Differential quadrature method in computational mechanics: New developments and applications

This dissertation is an outgrowth of continued efforts toward making the differential quadrature method (DQM) a practical numerical solution technique of computational mechanics. The objectives of the work were to broaden the scope of application of the DQM to some new problems, hitherto not reported in the literature, to propose simplifications of the quadrature analysis, and to develop a methodology for the quadrature solutions to the problems of irregular domains.; The dissertation is comprised of eight chapters. Chapter 1 provides a chronological review of the developments in the DQM and brings out the issues which a computational mechanist needs to be aware of and concerned with in using this method of analysis. The topics addressed in the succeeding chapters are as follows. Chapter 2 is related to the problem of invoking the boundary conditions in the quadrature solution of higher order differential equations. The problem is considered in detail through free vibration analysis of rectangular plates with a wide spectrum of boundary conditions. For the first time, the present work introduces the idea of a semi-analytical approach to differential quadrature solutions and its applications are demonstrated in Chapters 3, 4, and 5, through free vibration problems of increasing complexity including tapered, laminated, and Mindlin-type plates as well as circular cylindrical shells. A methodology extending the applicability of the DQM to irregular domains is presented in Chapter 6; its application is demonstrated via free vibration analysis of plates of various planforms. Chapter 7 presents a differential quadrature solution to the transient dynamics problem of gas-lubricated journal bearings. The work of the present research program is summarized and the possibilities of further research are mentioned in Chapter 8.; It is believed that the work reported here achieves its objectives and gives new directions for further developments in the quadrature method. Special mention is made of the quadrature solution of the cylindical shell problem which is a step forward in the application of the method in structural dynamics. The remarkable accuracy and high computational efficiency offered by the semi-analytical quadrature solutions, coupled with algorithmic convenience, point to possible use of the method for real time analysis and design. The extension of the method to irregular domains should go a long way in the development of the DQM for its employment in the class of problems which are presently considered to be in the territory of the finite element method.