Structural Mechanics: Graph and Matrix MethodsThis text combines concepts of graph theory and matrix algebra to present powerful tools for the analysis of large-scale structures. In this third edition, Kaveh (Iran University of Science and Technology, Tehran) develops approaches for the analysis of large-scale systems, and provides new material on vector spaces associated with graphs, algorith |
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adjacency matrix admissible cycle algebraic representation associate graph B₁ bandwidth bases bipartite graph C₁ calculated Chapter chords condition numbers connected considered contains contour core corresponding cutset basis cycle space cycles of length defined denoted depicted in Figure diagonal displacements eigenvalues eigenvectors embedding end nodes equations example Fiedler vector flexibility matrix force method formation functions Gaussian elimination global coordinate system graph model graph theory Greedy Algorithm grid illustrated in Figure incidence matrix independent integer k₁ Kaveh Laplacian matrix m₁ matroid n₁ nodal numbering nodal ordering null null graph number of members obtained optimal optimisation planar frame planar graph planar truss problem properties representative node rigid S₁ S₂ selected cycles shown in Figure skeletal structures space frame spanning tree starting node statically determinate Step stiffness matrix structural analysis subgraph submatrices suboptimal subset symmetric Theorem topological unused member vector y-cycle y-tree