Development of a mixed shell element for 7-parameter formulation and identification of lowest eigenvalues

This dissertation focuses on shell element since it is more complicated and important than solid element in the finite element method. Conventional shell formulation has widely been used, but it has a drawback when the thick shell is considered due to the assumption that thickness is constant. In order to overcome this, the 7-parameter shell formulation proposed by Michter is used in this dissertation. Since this formulation is a fully developed 3-dimensional shell formulation, it provides no distinction between thin shell and thick shell.; A new mixed shell element for the 7-parameter formulation is first developed here and a Discrete Shear Gap (DSG) shell element is also implemented and compared. The developed mixed shell element for 7-parameter formulation has good performance from a physical point of view. Its static and modal results are compared with other engineering commercial software, MSC/NASTRAN, ABAQUS, and ANSYS.; With the developed mixed shell element, modal analysis is also considered in this dissertation. In addition to the discussion of the conventional identification methods for the lowest eigenvalues, two new identification methods are also proposed: one is called the Numerical Modal Test (NMT) and the other is called the Frontal Stabilized Block Subspace Iteration (FSBSI). NMT is the numerical mimic of an experimental modal test. Its procedure was first introduced by Li and is enhanced in this dissertation. It consists of time integration of impact simulation, eigenvalue extraction from time history data, and modeshape extraction process from a few nodal eigenvectors. Matrix inversion is not necessary in NMT, but the speed of simulation is slow.; FSBSI is a modification of the Subspace Iteration method. In order to avoid increasing the control number of reduced stiffness and mass matrix, mass orthogonalization is inserted into the original algorithm. The general eigenvalue problem is changed into the standard eigenvalue problem in FSBSI. The frontal solver is also used to reduce memory requirement.; The developed mixed shell element is verified by several examples using other commercial software. It is also applied to a piezoelectric coupled problem. Combined with electric field, mixed piezoelectric shell elements are developed. The result of static analysis is compared with that in the literature and the results of modal analysis are also discussed.