Keywords: element-by-element iteration procedure, two-parameter elastic foundation, differential quadrature element method, differential quadrature model, kinematic transition conditions, natural transition conditions.

In recent years, some new DQ-related discrete element analysis methods were proposed by the present author. These methods are DQEM, DQFEM, DQFDM, GDQEM and GCDQEM [1,2,3,4,5,6]. The performance of these numerical methods is excellent. Moreover, they have the advantage of being suitable to consistently discretize continuum mechanics problems having arbitrarily complex geometries. They are all suitable for vector and parallel processing. In this paper, an element-by-element iteration procedure is proposed for solving the resulting discrete algebraic systems of the DQ-related discrete element analysis methods.

Instead of solving the assembled overall discrete algebraic systems from the DQ-related discrete element analysis methods, the solution of discrete algebraic systems can be carried out using an element-by-element iteration procedure. By using this computational procedure, the largest computation system for solving a discrete algebraic system is an element-basis. The kinematic transition conditions and natural transition conditions are used to carry out the iterative solution from one element to the next one. This iterative computation procedure is effective.

1

C.N. Chen, "A Differential Quadrature Element Method", Proceedings of the First International Conference on Engineering Computation and Computer Simulation, Changsha, China, 25-34, 1995.

2

C.N. Chen, "The Development of Irregular Elements for Differential Quadrature Element Method Steady-State Heat Conduction Analysis", Comput. Methods Appl. Mechs. Engrg., 170, 1-14, 1999. doi:10.1016/S0045-7825(98)00185-6

3

C.N. Chen, "A Generalized Differential Quadrature Element Method", Comput. Methods Appl. Mechs. Engrg., 188, 553-566, 2000. doi:10.1016/S0045-7825(99)00283-2

4

C.N. Chen, "Differential Quadrature Finite Difference Method for Structural Mechanics Problems", J. Commu. Numer. Methods Engr., 17, 423-441, 2001. doi:10.1002/cnm.418

5

C.N. Chen, "DQEM and DQFDM for the Analysis of Composite Two-dimensional Elasticity Problems", Comp. Struc., 59, 3-13, 2003. doi:10.1016/S0263-8223(02)00231-3

6

C.N. Chen, "Discrete Element Analysis Methods of Generic Differential Quadratures", Series of Lecture Notes in Applied Computational Mechanics, 25, Springer, Berlin, Germany, 2006.

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