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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.

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
Full Text: DOI
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