Title:
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Exploiting non-symmetry in composite laminates : application to stringer terminations
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This thesis challenges the existing composite design paradigm that prohibits the use of
non-symmetric laminates. The restrictive nature of "symmetric-only" stacking sequences
is identified, highlighting the potential benefit for structural optimisation on relaxing this
constraint. The thermal response of such laminates during manufacture is investigated ,
noting layup induced variation of the coefficients of thermal expansion is often cited as
a' major objection to their use. By extending known results for warp-free non-symmetric
laminates, it is shown that flattening of (some) moderately warped plates induces nominal
build strain . Allowing a tolerance to non-symmetry induced warping is presented in terms
of increased design space for a specified level of induced strain.
The direct benefits of non-symmetry, taking advantage of the coupling between in and
out-of-plane responses, is also considered. The increased performance of non-symmetric
configurations observed in this thesis counters the perceived wisdom that this coupling is
always unfavourable. Specifically, moderately non-symmetric laminates indicate the potential
to increase the load carrying capacity of stringer terminations. This was achieved
by improving the resistance to debonding as investigated using both analytical and finite
element techniques.
To better understand the underlying mechanisms, and the effect of non-symmetry on
stringer termination design, an optimisation framework is proposed. An established
Ritz-Galerkin hybrid model is employed to predict structural response, in conjunction
with analytical debonding and buckling constraints . A two-step process, making use of
lamination parameters and genetic algorithms, is able to find optimised designs. Significant
improvements over the quasi-isotropic configuration are observed including a
preference towards non-symmetric configurations.
Previously unknown limitations of the Ritz-Galerkin approach are identified during this
study. The choice of basis functions a re discussed a long with the validity of implicit assumptions
made regarding the geometric non-symmetry and energy formulation. A more
general, non-dimensional, Ritz based model was proposed to mitigate these limitations.
Although a general improvement is observed, there are further complexities in capturing
localised behaviour due to stiffness discontinuities. A series of further refinements and
investigations a re proposed as future directions of research.
Finally, via the use of Legendre polynomials, it is possible to reformulate the Ritz method
using the "triple-product" approach. Such an approach transforms the problem into a
summation of standardised integrals containing three term products of the basis functions.
Exploiting previously unused - in structural engineering - algebraic recursion
relations a significant increase in computational performance can be realised . The number
of numerical integrations that must be performed is shown to reduce by an order of
magnitude. This result is significant for the analysis and optimisation of any variable
stiffness plate/ shell-like structure where calculating these integrals often dominates the
computational expense of analysis.
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