Analysis of Structures on Elastic Foundation: Incorporating the Spectral Method of Boundary Elements

This book is devoted to the static and dynamic analysis of structures on elastic foundation. Through comprehensive analysis, the book shows analytical and mechanical relationships among classic and modern methods of solving boundary value problems. The book provides a wide spectrum of applications of modern techniques and methods of calculation of static and dynamic problems of engineering design. It pursues both methodological and practical purposes, and the accounting of all methods is accompanied by solutions of the specific problems, which are not merely illustrative in nature but may represent an independent interest in the study of various technical issues. Two special features of the book are the extensive use of the generalized functions for describing the impacts on structures and the substantiations of the methods of the apparatus of the generalized functions. The book illustrates modern methods for solving boundary-value problems of structural mechanics and soil mechanics based on the application of boundary equations. The book presents the philosophy of boundary equations and boundary element methods. A number of examples of solving different problems of static and dynamic calculation of structures on an elastic foundation are given according to the methods presented in the book.

• Introduces a general approach to the method of integral transforms based on the spectral theory of the linear differential operators. The Spectral Method of Boundary Element (SMBE) is developed based on using integral transforms with an orthogonal kernel in the extended domain.
• Presents a new, versatile foundation model with a number of advantages over the ground-based models currently used in practical calculations.
• Provides new transforms which will aid in solving various problems relevant to bars, beams, plates, and shells in particular for the structures on elastic foundation.
• Examines the methods of solving boundary-value problems typical for structural mechanics and related fields.

Levon G. Petrosian is a Professor of Structural Engineering and Structural Mechanics. He received his B.S.C.E. and M.S. degrees from the Armenian National University of Architecture & Construction. He received a Ph.D. from the Moscow State University of Civil Engineering (MGSU) and the degree of Doctor of Technical Science from the Moscow Research Center of Construction, Research Institute of Building Structures (TSNIISK). Dr. Petrosian is the author of more than 60 scientific works and publications, including monographs, books and textbooks. He has been associated with transportation and structural engineering industries for over 40 years as a research engineer, teacher, and scientist. Levon Gregory Petrosian is a renowned expert on the analysis of engineering structures.
Prior to his move to the United States, Professor Petrosian was the Chairman of Department of Structural Mechanics at the Armenian National University of Architecture & Construction as well as the Executive Director and Head of the Armenian Earthquake Engineering Research Institute. Currently, Dr. Petrosian serves as the Chief of the Plan Review Division at the District of Columbia Department of Transportation.