Civil Engineering ETDs

Publication Date



Most elastic bodies in the field of civil engineering are composed of discrete elements which are interconnected in some way. A distinct characteristic of such systems is the presence of jump discontinuity in the physical properties of the systems. Trusses, ribbed shells, multi­story frames, continuous and folded plates, built-in columns, etc. are a few examples of this kind. From the conventional methods of analysis of these systems, it can be realized that considerable effort is being expended to approximate the actual system by .means of a relatively simpler system. Most of the established methods of analysis of such systems involve approximation of these physically discrete systems by a continuum. Such approach of changing the physical model is restrictive and may induce error in the result.

Analysis of a discrete system should be based on the fact that the mathematical models for the system to be analyzed are discrete in nature and therefore should be based on the mathematical technique of discrete field theory.

In this paper an effort has been made to avoid the approximations made in conventional methods in the analysis of a discrete system. Discrete systems are not approximated by a continuum, but on the other hand, all the characteristics of the discrete functions have been retained throughout the paper. Mathematical techniques of the discrete field theory have been extensively used here in the analysis of such systems.

In general, a structural engineer spends a very small amount of his time in analyzing single elements like beams, rings, simple frames, etc. On the other hand, he is more concerned with the analysis of a network of members or elements such as building frames, trusses, built-in columns, etc. Under a broad definition, any such network of elements may be termed as a lattice; the analysis of a latticed system is currently a problem of major concern in the field of engineering. The branch of mathematics, suitable for the analysis of latticed systems, is the calculus of finite differences with major emphasis on the use of difference equations.

Document Type




Degree Name

Civil Engineering

Level of Degree


Department Name

Civil Engineering

First Committee Member (Chair)

Cyrus Omid'varan

Second Committee Member

James Tsu-Ping Yao

Third Committee Member

Marion Marvin Cottrell