By A. Kaveh
Effective equipment resulting in hugely sparse and banded structural matrices
Application of graph concept for effective research of skeletal structures
Many labored examples and workouts may help the reader to understand the theory
Graph thought won preliminary prominence in technological know-how and engineering via its powerful hyperlinks with matrix algebra and laptop technological know-how. additionally, the constitution of the maths is easily suited for that of engineering difficulties in research and layout. The tools of research during this booklet hire matrix algebra, graph idea and meta-heuristic algorithms, that are ultimate for contemporary computational mechanics. effective tools are offered that result in hugely sparse and banded structural matrices. the most positive aspects of the booklet contain: program of graph conception for effective research; extension of the strength technique to finite aspect research; program of meta-heuristic algorithms to ordering and decomposition (sparse matrix technology); effective use of symmetry and regularity within the strength strategy; and simultaneous research and layout of structures.
Content point » Research
Keywords » program of Graph idea for effective research - Finite aspect research - Meta-heuristic Algorithms
Related matters » Computational Intelligence and Complexity - Computational technological know-how & Engineering
Read Online or Download Computational Structural Analysis and Finite Element Methods PDF
Similar graph theory books
This Festschrift quantity, pubished in honor of Ugo Montanari at the social gathering of his sixty fifth birthday, comprises forty three papers, written through buddies and associates, all major scientists of their personal correct, who congregated at a celebratory symposium hung on June 12, 2008, in Pisa. the quantity comprises seven sections, six of that are devoted to the most study components to which Ugo Montanari has contributed: Graph Transformation; Constraint and good judgment Programming; software program Engineering; Concurrency; types of Computation; and software program Verification.
The speculation of matroids is exclusive within the quantity to which it connects such disparate branches of combinatorial idea and algebra as graph thought, lattice concept, layout conception, combinatorial optimization, linear algebra, workforce idea, ring thought, and box thought. moreover, matroid thought is on my own between mathematical theories a result of quantity and diversity of its similar axiom platforms.
This reference textual content, now in its moment version, deals a latest unifying presentation of 3 simple components of nonlinear research: convex research, monotone operator conception, and the fastened aspect conception of nonexpansive operators. Taking a different complete procedure, the speculation is constructed from the floor up, with the wealthy connections and interactions among the parts because the imperative concentration, and it really is illustrated by way of numerous examples.
- Handbook of Graphs and Networks: From the Genome to the Internet
- Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture (Wiley Series in Discrete Mathematics and Optimization)
- The Algorithmic Beauty of Seaweeds, Sponges and Corals
- Graph algorithms
- The mathematics of Paul Erdos
Additional info for Computational Structural Analysis and Finite Element Methods
Prentice-Hall, Upper Saddle River, NJ, USA 10. Kaveh A (1974) Application of topology and matroid theory to the analysis of structures. D. 1 Introduction This chapter starts with presenting simple and general methods for calculating the degree of static indeterminacy of different types of skeletal structures, such as rigidjointed planar and space frames, pin-jointed planar trusses and ball-jointed space trusses. Then the progress made in the force method of structural analysis in recent years is presented, and the state of art is summarized.
3. 4. 5. 6. Topological force methods, Combinatorial force methods, Algebraic force methods, Mixed algebraic-combinatorial force methods, Integrated force method, and Metaheuristic based methods. Topological methods have been developed by Henderson , Maunder  and Kaveh . Combinatorial force method is mainly developed by Kaveh  using different graph theoretical algorithms. Algebraic topology is employed extensively in the work of Langefors . Algebraic methods have been developed by Denke , A.
Q γ ð SÞ : ð2:7Þ Remove the constraints corresponding to redundants, in order to obtain the corresponding statically determinate structure, known as the basic (released or primary) structure of S. Obviously, a basic structure should be rigid. 3 Formulation of the Force Method 47 p ¼ fp1 ; p2 ; . . ; pn g t , ð2:8Þ where n is the number of components for applied nodal loads. Now the stress resultant distribution r, due to the given load p, for a linear analysis by the force method can be written as, r ¼ B0 p þ B1 q, ð2:9Þ where B0 and B1 are rectangular matrices each having m rows, and n and γ(S) columns, respectively, m being the number of independent components for member forces.
Computational Structural Analysis and Finite Element Methods by A. Kaveh