Higher-order coupled beam theory

Today, more and more cruise ships are built every year. As the market expands, so change the requirements from new-build vessels. Typically, this means the increase in ships gross tonnage, which requires an increase in dimensions, or more complex structures due to the desired design. Despite the requirements set by the industry, the ship's internal and external structures must provide a safe voyage for passenger and the crew. In standard ship design practice, initial strength evaluation is performed with a small amount of structural detail, for which there are numerous different methods. This thesis introduces a new shear deformation theory designed for accurate assessment of global displacements and stresses. The theory utilises a beam element with 6 variables defined in each beam element node. Deflection and rotation of cross-section is defined at reference line, where as displacement due to shear and axial forces and shear deformation is defined in beam element bottom surface and top surface separately. Approximations are presented so that variables could be described over the length and width of the beam elements. Coupling of beam elements in the global matrix has been presented for the holistic behaviour of the beam theory. The thesis provides a comparative analysis between higher-order shear deformation theory calculations and FEM results performed with NX Nastran on two structures, first of which is a simple box structure and second is a nonuniform beam model, where three layers of beams are of different length. The analysis shows a very good coincidence between analytically calculated displacements and stresses and FEM results for the box struct and between displacements for the nonhomogeneous structure and FEM results. In nonhomogeneous beam element configuration, the theory proved to lack the capability of assessing peak stress values and showed deficiencies in describing vertical stress distribution. Based on the results, the theory needs additional research to be done in terms of defining boundary conditions and element coupling to provide better results in the case of more complex structures