Analysis of interacting subdomains in structural mechanics problems by the differential quadrature method.

摘要

A numerical procedure using the differential quadrature method (DQM) to analyze structural mechanics problems involving discontinuities in the domain due to geometry, material properties and loading, and different governing differential equations, is developed and presented. The compatibility conditions when two or three such subdomains meet at an interface are derived. Only the nonzero elements of the final coefficient matrix are stored for problems involving larger numbers of degrees of freedom. This treatment saves computer time and memory, reduces the round-off errors, and increases the capabilities of the DQM to solve larger size problems. This research opens new areas in which the DQM may be applied to obtain accurate and complete solutions with much less computational effort in comparison to other numerical techniques available to solve similar structural mechanics problems.; The dissertation starts with an introduction to the DQM both in terms of its application and its historical development. The first problem numerically solved by the DQM is a cylindrical liquid storage tank connected to a circular base plate foundation which directly rests on a soil surface. The tank wall and the base plate have different governing differential equations. The interaction between the foundation and the soil media and between the tank wall and the foundation are considered in the analysis.; The numerical solution of stiffened plate systems subjected to static loads is presented next. In this analysis, the eccentricity between the stiffeners and the plate mid-surface is considered. Then the free vibration analysis of the same problem is presented. In these two analyses, the boundary conditions for the plate segments at their junction with stiffeners are merged with the governing differential equation for the stiffeners to obtain the final compatibility equations at the common interface. This static load analysis methodology of stiffened plates is finally extended to analyze large size reinforced concrete bridge deck slabs supported on a number of wide flange steel I-beams running parallel to the longitudinal and cross directions. Finally, the conclusions of the research are summarized, and the possibilities of further research are discussed.