The computer analysis of structures and solids using finite element methods has now taken on very significant proportions [1-4J. In many cases the safety of a structure may be significantly increased and its cost reduced if an appropriate finite element analysis can be and is performed. In the development and use of finite element methods, we recognize that, considering static linear analysis, already towards the end of the nineteen sixties the methods were highly developed -- thus it had taken only about one decade from the inception to the extensive practical use of finite element methods. Although difficulties were still encountered in the linear static analysis of some structures, e.g. complex shells, most of the structures could already be analysed in a routine manner. This situation in engineering analysis was, however, quite different when dynamic or nonlinear conditions had to be considered. Whereas the finite element methods could be developed relatively quickly for linear static analysis, methods for practical dynamic and nonlinear analyses are much more difficult to establish. Although much emphasis has been placed on research in nonlinear analysis, the progress in the development of valuable techniques has been quite slow [5-7J. The practical objectives in the development of finite element methods for dynamic and nonlinear analysis are, in essence, that we want to be able to analyze increasingly more complex structures which are subjected to loads that vary rapidly -- causing dynamic response -- and loads of high intensity -- causing the structure to respond beyond its linear range. In nonlinear conditions, geometric and/or material non1inearities may have to be taken into consideration. These analysis conditions are encountered already in many industries (e.g. design of nuclear power plants) and, with the current needs towards usage of new materials and more efficient structures, nonlinear analysis will undoubtedly be required to an increasing extent. Considering research in finite element analysis procedures, emphasis must be placed on the development of reZiabZe~ generaZ and cost-effective techniques. The reliability of the analysis techniques is of utmost concern in order that the analyst can employ the methods with confidence. The results of an analysis can only be interpreted with confidence if reliable methods have been employed. The generality and cost-effectiveness of the methods are important in order to produce analysis tools that, in a design office, are applicable to a relatively large number of problems. With the above aims in mind, the development of finite element procedures for dynamic and nonlinear analysis becomes a very formidable task. Not only is it necessary to propose -guided by knowledge and intuition -- improved analysis techniques and then to implement and test these methods, but it is of major importance and di ffi cul ty to "fully" veri fy and qualify these theories and their computer program implementations. Whereas the verification and qualification of a finite element method is usually quite straight-forward in linear static analysis, this process may represent the major task in the development of a method for nonlinear analysis. During the last decade I have endeavored to advance the state-of-the-art of general and reliable finite element analysis procedures for dynamic and nonlinear response calculations. The areas in which I have worked primarily are - the development of eigensolution methods for large eigenproblems that arise in dynamic and buckling analysis of structures; - the development of finite element procedures for nonlinear analysis with emphasis on - the formulation of finite elements and material models, - the methods of solution for the nonlinear equations. The finite element procedures proposed in this research have been implemented in computer programs that are now in very wide use [8-12]. In accordance with the above areas of my research activities, I am presenting in this document relevant papers in three different Parts. The contents of each Part are briefly described below. Part I Solution Methods for Large Generalized Eigenproblems The eigenproblems considered in this research are the one arising in dynamic analysis, -K I"',. = A,. -~1 I"',. and the one arising in linearized buckling analysis, -K I",'. = A,. K,. "'. ~ I, (1) (2) where ~, ~ and M are the linear stiffness, geometric stiffness and mass matrices of the finite element assemblage, and (Ai' 1i)' i=l, 2, 3 ... are the eigenpairs to be evaluated.

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