This study is concerned with the development of simple and accurate alternative finite element models to displacement finite element models for geometrically nonlinear bending analysis of beams and plates. First, a unified corotational beam finite element that incorporates the kinematics of classical as well as refined beam theories, including the Timoshenko and Reddy beam theories, is developed in a single finite element. The governing equations are written in a "corotational" local frame that rotates with the element and with respect to which the standard linear engineering relations between strains and internal forces are valid. The element is based on Lagrange interpolation of the axial displacement, Hermite cubic interpolation of the transverse displacement, and related quadratic interpolation of the rotation, and it does not experience shear locking. The model is verified by comparisons with exact and/or approximate solutions available in the literature. Very good agreement is found in all cases. Next, a finite element model is developed using a mixed formulation of the first-order shear deformation theory of laminated composite plates. A p-type Lagrangian basis is used to approximate the nodal degrees of freedom that consist of three displacements, two rotations, and three moment resultants. The geometric nonlinearity, in the sense of the von Kµarman, is included in the plate theory. The mixed plate element developed herein is employed in the linear and nonlinear bending analysis of a variety of layered composite rectangular plates. The effects of transverse shear deformation, material anisotropy, and bending-stretching coupling on deflections and stresses are investigated. The predictive capability of the present model is demonstrated by comparison with analytical, experimental, and numerical solutions available in the literature. The model provides an accurate prediction of the global bending response of thin and moderately thick plates subjected to moderate and moderately large rotations. The inclusion of the bending moments at the nodes results in increased accuracy in the computation of stresses over those determined by conventional displacement-based finite element models. The many results presented here for geometrically nonlinear bending analysis of beams and plates should serve as reference for future investigations.

Thesis (Ph. D.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 235-249).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 190-202). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--University of Hong Kong, 1980.

Thesis--M. Sc.(Eng.), University of Hong Kong, 1983.

Not available / text

published_or_final_version / Civil and Structural Engineering / Master / Master of Philosophy

A new methodology is introduced where the natural hierarchical character of model descriptions and simulation results are exploited to expedite analysis of problems. The philosophy and the different concepts involved are illustrated by implementing the strategy to solve some practical problems. The end result was a mix of mechanics, well-designed data structures and software interfaces that forms a rapid analysis environment. This can be very advantageous for cases where a sequence of analyses is required because of safety concerns or cost. When designing a structure, it is common to make frequent modifications to the model during the process. In such cases, the ability to use data from different models within the same analysis environment becomes a major advantage. The proposed system's forte is its hierarchical framework that allows models to communicate with each other and share information with one another. This makes it ideal for global local analyses where solutions from a global model are used to derive the boundary conditions for the local model. The system was also used to conduct a micro mechanical analysis on unidirectional composites that have a non-uniform spatial distribution of the fibers. The hierarchical strategy is not tied to any specific methodology and can be adapted to solve problem using different technologies. This allows the strategy to be used across multiple length scales and governing equations.

No description available.