A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Nested iterations for symmetric eigenproblems
SIAM Journal on Scientific Computing
Group-theoretic applications in solid and structural mechanics: a review
Computational structures technology
A paralleled element-free Galerkin analysis for structures with cyclic symmetry
Engineering with Computers
Parallel computation of the eigenvalues of symmetric Toeplitz matrices through iterative methods
Journal of Parallel and Distributed Computing
A new formulation for fictitious mass of the Dynamic Relaxation method with kinetic damping
Computers and Structures
Canonical Forms for Symmetric and Regular Structures
Journal of Mathematical Modelling and Algorithms
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Eigenproblems play a key role in the stability and free vibration analysis of structures. In large structural models, the solutions of these problems need a considerable computational effort. There are special types of structures whose special properties can be utilized to achieve solutions in a much simpler way. In this paper, an efficient method is presented for buckling and free vibration analysis of cyclically repeated space truss type structures. First, for a three dimensional truss element, stiffness, geometric stiffness and mass matrices are expressed in cylindrical coordinate system and this leads to the formation of a special pattern for the related matrices of entire of such structures. Second, using this pattern where some concepts of Kronecker product, initial generalized eigenproblems are decomposed into some subproblems with smaller dimensions and their solutions can easily be obtained. Finally, the efficiency of the present method is illustrated through some examples.