Implicit algorithms for eigenvector nonlinearities

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit viewpoint. More precisely, we change the Newton update equation in a way that the next iterate does not only appear linearly in the update equation. Although, the modifications of the update equation make the methods implicit we show how corresponding iterates can be computed explicitly. Therefore we can carry out steps of the implicit method using explicit procedures. In several cases, these procedures involve a solution of standard eigenvalue problems. We propose two modifications, one of the modifications leads directly to a well-established method (the self-consistent field iteration) whereas the other method is to our knowledge new and has several attractive properties. Convergence theory is provided along with several simulations which illustrate the properties of the algorithms

Application of a systematic finite-element model modification technique to dynamic analysis of structures

For abstract see A82-30178

Identification of the dynamic characteristics of nonlinear structures

Imperial Users onl

Fibers and global geometry of functions

Since the seminal work of Ambrosetti and Prodi, the study of global folds was enriched by geometric concepts and extensions accomodating new examples. We present the advantages of considering fibers, a construction dating to Berger and Podolak's view of the original theorem. A description of folds in terms of properties of fibers gives new perspective to the usual hypotheses in the subject. The text is intended as a guide, outlining arguments and stating results which will be detailed elsewhere

Structural optimization incorporating centrifugal and Coriolis effects

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76768/1/AIAA-1989-1310-955.pd

Numerical methods and computers used in elastohydrodynamic lubrication

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers

Solution methods for dynamic and non-linear finite element analysis

The computer analysis of structures and solids using finite element methods has now taken on very significant proportions. 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. 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 nonlinearities 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 reliable, general 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 difficulty to "fully" verify 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