Abstract:
The finite element method (FEM) is at present firmly established as a powerful and popular
numerical analysis technique for finding approximate solutions to a wide range of problems in
structural mechanics. Ship structures consist of various plates. Plane stress and plane strain
analysis of these plates are very important. Configuring the plate type structures especially with
discontinuities is one of the most important topics in the construction of not only ships but also
for aircrafts and many other structures. Whenever the cross section of a structural member
changes suddenly, a structural discontinuity arises, e.g. deck openings like hatch and machinery
openings, access openings on side wall, cutout in the web plate, and cracks, usually a result of
material imperfections or areas of high stress. This thesis concerns mainly with the fundamentals
of FEM for solving plane stress and plane strain problems to analyze stresses like normal stress,
shear stress and von-mises stress at the four integration points and displacements at nodes for
different sections of ship structures such as plate with holes, plate with bracket and holes, and
plate with fillets. Object Oriented Programming technique has been used to develop a finite
element program in C++ for four node quadrilateral elements to analyze the structural
discontinuity problems for various ship structures. The analysis results of gauss point stresses
and nodal displacements for different models obtained from the developed program are validated
with the help of commercial finite element analysis software SIMULIA ABAQUS. A mesh
viewer program is also developed using the PYTHON programming language to view the
generated mesh for analysis by the developed program. Fracture mechanics problem is
performed for a two-dimensional plane strain single edge crack to determine the elastic fracture
parameter, i.e., stress intensity factor based on stress distribution along the crack ligament. The
value of stress intensity factor from the computational analysis is compared with the value
obtained from the empirical formula. The typical stress distribution curve along the crack
ligament has also been shown.
