Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells
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This thesis presents new boundary element formulations for solution of bending problems
in plates and shells. Also presented are the dual boundary element formulations for analysis
of crack problems in plates and shells.
Reissner plate theory is adopted to represent the bending and shear, and two dimensional
(2-D) plane stress is used to model the membrane behaviour of the plate. New set of boundary
element formulations to solve bending problems of shear deformable shallow shells having
quadratic mid-surface is derived based on the modified Reissner plate and two dimensional
plane stress governing equations which are now coupled due to the curvature of the shell.
Dual Boundary Element Methods (DBEM) for plates and shells are developed for fracture
mechanics analysis of structures loaded in combine bending and tension. Five stress intensity
factors, that is, two for membrane and three for bending and shear are computed. The JIntegral
technique and Crack Surface Displacements Extrapolation (CSDE) technique are
used to compute the stress intensity factors. Special shape functions for crack tip elements
are implemented to represent mom accurately displacement fields close to the crack tip.
Crack growth processes are simulated with an incremental crack extension analysis. During
the simulation, crack growth direction is determined using the maximum principal stress
criterion. The crack extension is modelled by adding new boundary elements to the previous
crack boundaries. As a consequence remeshing of existing boundaries is not required, and
using this method the simulation can be effectively performed.
Finally, a multi-region boundary element formulation is presented for modelling assembled
plate-structures. The formulation enforces the compatibility of translations and rotations
as well as equilibrium of membrane, bending and shear tractions.
Examples are presented for plate and shell structures with different geometry, loading and
boundar-y conditions to demonstrate the accuracy of the proposed formulations. The results
obtained are shown to be in good agreement with analytical and other numerical results.
Also presented are crack growth simulations of flat and curved panels loaded in combine
bending and tension. The DBEM results are in good agreement with existing numerical and
experimental results. Assembled plate-structure and a non-shallow shell bending problems
are also analysed using a multi-region formulation developed in this thesis.
Authors
Dirgantara, TataciptaCollections
- Theses [4235]