Ali Kaveh

Optimal Structural Analysis

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• RSP Bird
• Verlag: Wiley & Sons
• Artikelnr. des Verlages: 14503015000
• 2. Aufl.
• Seitenzahl: 532
• Erscheinungstermin: 1. August 2006
• Englisch
• Abmessung: 239mm x 164mm x 37mm
• Gewicht: 880g
• ISBN-13: 9780470030158
• ISBN-10: 0470030151
• Artikelnr.: 20873143

Autorenporträt

Ali Kaveh is Professor of Structural Engineering at Iran University of Science & Technology, Tehran. He has had over 200 papers published in international journals and conferences. He has held the position of Chief editor of the Asian Journal of Structural Engineering and was a member of the editorial board for 5 international journals and 3 national journals. His research interests include structural mechanics: graph and matrix methods, strength of materials, stability, finite elements and comptuer methods of structural analysis. He is the recipient of various awards, including: Press Media Prize; Educational Gold Medal; Kharuzmi Research Prize and the Alborz Prize; and his previous book "Structural Mechanics: Graph and Matrix Methods, 2nd Edition, 1995" won an award for the best engineering book of its year in Iran.

Inhaltsangabe

Foreword of the First Edition. Preface. List of Abbreviations. 1. Basic
Concepts and Theorems of Structural Analysis. 1.1 Introduction. 1.2 General
Concepts of Structural Analysis. 1.3 Important Structural Theorems.
Exercises. 2. Static Indeterminacy and Rigidity of Skeletal Structures. 2.1
Introduction. 2.2 Mathematical Model of a Skeletal Structure. 2.3 Expansion
Process for Determining the Degree of Statical Indeterminacy. 2.4 The DSI
of Structures: Special Methods. 2.5 Space Structures and Their Planar
Drawings. 2.6 Rigidity of Structures. 2.7 Rigidity of Planar Trusses. 2.8
Connectivity and Rigidity. Exercises. 3. Optimal Force Method of Structural
Analysis. 3.1 Introduction. 3.2 Formulation of the Force Method. 3.3 Force
Method for the Analysis of Frame Structures. 3.4 Conditioning of the
Flexibility Matrices. 3.5 Generalized Cycle Basis of a Graph . 3.6 Force
Method for the Analysis of Pin-jointed Trusses. 3.7 Force Method Analysis
of General Structures. Exercises. 4. Optimal Displacement Method of
Structural Analysis. 4.1 Introduction. 4.2 Formulation. 4.3 Transformation
of Stiffness Matrices. 4.4 Displacement Method of Analysis. 4.5 Stiffness
Matrix of a Finite Element. 4.6 Computational Aspects of the Matrix
Displacement Method. 4.7 Optimal Conditioned Cutset Bases. Exercises. 5.
Ordering for Optimal Patterns of Structural Matrices: Graph Theory Methods.
5.1 Introduction. 5.2 Bandwidth Optimisation. 5.3 Preliminaries. 5.4 A
Shortest Route Tree and its Properties. 5.5 Nodal Ordering for Bandwidth
Reduction; Graph Theory Methods. 5.6 Finite Element Nodal Ordering For
Bandwidth Optimisation. 5.8 Finite Element Nodal Ordering for Profile
Optimisation. 5.8 Element Ordering for Frontwidth Reduction. 5.9 Element
Ordering for Bandwidth Optimisation of Flexibility Matrices. 5.10 Bandwidth
Reduction for Rectangular Matrices. 5.11 Graph-Theoretical interpretation
of Gaussian Elimination. Exercises. 6. Ordering for Optimal Patterns of
Structural Matrices: Algebraic Graph Theory Methods. 6.1 Introduction. 6.2
Adjacency Matrix of a Graph for Nodal Ordering. 6.3 Laplacian Matrix of a
Graph for Nodal Ordering. 6.4 A Hybrid Method for Ordering. Exercises. 7.
Decomposition for Parallel Computing: Graph Theory Methods. 7.1
Introduction. 7.2 Earlier Works on Partitioning. 7.3 Substructuring for
Parallel Analysis of Skeletal Structures. 7.4 Domain Decomposition for
Finite Element Analysis. 7.5 Substructuring; Force Method. 7.6
Substructuring for Dynamic Analysis. Exercises. 8. Decomposition for
Parallel Computing: Algebraic Graph Theory Methods. 8.1 Introduction. 8.2
Algebraic Graph theory for Subdomaining. 8.3 Mixed Method for Subdimaining.
8.4 Spectral Bisection for Adaptive FEM; Weighted Graphs. 8.5 Spectral
Trisection of Finite Element Models. 8.6 Bisection of Finite Element Meshes
Using Ritz and Fiedler Vectors. Exercises. 9. Decomposition and Nodal
Ordering of Regular Structures. 9.1 Introduction. 9.2 Definitions of
Different Graph Products. 9.3 Eigenvalues of Graphs Matrices for Different
Products. 9.4 Eigenvalues of A and L Matrices for Cycles and Paths. 9.5
Numerical Examples. 9.6 Spectral Method for Profile Reduction. 9.7
Non-Compact Extended p-Sum. Exercises. References. Appendix A Basic
Concepts and Definitions of Graph Theory. A.1 Introduction. A.2 Basic
Definitions. A.3 Vector Spaces Associated with a Graph. A.4 Matrices
Associated with a Graph. A.5 Directed Graphs and Their Matrices. A.6 Graphs
Associated with Matrices. A.7 Planar Graphs: Euler's Polyhedron Formula.
A.8 Maximal Matching in Bipartite Graphs. Appendix B Greedy Algorithm and
its Applications. B.1 Axiom System for a Matroid. B.2 Matroids Applied to
Structural Mechanics. B.3 Cocycle Matroid of a Graph. B.4 Matroid for Null
Bases of a Matrix. B.5 Combinatorial Optimisation: the Greedy Algorithm.
B.6 Application of the Greedy Algorithm. B.7 Formation of Sparse Null
Bases. Index. Index of Symbols.