriate model for the structural element
under consideration.
To start the analysis (Fig.
32.1),
one must
know the geometric configuration of the struc
ture, material properties, environmental and
operational conditions along with the applied
loads. It must be noted that the available data
on material properties and loading conditions
affect accuracy, duration and cost of the analy
sis. As an illustration, consider a cylindrical
shell loaded with a concentrated radial force.
The solution for this problem can be obtained
EQUl LI BRI UM
EQUATIONS
LOROS
I
I
STRAINDI SPLRCEMENT
EOURTIONS
r
I
I
EXPERIMENTAL
I
RNRLYSIS
INLRMINRR
CONSTlTUlTlUE
STRENGTH

UERlFlCRTlON
Handbook of Composites. Edited by S.T. Peters. Published
in 1998
by
Chapman
&
Hall, London. ISBN 0
412
54020
7
Fig. 321
Outline
of
analysis
for
composite
StrUC
tures.
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View Full Documentin the form of a Fourier series that has a very
poor convergence at the
loaded point.
However, a closer inspection of the loading
conditions often shows that the concentrated
force is the resultant of some distributed load
over an infinitesimal area; this distributed load
can then be expressed by the series with a
finite number of terms to achieve convergence.
Operational requirements for the composite
structures are also of great importance. For
example, a filament wound composite shell of
revolution can be a model for either a gas pres
sure vessel or a solid propellant rocket motor
case for which, in contrast to the pressure ves
sel, time dependent material properties need
not be considered.
On
the basis of this knowl
edge, assumptions are formulated for the
model of the structural component under
study. This model should consider only the
key factors affecting the capability of the struc
ture and ignore the secondary effects that
complicate the analysis without significant
improvement.
The next step implies analytical formula
tion of the problem, i.e. development of a
complete set of the governing equations with
the pertinent boundary conditions. For struc
tural analysis, the governing set of equations
consists of equilibrium equations (or equa
tions of motion), straindisplacement and the
constitutive equations which are material
dependent. The constitutive equations include
stiffness coefficients which are determined by
either of the following two methods:
0
The first method is associated with direct
experimental analysis of test specimens cut
out of the structure or its excess length. This
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 Spring '10
 Prof.Sulis
 Equations, Force, Shear Stress, Strain, Stress, Boundary conditions, eqns, basic surface

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