An Efficient Packed-Store Solver for Structural Frameworks

Abstract

This paper deals with a proposed new method for solving the systems of linear simultaneous equations generated by matrix methods of structural analysis.

The solver, which uses a slightly modified form of the ‘packed store’ concept, can directly determine and store any pattern of coefficients and the corresponding out-of-core requirements beforehand. Hence with this solver one is not limited by the necessity to minimise the band-width or profile. With some ‘unconventional’ but easy to produce ‘patterns' it is possible to greatly reduce the number of numerical operations required and in addition use considerably less memory. For example to analyse a 100-joint rectangular plane frame, the method needs about half the arithmetical operations and three quarters of the memory requirements of conventional solvers. Since only minimal ‘house-keeping’ is required, the execution time is approximately halved.

The solver has been incorporated into a structural analysis package which over the past two years was used to analyse a large number of examples.

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References

Bathe

Klaus-Jurgen

Bathe

Edward L.

, Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1976.

Falzon

, Pattern Solver for the Static and Dynamic Analysis of Framework Models, M.Phil. Thesis, Civil Engineering Department, University of Hong Kong, 1985.

Jennings

Alan

, Matrix Computation for Engineers and Scientists, John Wiley & Son, New York, 1977.

George

Liu

J. W.

, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.

Chan

H. C.

Falzon

, Pattern solver for space frame structures, In: Third International Conference on Space Structures, ed. Nooshin

, Elsevier Applied Science Publishers, London, 1984.

Atkinson

K. E.

, An Introduction to Numerical Analysis, John Wiley & Sons, New York, 1978.

Braemeller

Allan

R. N.

Hamam

Y. M.

, Sparsity, Its Practical Application to System Analysis, Pitman, London, 1975.

Cheung

Y. K.

Yeo

M. F.

, A Practical Introduction to Finite Element Analysis, Pitman, London, 1979.

Coates

R. C.

Contie

M. G.

Kong

F. K.

, Structural Analysis, Second Edition, Thomas Nelson, Walton-on-Thames, 1980.

10.

Conte

S. D.

De Boor

Carl

, Elementary Numerical Analysis, Third Edition, McGraw-Hill Kogakusha, Ltd, Tokyo, 1980.

11.

Falzon

Chan

H. C.

, Pattern Solver for Framework/Network Numerical Models, Research Report, Department of Civil Engineering, University of Hong Kong, September 1983.