The optimal design of laminated plates for maximum buckling load using finite element and analytical methods.
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Date
1994
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Abstract
In the first part of the study, finite element solutions are presented for the optimal
design of symmetrically laminated rectangular plates subject to a combination of
simply supported, clamped and free boundary conditions. The design objective
is the maximisation of the biaxial buckling load by determining the fibre orientations
optimally with the effects of bending-twisting coupling taken into account.
The finite element method coupled with an optimisation routine is employed in
analysing and optimising the laminated plate designs. The effect of boundary
conditions, the number of layers and bending-twisting coupling on the optimal
ply angles and the buckling load are numerically studied.
Optimal buckling designs of symmetrically laminated rectangular plates under
in-plane uniaxial loads which have a nonuniform distribution along the edges
are presented in the second part of the study. In particular, point loads, partial
uniform loads and nonuniform loads are considered in addition to uniformly distributed
in-plane loads which provide the benchmark solutions. Poisson's effect
is taken into account when in-plane restraints are present along the unloaded
edges. Restraints give rise to in-plane loads at unloaded edges which lead to biaxial
loading, and may cause premature instability. The laminate behavior with
respect to fiber orientation changes significantly in the presence of Poisson's effect
as compared to that of a laminate where this effect is neglected. This change in
behavior has significant implications for design optimisation as the optimal values
of design variables with or without restraints differ substantially. In the present
study, the design objective is the maximisation of the uniaxial buckling load by
optimally determining the fiber orientations. Numerical results, determined using
the finite element method, are given for a number of boundary conditions
and for uniformly and non-uniformly distributed buckling loads.
In the third part of the study, finite element solutions are presented for the optimal
design of symmetrically laminated rectangular plates with central circular
cut-outs subject to a combination of simply supported, clamped and free boundary
conditions. The design objective is the maximisation of the biaxial buckling
load by determining the fiber orientations optimally. The effect of boundary conditions
and bending-twisting coupling on the optimal ply angles and the buckling
load are numerically studied. The results are compared to those for laminates
without holes.
The fourth part of the present study gives optimal designs of symmetrically
laminated angle-ply plates, which are obtained with the objective of maximising
the initial post buckling stiffness. The design involves optimisation over the ply
angles and the stacking sequence to obtain the best laminate configuration. The
stacking sequence is chosen from amongst five candidate designs. It is shown that
the best configuration depends on the ratio of the in-plane loads in the x and y
directions. Results are also given for two additional configurations which do not
exhibit bending-twisting coupling.
The final section of the present study deals with the optimal design of uniaxially
loaded laminated plates subject to elastic in-plane restraints along the unloaded
edges for a maximum combination of prebuckling stiffness, postbuckling
stiffness and buckling load. This multiobjective study illustrates that improved
buckling and post buckling performance can be obtained from plates which are
designed in this fashion. The multiobjective results are also compared to single
objective design results.
Description
Thesis (Ph.D.)-University of Natal, Durban, 1994.
Keywords
Plates (Engineering), Laminated materials., Finite element method., Theses--Mechanical engineering.