Three 3D nonlinear finite-element (FE) models are developed to study the behavior of concrete beams and plates with and without externally reinforcement of fibre reinforced polymer (FRP). Ramtekkar’s mixed layer-wise 3 dimensional (3D) 18-node FE model (108 degrees-of-freedom, DOFs) is modified to accommodate the nonlinear concrete and elasto-plastic steel behaviour. Saenz’s stress-strain equation is used for material nonlinearity of concrete. As in any 3D mixed FE analysis, the run time using the model can be computationally expensive. Two additional layer-wise 18-node FE models: Displacement FE model (54 DOF) and transitional FE model (81 DOF) are developed. The displacement FE model is based on purely displacement field, i.e. only displacement components are enforced throughout the thickness of the structures. The transitional FE model has six DOF (three displacement components in the coordinate axis direction and three transverse stress components - where z is the thickness direction) per node in the upper surface and only three DOF (three displacement components in the coordinate axis direction) per node in the bottom surface.The analysis of reinforced concrete (RC) beam strengthened with FRP and composite plate using these models are verified against the experimental results and the results from the commercial software, ANSYS respectively. Several parametric studies are done on composite RC beam and composite plate. / May 2006

Techniques for a posteriori error estimation for finite element approximations of an elliptic partial differential equation are studied.This extends previous work on localized error control in finite element methods for linear elasticity.The methods are then applied to the problem of homogenization of periodic structures. In particular, error estimates for the effective elastic properties are obtained. The usefulness of these estimates is twofold.First, adaptive methods using mesh refinements based on the estimates can be constructed.Secondly, one of the estimates can give reasonable measure of the magnitude ofthe error. Numerical examples of this are given.

In this thesis, mixed finite element models of beams and plates bending are developed to include other variables (i.e., the membrane forces and shear forces) in addition to the bending moments and vertical deflection, and to see the effect of it on the nonlinear analysis. Models were developed based on the weighted residual method. The effect of inclusion of additional variables is compared with other mixed models to show the advantage of the one type of model over other models. For beam problems the Euler-Bernoulli beam theory and the Timoshenko beam theory are used. And for the plate problems the classical plate theory and the first-order shear deformation plate theory are used. Each newly developed model is examined and compared with other models to verify its performance under various boundary conditions. In the linear convergence study, solutions are compared with analytical solutions available and solutions of existing models. For non-linear equation solving direct method and Newton-Raphson method are used to find non-liner solutions. Then, converged solutions are compared with available solutions of the displacement models. Noticeable improvement in accuracy of force-like variables (i.e., shear resultant, membrane resultant and bending moments) at the boundary of elements can be achieved by using present mixed models in both linear and nonlinear analysis. Post processed data of newly developed mixed models show better accuracy than existing displacement based and mixed models in both of vertical displacement and force-like variables. Also present beam and plate finite element models allow use of relatively lower level of interpolation function without causing severe locking problems.

Abstract This thesis applies the method of finite-difference frequency -domain to solve the field when light propagating through the optical waveguide. Comparing with other method, method of finite-difference time-domain which required to be calculated with larger matrices and without any ideal approximate rapid solution, our method only needs to solve the joint equations. Method of finite-difference frequency -domain will be more efficient than method of finite- difference time-domain in optical waveguide simulation. However, all that we need to confer with are how to sample the effective indices for set grind points and the deal for the boundary conditions in partial differential equations, including electric wall, magnetic wall, absorption boundary and other boundary conditions, etc. Next, we confer with the difference deal between TE and TM waves respectively. Final, we confer with high-order finite-difference and the method for calculating extremely large area or extremely high precision in order to use the method of finite-difference frequency-domain to find the incident, reflective, and scattering fields by the fastest and the exactest procedures.

Free vibration of beam with moderate thickness is analyzed in the present study. Plane strain finite element is employed, which is based on 2-D elasticity. The conventional displacement-type variational principle is combined with Reissner¡¦s principle and a mixed-type variational formulation is derived. With such formulation, stresses, as well as displacements, are the primacy variables and both boundary conditions can be imposed exactly and simultaneously. Beams with various aspect ratios and boundary conditions are analyzed. Vibration frequencies and modes are obtained and compared to those by Euler¡¦s beam theory, Timoshenko beam theory, higher-order theory and displacement-type plane strain finite element method to see the effects of 2-D elasticity beam analysis compared to traditional 1-D theories, and the satisfying of stress boundary conditions, in addition to the displacement ones.

This paper uses a finite element code¡©DEFORM 3D¡ªto simulate the plastic deformation behavior in extrusion processes of heat sink for CPU. The relationships between the loading, strain, velocity distribution, and formability of the extruded product as well as the extrusion conditions are discussed. Furthermore, this research will propose a criterion for the die design of heat sink and to prove the validity of this proposed criterion by the experiments.

In the present study, the buckling behavior of beams is analyzed by a plane strain finite element. The displacement-type finite element formulation based on two-dimensional elasticity of a buckling beam leads to an eigenvalue problem and is transformed again into another type of eigenvalue problem to eliminate iterations and possible difficulty during iterations and to obtain the various critical loads simultaneously. Comparing with conventional beam theories, the present approach needs no approximations or assumptions except that the width-to thickness ratio should be large enough for the beam to be considered as a plane strain case. Theoretically the present method should be more accurate than conventional beam theories and attractive than iterative method if the same accuracy is obtained, due to the economy in computation of the present method. Buckling strength under different beam geometry, type of loading, and boundary condition by the present approach will be compared with those by iterative method and various beam theories to test its validation and accuracy.

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.

In the present study, a fully nonlinear 2-D finite difference scheme has been developed based on inviscid and incompressible flow in a rectangular tank. The rectangular tank is coupled to a linear elastic-supported structure made up by reinforced concrete. Wave breaking and run-up are not considered in the present numerical model due to the free surface is assumed as a single-value function. The main purpose of this study is to analyze interactions between sloshing forces generated by system vibrations and structure motions. The accuracy of present study is made by comparing to other reported numerical results and the consequence shows well agreement. The present study can be applied for designing various combinations of coupled structure systems for different necessity. The analyses of practical examples are also presented in this study. The present numerical model can provide a quick and accurate way on determining the natural frequencies of connecting fluid-structure system and this is hard to identify through experiment.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.