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Abstract

A comprehensive literature study is devoted to Chapter 1. Starting from the linear analysis approach, the study points out the steady progress and development of numerical methods adopted by several authors, in the domain on nonlinear static and dynamic analysis. With regard to the nonlinear dynamic interaction be-tween the superstructure and supporting soil mechanism, it is observed that research in this field is very sparse and inadequate, therefore the underlying motivation to dwell in this very interesting and complex field of research and investigation becomes obvious.

Chapter 2 contains the introduction to the problem concerned, and outlines the basic assumption, analytical procedure, and the limitations of the method applied in the solution technique. In a subsection of this chapter, an introduction to the general purpose nonlinear analysis is given. It is pointed out that certain design problems, particularly the design of nuclear power plants, the realization and reliable testing of the full scale structure, are almost prohibitive as far as cost is concerned, and in addition to this, is the problem of reliable monitoring and processing of response signals, during testing. Appropriate analytical procedures, if available, will therefore reduce the testing significantly and a better understanding of the structural behavior can be attained. Therefore it is pointed out here that a consistent continuum mechanics formulation and effective finite element discretization is the most important aspect of non-linear analysis. The other aspect is the use of proper material models to account for the nonlinear behavior of material which should adequately represent the actual material under field conditions.

In the third chapter, a historical development of non-linear analysis of static and dynamic problems is presented, which goes back as far as 19&0. Since then, numerous papers have been published, using these methods, as proposed by the earlier authors who actually founded the basic concept of non-linear analysis. Continuous researches are going on in this field, to understand many problems, contrary to many notions we inherit from classical mechanics. As Professor Oden [12] pointed out, "No structure or machine ever built behaved linearly. All deformation need not be small, nor need they be reversible.
Few materials are truly elastic, and fewer are linear."

In Chapter 4, the concept of continuum mechanics is explained, in the light of virtual work principle, and in the subsection, the appropriate finite element discretization of the continuum is given for the matrix calculation. In this subsection, basically the essential tools involved in nonlinear analysis are systematically discussed.

Formulation of the governing equation of motion for the structure and soil subgrade system due to support motion is explained in Chapter 5. The support motion is caused by time varying ground acceleration which characterizes the earthquake load.

In Chapter 6, some salient points of temporal integration operator are illustrated. Understanding of the basic principle of temporal integration in one dimensional problems is the key to more complex problems dealing with finite element applications.

Chapter 7 is devoted to temporal integration of the assembled finite elements. To avoid large integration error, which causes the calculated solution to "drift away" from the exact solution, as a consequence of linearization, equilibrium iteration is introduced [18], [23], to assure convergence to the solution within acceptable limits.

In chapter 8, a refined modelling technique using principle modes of vibration is discussed.

Travelling P and S waves in the finite element grid are reflected back from the fixed boundary. This can cause serious perturbations in the displacement and stress output in the vicinity of the structure. In chapter 9, a simple but effective way of approach used in this study to suppress the unwanted reflection is explained.

In chapter 10 a comparative study was made between the closed form solution and finite element solution of soil-structure interaction problem. The theoretical formulation is based on one dimensional wave propagation in an elastic medium.

In chapter 11 the stress profiles obtained by finite element method of one dimensional wave propagation in elastic, and inelastic medium are compared with the exact solution. This was done mainly to show the convergence of the finite element solution to the exact solution using modified NONSAP program in vol. 2.

In chapter 12 a case study is presented, and results are analyzed to gain an insight in the domain of non-linear soil-structure interaction. It is also pointed out the need for further research, and experiment in this highly complicated field on engineering, where the civil and mechanical engineers with their concerted effort can achieve an acceptable, economical and meaningful solution to this problem.

In appendix A failure behaviour of soil is discussed. Some experimental data obtained by Swarz (33) in bi and triaxal tests of soil were used to determine the Yield function and Yield criteria of soil.

In appendix B proposed experimental study of non-linear soil-structure interaction is suggested.

In appendix C, a comparative study between the elastic half space solution and solution of the equivalent finite element model of the elastic half space was made. The response spectrum obtained from the both analyses show fairly good agreement between the two methods.

In vol. 2 of the thesis the modified version of NONSAP program is presented . The program organization , the flow chart and the use of high speed storage of nodal and element data and the stiffness matrix are explained in block diagram.

The subroutine VELCOR, which is used in conjunction with the NONSAP is presented separately. This will enable the reader to follow the programming technique and ideas behind the program. A flow chart is provided so that the readers have a clear understanding of the program algorithm.

Publication Type:	Thesis (Doctoral)
Subjects:	G Geography. Anthropology. Recreation > GE Environmental Sciences T Technology T Technology > TH Building construction T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments:	School of Science & Technology > Engineering School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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