Graph symmetry and dynamic systems

Computers and Structures

Volumn 82, Issue 23-26, 2004, Pages 2229-2240

  Kaveh, A ^a   Sayarinejad, M A ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Decomposition; Dynamic cores; Eigensolution; Graph; Healing; Laplacian; Mass spring vibrating system; Symmetry

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; NATURAL FREQUENCIES; NUMBER THEORY; STIFFNESS; VECTORS;

DYNAMIC CORES; HEALING; LAPLACIAN; MASS-SPRING VIBRATING SYSTEMS; SYMMETRY;

GRAPH THEORY;

EID: 4944232639     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2004.03.066     Document Type: Conference Paper

References (19)

1. Glockner PG. Symmetry in structural mechanics. ASCE, J Struct Div 1973;99(ST1):71-89.
2. Zingoni A. Group-theoretical applications in solid and structural mechanics: a review. In: Topping BHV, Bittnar Z, editors. Computational structures technology. UK.: Saxe-Coburg Publication; 2002 (Chapter 12).
3. Zingoni A, Pavlovic MN, Zlokovic GM. A symmetry-adapted flexibility approach for multi-storey space frames: general outline and symmetry-adapted redundants. Struct Eng Rev 1995;7(2): 107-19.
4. Kron G. Diakoptics, piecewise solution of large-scale systems. A series of chapters in the Electrical Journal (London), June 1957-February 1959.
5. Przemieniecki JS. Theory of matrix structural analysis. New York: McGraw-Hill Book Company; 1986.
6. Farhat C. A simple and efficient automatic FEM domain decomposer. Comput Struct 1988;28(5):579-602.
7. Topping BHV, Khan AI. Parallel finite element computations. UK: Saxe-Coburg Publications; 1996.
8. Kaveh A. Structural mechanics: graph and matrix methods, third ed. UK: Research Studies Press; 2004.
9. Kaveh A, Rahimi Bondarabady HA. Finite element mesh decompositions using complementary Laplacian matrix. Commun Numer Methods Eng 2000;16:379-89.
10. Kaveh A, Roosta GR. An algorithm for partitioning finite element meshes. Adv Eng Software 1999;30:857-65.
11. Kaveh A. Optimal structural analysis. UK: Research Studies Press (John Wiley); 1997.
12. McPhee JJ, Ishac MG, Anderw GC. Willenburg's formulation of multibody dynamic equations from a graph-theoretical perspective. Mech Mach Theory 1996;31(2): 201-13.
13. Arczewski K. Application of graph theory to the mechanical modeling of rigid body systems. J Franklin Inst 1990;327(2):209-23.
14. Livesley RK. Mathematical methods for engineers. In: Ellis Horwood series in mathematics and its applications, UK, 1989.
15. Jennings A, McKeown JJ. Matrix computation. UK: John Wiley and Sons; 1992.
16. Bathe KJ, Wilson EL. Numerical methods for finite element analysis. Englewood Cliffs, USA: Printice Hall; 1976.
17. Kaveh A, Sayarinejad MA. Eigenvalues of matrices with special patterns using symmetry of graphs. Scientia Iranica 2003;10:220-6.
18. Kaveh A, Sayarinejad MA. Eigensolutions for matrices of special patterns. Commun Numer Methods Eng 2003; 19: 125-36.
19. Cvetkovié DM, Doob M, Sachs H. Spectra of graphs. New York: Academic Press; 1980.