|dc.description.abstract||This thesis presents boundary element formulations for buckling and nonlinear
buckling analysis of plates. Dual boundary element formulations are
also presented for linear and nonlinear buckling, and large deformation analysis
of crack behaviour in plates.
Reissner plate theory is adopted to represent shear deformable plate bending,
and two dimensional plane stress is used to model the membrane behaviour
of plate. By taking into account the nonlinear interaction between
forces and rotations in the equilibrium equation, the nonlinear formulation
is formed by coupling equations of shear deformable plate bending and two
The boundary element formulation for plate buckling is developed. Plate
buckling equations are written as a standard eigenvalue problem. Buckling
coefficients and buckling modes are obtained using this formulation. Initially,
the boundary is discretised into quadratic isoparametric elements, and the
domain is discretised using constants cells. Next, the dual reciprocity method
is utilized to transform the domain integral into equivalent boundary integrals.
Examples are presented for plate buckling problems with different geometry,
loading and boundary conditions. The results obtained are shown to be in
good agreement with analytical and finite element results.
The Dual Boundary Element Method (DBEM) for buckling analysis of
plate is also developed. The plate buckling equations are also presented as a
standard eigenvalue problem, which would allow direct evaluation of critical
load factor and buckling modes for cracked plates.
Geometrically nonlinear boundary element formulation is developed to
analyse large deformation and nonlinear buckling of plates. Different load incremental
approaches and solution procedures are presented. Nonlinear terms
are evaluated using a radial basis function. Large deformation analysis for
Fracture Mechanics problems is also presented. Five stress intensity factors
are calculated, i. e. three for plate bending and two for membrane. Crack
Opening Displacement (COD) is used to compute the stress intensity factors.
The nonlinear buckling of thin plate is also presented. Two models of
imperfection are introduced in the formulation, i. e. a small uniform transverse
loads and distributed transverse loads based on eigenvectors. A simple
numerical algorithm is presented to analyse the problems. Finally, nonlinear
buckling analysis of cracked plate is presented. Numerical examples of
nonlinear buckling and large deformation problems are presented. The BEM
results presented are shown to be in good agreements with analytical and other