Analysis of Regular Structures with Member Irregularity Using the Equilibrium Equations and the Singular Value Decomposition

In this paper an efficient method is presented for the analysis of those structures which can be formed by addition some members to regular structures. This method is also applicable when some members are reduced from regular structures. If a model is the union of a regular structure and some additional members, then these members are separated from the structure, and their effect is introduced through equilibrium matrix and added to that of the regular structure. For models which lack some members, pairs of hypothetical elements with positive and negative modulus of elasticity are added, and the members with negative modulus are separated from the structure resulting in a regular structure.

[1]  Ali Kaveh,et al.  Block circulant matrices and applications in free vibration analysis of cyclically repetitive structures , 2011 .

[2]  Ali Kaveh,et al.  EIGENVALUES OF THE ADJACENCY AND LAPLACIAN MATRICES FOR MODIFIED REGULAR STRUCTURAL MODELS , 2010 .

[3]  Jaya Singhal,et al.  Structural Properties Of The Compatibility Matrix: Existence Of Mathematical Relationships , 1988 .

[4]  Ali Kaveh,et al.  Optimal Structural Analysis , 1997 .

[5]  S. R. Mirghaderi,et al.  Analysis of near‐regular structures using the force method , 2012 .

[6]  S. Pellegrino.  Analysis of prestressed mechanisms , 1990 .

[7]  F. Filippou,et al.  Mixed formulation of nonlinear beam finite element , 1996 .

[8]  Yaozhi Luo,et al.  An incremental algorithm to trace the non-linear equilibrium paths of pin-jointed structures using the singular value decomposition of the equilibrium matrix , 2009 .

[9]  Yaozhi Luo,et al.  Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD , 2007 .

[10]  Hossein Rahami,et al.  Vibration analysis of regular structures by graph products: Cable networks , 2010 .

[11]  Simon D. Guest,et al.  The stiffness of prestressed frameworks: A unifying approach , 2006 .

[12]  A. Kaveh,et al.  Analysis of space truss towers using combined symmetry groups and product graphs , 2011 .

[13]  Ali Kaveh,et al.  Approximate eigensolution of locally modified regular structures using a substructuring technique , 2011 .

[14]  S. Pellegrino,et al.  AN INTRODUCTION TO THE ANALYSIS OF SYMMETRIC STRUCTURES , 1999 .

[15]  Ali Kaveh,et al.  Compound matrix block diagonalization for efficient solution of eigenproblems in structural mechanics , 2007 .

[16]  Ali Kaveh,et al.  Eigensolutions for factorable matrices of special patterns , 2003 .

[17]  Ali Kaveh,et al.  Factorization for efficient solution of eigenproblems of adjacency and Laplacian matrices for graph products , 2008 .

[18]  Reg Connelly,et al.  Globally rigid Symmetric Tensegrities , 1995 .

[19]  Zhong Wan-xie,et al.  Analysis of symmetric or partially symmetric structures , 1983 .

[20]  S. Pellegrino.  Structural computations with the singular value decomposition of the equilibrium matrix , 1993 .

[21]  Ali Kaveh,et al.  An efficient analysis of repetitive structures generated by graph products , 2010 .

[22]  S. Pellegrino,et al.  Matrix analysis of statically and kinematically indeterminate frameworks , 1986 .

[23]  Gert Sabidussi,et al.  Graph multiplication , 1959 .

[24]  Simon D. Guest,et al.  Symmetry-adapted equilibrium matrices , 2000 .

[25]  Ali Kaveh.  Graph theoretical methods for efficient flexibility analysis of planar trusses , 1986 .

[26]  S. Pellegrino,et al.  First-order infinitesimal mechanisms , 1991 .

[27]  Ali Kaveh,et al.  Block diagonalization of adjacency and Laplacian matrices for graph product; applications in structural mechanics , 2006 .

[28]  Ali Kaveh.  Graphs and structures , 1991 .

[29]  R. Connelly,et al.  Mathematics and Tensegrity , 1998, American Scientist.

[30]  Kalyan Singhal,et al.  The number of feasible designs in a compatibility matrix , 1996 .

[31]  C. Calladine.  Buckminster Fuller's “Tensegrity” structures and Clerk Maxwell's rules for the construction of stiff frames , 1978 .

[32]  S. Dinkevich.  Finite symmetric systems and their analysis , 1991 .

[33]  Liu Wing-Kam.  Introduction to applied mathematics: Gilbert Strang (Wellesley-Cambridge press, Wellesley, MA, 1986) 758 pp , 1987 .

[34]  Hoang Chi Tran,et al.  Advanced form-finding for cable-strut structures , 2010 .

[35]  A. Kaveh.  Optimal Structural Analysis: Kaveh/Optimal Structural Analysis , 2006 .

[36]  T. Healey,et al.  Exact block diagonalization of large eigenvalue problems for structures with symmetry , 1991 .