A new solution technique is proposed for the static analysis of cyclic symmetric structures, in order to reduce computational effort. Efficient node numbering methods and the selection of a basic substructure for the cyclic symmetric analysis are suggested. Extension of cyclic symmetric analysis to an axisymmetric structure subjected to unsymmetric loading also is discussed. Another new method based on load norms is presented for selection of the Fourier harmonics indices for the analysis. © 1991.

Viswanatha Ramamurti

MATHEMATICAL TECHNIQUES - Numerical Methods

STRUCTURAL DESIGN - Loads

CYCLIC STRUCTURES

SKYLINE SOLVERS

SYMMETRIC STRUCTURES

Structural analysis

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

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IIT Madras

Skyline solver for the static analysis of cyclic symmetric structures

Computers and Structures

In this paper, the modal displacement and modal acceleration methods have been extended to the cyclic symmetry analysis in the semi-complex domain. The study of the influence of forcing frequency on the relative accuracy of the two modal methods is also made. It is shown that only few modes are sufficient to get accurate stresses in the case of modal acceleration method. © 1994.

Modal methods for the analysis of cyclic symmetric structures

In this study the free vibration of circumferentially periodic structures has been analysed using the block Lanczos method in a semi complex domain for extracting real natural frequencies and complex mode shapes. The influence of the number of vectors in the block and also the effect of renumbering of nodes, depending on whether they are internal, adjacent or boundary nodes, on the CPU time are studied. The efficiency of the present method is compared with the subspace iteration schemes. Copyright © 1993 John Wiley & Sons, Ltd

International Journal for Numerical Methods in Engineering

Application of block Lanczos method for analysis of cyclic symmetric structures

To obtain the natural frequencies of rotationally periodic structures, a simple block solver is developed. Complex arithmetic is used to reduce the analysis region to a repeating substructure; characteristic matrices are considered to be cyclic in nature (S. Michimura et al., Bull. Jap. Soc. Mech. Engrs24,1968-1993, 1981). Most of the decomposition operations involved in the complex stiffness matrix are done only once, also in real mode. Simple examples are included to illustrate this solution scheme. Triangular finite elements are used to form the characteristic matrices of repeating substructures. © 1987.

An equation solver for eigenvalue problems of cyclic symmetric structures

Cyclic symmetric structures such as centrifugal fan impellers are considered in this paper. One of the identical sectors is chosen for the finite element analysis. A triangular plate element is employed. The stiffness and load matrices are obtained in cylindrical coordinates. The displacements are obtained using a modified submatrices elimination scheme. The efficiency of this scheme is discussed. Impeller stresses are calculated and checked with the results obtained using a strain gauge technique. © 1987.

Steady state stress analysis of centrifugal fan impellers

A rotationally or circumferentially periodic structure is one in which a series of identical sectors is repeated in the circumferential direction. Each sector is assumed to be loaded identically. Since the deflection shape of each sector is identical, only one sector has been taken for the analysis. The Potters' scheme of solving simultaneous equations is modified for the above analysis. This method is applied to different kinds of problems and results are compared. © 1986.

Static analysis of circumferentially periodic structures with Potters' scheme

In-plane analysis of annular disks using the finite element method is presented. A semi-analytical, one-dimensional finite element model is developed using a Fourier series approach to account for the circumferential behaviour. Using displacement functions which are exact solutions of the two dimensional elasticity plane stress problem, the shape functions, stiffness matrices and mass matrices corresponding to the 0th, 1st and nth harmonics are derived. To show the utility of this new element, example probelms have been solved and compared with the exact solution. The present element can be readily coded into any general purpose finite element program. © 1981.

Journal	Computers and Structures
ISSN	00457949
Open Access	No