Engineering Transactions, 31, 3, pp. 331-340, 1983

Choice of Collocation Points for Axisymmetric Nonlinear Two-Point Boundary Value Problems In Statics Of Shallow Spherical Shells

Y. Nath
Indian Institute of Technologi, Delhi
India

P.C. Dumir
Indian Institute of Technologi, Delhi
India

M.L. Gandhi
Indian Institute of Technologi, Delhi
India

The present work investigates the optimum choice of collocation points which gives for а given accuracy the minimum number of collocation points. А convergence study has been conducted for the axisymmetric nonlinear analysis of а shallow spherical shell under а unif­ormly distributed Joad with four different choices of collocation points, viz. equidistant collo­cation points; collocation at maxima of а Chebysbev polynomial; collocation at zeros of а Chebyshev polynomial and zeros of а Legendre polynomial (Gaussian points) as collocation points. It has been found that the Gaussian collocation method has the fastest rate of convergence and it yields accurate results even with small numbеr of collocation points. Тhе results for the nonlinear static analysis of elastic circular plates апd shallow spherical shells obtained bу the Gaussiau collocation method hаvе been presented and аre found to be in good agreement with the гesults available.
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References

В. А. FINLAYSON, Тhе method of weighted residuals and variational principles, Academic Press, N.Y. 1972.

J. VILLADSEN аnd L. МICНELSON, Solution of differential equation models bу polynomial appгoxi­mation, Prentice Hall 1978.

С. DЕВOOR and В. SWARTZ, Collocation at Gaussian points, SIAM J. Numerical Analysis, 10, 582-606, 1973.

R. D. RussвL and J. М. VARAН, А comparison of global methods for-linear two-point boundary value problems, Maths Comput, 29, 1007-1019, 1975.

С. LANCZOS, Trigonometric interpolation of empirical and analytical functions, J. Maths. Phys., 17, 123, 199, 1938.

Y. NATH and R.S. ALWAR, Noпlineaг static and dynamic response of spherical shells, Int. J, Nonlin. Mech., 13, 157-170, 1978.

О. С. ZIENKIEWICZ, Тhе finite element method in engineering science, McGraw Hill, London 1971.

В. BUDIANSKY, Buckling of clamped shallow spherical shells, I, Proc. IUTAM SYMP. On Theory of Thin Elastic Shells, Delft, the Netherlands 64-94, 1959.

S. Р. TIMOSHENKO and S. WOINOWSKY-KRIEGER, Theory of plates and shells, McGгaw Нill, N.Y. 1959.

R. S. ALWAR апd Y. NATH, Application of Chebyshev polynomials to the non-linear analysis of circular plates, Int. J. Mech. Sci., 18, 589-595, 1976.

Н. KANEMATSU апd W. А. NASH, Random vibration of thin elastic plates and shallow spherical shells AFOSR, Scientific Raport AFCSRTR-71-1860 Univ. of Mass, 1971.




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