Optimal Structural Analysis (Applied & Engineering Mathematics S.)

Recent advances in structural technology require greater accuracy, efficiency and speed in the analysis of complex structural systems; methods that are particularly suited to this purpose are described in this book. Professor Kaveh applies abstract mathematical concepts from graph theory and topology to important problems of computational mechanics. Powerful algorithms are used to create highly sparse matrices of specified patterns, thereby achieving a considerable saving on computer storage and time, as well as increasing the accuracy of the solutions. The methods presented for substructuring and subdomaining are vital for parallel computations and examples of these are included for static as well as dynamic problems. Direct improvement of the conditioning structural matrices, in particular for the force method, is another special feature of the book. The methods in this book are not only applicable to skeletal structures, but can equally be used for the analysis of other systems such as electrical and hydraulic networks. Examples are given to illustrate the application of the methods, and exercises, with solutions.

The increasing need to demonstrate structural safety has driven many recent advances in structural technology that require greater accuracy, efficiency and speed in the analysis of their systems. These new methods of analysis have to be sufficiently accurate to cope with complex and large-scale structures. In addition, there is also a growing need to achieve more efficient and optimal use of materials.

Following on from the highly acclaimed and successful first edition, Optimal Structural Analysis now deals primarily with the analysis of structural engineering systems, with applicable methods to other types of structures.

• Presents efficient and practical methods for optimal analysis of structures.
• Provides a complete reference for many applications of graph theory, algebraic graph theory and matroids in computational structural mechanics.
• Substantially revised to include recent developments and applications of the algebraic graph theory and matroids, which are ideally suited for modern computational techniques.
• Describes recent developments in the matrix force methods of structural analysis.
• Presents novel applications of graph products in structural mechanics.

Optimal Structural Analysis will be of interest to post-graduate students in the fields of structures and mechanics, and applied mathematics particularly discrete mathematics. It will also appeal to practitioners developing programs for structures and finite element analysis.