Sandwich plates and layered composites are common in many structural applications because of their combination of high stiffness and low weight. These plates combine top and bottom layers of high Young's modulus with intermediate layers of material carrying predominantly shear loads. Finite elements developed for the analysis of sandwich plates need to accurately model transverse shear stresses through the plate thickness. This study was inspired by an Office of Naval Research project to investigate the suitability of steel sandwich plates as ship hulls. A finite element implementation based on a third-order shear deformation element was used in a standard finite element program to model transverse shear stresses in a simply supported plate. Four elements based on third-order theory are developed and tested. Using static condensation to reduce the number of degrees of freedom required by a third-order plate element does not preserve the element's accuracy in either displacements or stresses, and stresses do not converge with refinement of the mesh. For the thin isotropic plate case, some condensed elements give reasonable displacement and stress results, but only for certain choices of mesh and the element is less versatile than one based on first order plate theory. None of the condensed elements give good results for composite plates of any thickness. / Master of Science

The concept of using aluminum as the primary construction material for high speed ships and the hydroelastic behavior of the structure is widely gaining importance as a significant research topic in naval architecture. Aluminum is lighter than steel and hence can be predominantly used in high speed crafts which experiences significant slamming. This thesis work is focused on wedge shaped models. Free fall wedge impact is studied and a FORTRAN 90 computer program is developed to estimate the structural response of the wedge experiencing slamming by the use of matrix methods, finite element techniques and Newmark-Beta numerical time integration methods. The numerical solution is validated by comparison with the static solution. The theoretical hydrodynamic pressures which are used as input for this work was originally developed by using a flat cylinder theory [26]. The wedge drop at 0.6096 m (24 inch) drop height with an impact veloc- ity of v=3.05 m/s is based as the premise and the experimental pressure distributions measured by the pressure-transducers and the theoretical pressure predictions are used as inputs and the structural response is derived. Additionally, the response is compared for three different plate thicknesses and the results are compared against each other. The maximum deflection is comparable to the deflection evaluated from the experiment and tends to attain convergence as well. As the plate thickness reduces there tends to be a significant rise in the deflection values for the wedge plate, in the manner that when the plate thickness is halved there is a deviation of more than 75% in the deflection values as such.

Abstract This study focuses on the development of a plate-shell element using the vector form intrinsic finite element (VFIFE) method to analyze the structural behavior of thin shell structure subjected to various exerting forces. The shell element employed here is the flat three-node triangular shell element proposed by Bathe and Ho, which is obtained by superimposing CST (constant strain triangle) element with DKT (discrete Kirchhoff theory) triangular plate element. The nodal coordinates, displacements, rotations, and the motion equations of the structure are defined in a fixed global set of coordinates. The strains of the shell element, the element internal nodal forces and the element stiffness matrix are defined in terms of co-rotational coordinates, which are corresponding to the configuration of the shell element. Based on the co-rotational coordinate principle, the nodal displacement between two adjacent time steps can be separated into displacements induced from rigid body motion or deformation, and the incremental internal nodal forces can also be obtained. Finally, following the Newton's 2nd law, the equations of motion can be built to analyze the dynamic responses of thin shell structures. The theory derived in this study, were further verified to be able to simulate the behavior of thin shell structures subjected to both static and dynamic loadings. This new analytical model was proved to be an effective tool that can be an alternertive to traditional finite element procedure to solve for complicated engineering problems in thin shell structures.

This study aims to investigate the behaviour of low-order beam and plate elements especially for their application to laminated structures. The merits and dements of the existing elements are brought out and new low-order elements with better interpolation polynomials are proposed. Two new beam elements are proposed for laminated composite beams that yield better representation of twist due to material coupling. Out of the two elements developed, one is based on the conventional formulation and the other on the coupled-field formulation, both capturing material induced coupling. The beam developed using coupled field formulation shows a novel way of obtaining a fully coupled interpolation function for field variables using the complete set of equilibrium equations for the composite beams. The element has shown a superior coarse mesh performance. These elements can practically capture plate behaviour in beam elements for a wide range of plate thickness. The locking problems in conventional 4-node quadrilateral elements, such as shear locking and geometric locking are studied. Various techniques available in literature to remedy these problems are also studied. A suite of QUAD4 with conventional techniques such as. Reduced Integration, Field Consistency, Mixed Interpolation of Tensorial strain Components, Assumed Natural Strain, Discrete Shear Gap, Incompatible modes Q6 and QM6 is developed. An effort is made to combine these techniques to develop new element that yields improved performance. The element is shown to exhibit improved performance for certain cases. Several four-node rectangular elements are developed based on the coupled-field techniques. First two new-coupled elements are formulated that employ Sabir's [101] plane bending formulation with drilling degree of freedom, and the plate bending rotations are generated using equilibrium equations. However, since Sabir's plane bending interpolation polynomials yielded inaccurate performance for composites, it led to development of elements with fully coupled field formulations. Finally, two new 4-node rectangular elements are developed using coupled-field formulations with six and seven dof freedom per node respectively. Here the interpolation polynomials are derived using the complete equilibrium equations. The elements are extensively tested for static deflection, dynamics and buckling of isotropic and laminated plates/beams. The elements show superior coarse mesh convergence. Several problems pertaining to vibration and buckling of composite plates/beams are solved using the elements developed in this work.