Finite element and analytical solutions for the optimal design of laminated composites.
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Date
1996
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Abstract
The present study involves the analysis and design optimisation of composite structures
using analytical and numerical methods. Five different problems are considered.
The first problem considers the design of laminated plates subject to non-uniform
temperature distributions. The plates are optimised for maximum buckling temperature
using the fibre angle as the optimising variable. The method of solution involves
the finite element method based on Mindlin theory for thin laminated plates and
shells, and numerical optimisation. A computational approach is developed which
involves successive stages of solution for temperature distribution, buckling temperature
and optimal fibre angle. Three different temperature loadings are considered
and various combinations of simply supported and clamped boundary conditions are
studied. The effect of plate aspect ratio on the optimal fibre angle and the maximum
buckling temperature is investigated. The influence of bending-twisting coupling on
the optimum design is studied by considering plates with increasing number of layers.
The second problem concerns the optimal design of composite pressure vessels.
Finite element solutions are presented for the design of hemispherically and flat
capped symmetrically laminated pressure vessels subjected to external pressure.
The effect of vessel length, radius and wall thickness, as well as bending-twisting
coupling and hybridisation on the optimal ply angle and buckling pressure are numerically
studied. Comparisons of the optimal fibre angles and maximum buckling
pressures for various vessel geometries are made with those for hybrid pressure vessels.
In the third problem, the multiobjective design of a symmetrically laminated
shell is obtained with the objectives defined as the maximisation of the axial and
torsional buckling loads. The ply angle is taken as the optimising variable and the
performance index is formulated as the weighted sum of individual objectives in
order to obtain Pareto optimal solutions of the design problem. Single objective
design results are obtained and compared with the multiobjective design. The effect
of weighting factors on the optimal design is investigated. Results are given
illustrating the dependence of the optimal fibre angle and performance index on the
cylinder length, radius and wall thickness.
In the fourth problem, the optimal layup with least weight or cost for a symmetrically
laminated plate subject to a buckling load is determined using a hybrid
composite construction. A hybrid construction provides further tailoring capabilities
and can meet the weight, cost and strength constraints while a non-hybrid construction
may fail to satisfy the design requirements. The objective of the optimisation
is to minimise either the weight or cost of the plate using the ply angles, layer thicknesses
and material combinations as design variables. As the optimisation problem
contains a large number of continuous (ply angles and thicknesses) and discrete (material
combinations) design variables, a sequential solution procedure is devised in
which the optimal variables are computed in different stages. The proposed design
method is illustrated using graphite, kevlar and glass epoxy combinations and the
efficiency of the hybrid designs over the non-hybrid ones are computed.
Finally, the minimum deflection and weight designs of laminated composite
plates are given in the fifth and last problem. The finite element method is used
in conjunction with optimisation routines in order to obtain the optimal designs, as
was the procedure in the first problem. Various boundary conditions are considered
and results are given for varying aspect ratios and for different loading types.
Description
Thesis (Ph.D.)-University of Natal, Durban, 1996.
Keywords
Composite construction., Composite materials., Finite element method., Strains and stresses., Laminated materials., Theses--Mechanical engineering.