×

zbMATH — the first resource for mathematics

A new approach to the differential quadrature method for fourth-order equations. (English) Zbl 0886.73078
Summary: A generalized methodology for treating boundary conditions in the differential quadrature method (DQM) is presented. This improved approach eliminates the deficiencies of the \(\delta\)-type grid arrangement, which represents an approximation, by applying the boundary conditions exactly. Two kinds of basis functions, Chebyshev and Lagrange, are used for concept demonstration. It is found that the new approach cures most deficiencies of the current DQM.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bert, AIAA J. 26 pp 612– (1988) · Zbl 0661.73063 · doi:10.2514/3.9941
[2] Sherbourne, Comput. Struct. 40 pp 903– (1991) · Zbl 0850.73355 · doi:10.1016/0045-7949(91)90320-L
[3] Bert, Int. J. Solids Struct. 30 pp 1737– (1993) · Zbl 0800.73182 · doi:10.1016/0020-7683(93)90230-5
[4] Gutierrez, Ocean Eng. 21 pp 57– (1994) · doi:10.1016/0029-8018(94)90029-9
[5] Jang, Int. j. numer. methods eng. 28 pp 561– (1989) · Zbl 0669.73064 · doi:10.1002/nme.1620280306
[6] Wang, Comput. Struct. 48 pp 473– (1993) · doi:10.1016/0045-7949(93)90324-7
[7] Striz, Int. J. Solids Struct. 31 pp 2807– (1994) · Zbl 0943.74562 · doi:10.1016/0020-7683(94)90070-1
[8] and , Theory of Plates and Shells, 2nd edn, McGraw-Hill, New York, 1959.
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.