×

zbMATH — the first resource for mathematics

Application of differential quadrature to static analysis of structural components. (English) Zbl 0669.73064
The numerical technique of differential quadrature for the solution of linear and nonlinear partial differential equations, first introduced by Bellman and his associates [R. Bellman, Methods of nonlinear analysis, Vol. II. (1973; Zbl 0265.34002); Chapter 16; with J. Casti, J. Math. Anal. Appl.34, 235-238 (1971; Zbl 0236.65020); with B. G. Kashef and J. Casti, J. Comput. Phys. 10, 40-52 (1972; Zbl 0247.65061)], is applied to the equations governing the deflection and buckling behaviour of one-and two-dimensional structural components. Separate transformations are used for higher-order derivatives as suggested by J. O. Mingle [J. Math. Anal. Appl. 60, 559-569 (1977; Zbl 0372.65049); Int. J. Numer. Methods Eng. 7, 103-116 (1973; Zbl 0263.65102)], thus extending the method to treat fourth-order equations and to include multiple boundary conditions in the respective co-ordinate directions. Results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods. The application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74G60 Bifurcation and buckling
65D25 Numerical differentiation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bellman, J. Math. Anal. Appl. 34 pp 235– (1971)
[2] Bellman, J. Comp. Phys. 10 pp 40– (1972)
[3] Methods of Nonlinear Analysis, Vol. 2, Academic Press, New York, 1973. Chapter 16.
[4] Bellman, Math. Biosci. 19 pp 1– (1974)
[5] Mingle, Int. j. numer. methods eng. 7 pp 103– (1973)
[6] Mingle, J. Math. Anal. Appl. 60 pp 559– (1977)
[7] Bellman, J. Math. Anal. Appl 68 pp 321– (1979)
[8] Bellman, J. Math. Anal. Appl. 71 pp 403– (1979)
[9] Naadimuthu, J. Math. Anal. Appl. 98 pp 220– (1984)
[10] Civan, J. Math. Anal. Appl. 93 pp 206– (1983)
[11] Civan, Int. j. numer. methods eng. 19 pp 711– (1983)
[12] Civan, J. Math. Anal. Appl. 101 pp 423– (1984)
[13] Civan, J. Comp. Phys. 56 pp 343– (1984)
[14] and , ’Solving integro-differential equations by the quadrature method’, Integral Methods in Science and Engineering, Hemisphere Publishing, Washington, DC, 1986. pp. 106-113.
[15] and , ’New methods for analyzing vibration of structural components’, Proc. AIAA Dynamics Specialist Conference, Monterey, CA, 1987, part 2B, pp. 936-943;
[16] AIAA J. 26 pp 612– (1988)
[17] and , ’Analysis by differential quadrature of thin circular plates undergoing large deflections’, Developments in Mechanics, Vol. 14, Proc. 20th Midwestern Mechanics Conference, Purdue University, West Lafayette, IN, 1987. pp. 900-905.
[18] Striz, Thin-Walled Structures 6 pp 51– (1988)
[19] and , ’Nonlinear deflection of rectangular plates by differential quadrature’, Computational Mechanics ’88, Int. Conf. Computational Engineering Science, Atlanta, GA, Apr. 1988. Vol. I, Chapter 23, pp. iii.1-iii.4.
[20] Numerical Methods for Scientists and Engineers, 2nd edn, McGraw-Hill, New York, 1973.
[21] Newberry, J. Eng. Mech. 113 pp 873– (1987)
[22] Bert, J. Eng, Mech. 110 pp 1655– (1984)
[23] Swenson, J. Aeronaut. Sci. 19 pp 273– (1952) · doi:10.2514/8.2245
[24] Energy and Variational Methods in Applied Mechanics, Wiley, New York, 1984. pp. 218-219.
[25] and , Theory of Plates and Shells, 2nd edn, McGraw-Hill, New York, 1959. p. 57.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.