Keywords: differential quadrature, extended differential quadrature, differential quadrature element method, weighting coefficients, incremental/iterative analysis, global secant relaxation based accelerated constant stiffness iteration, plastic collapse.

A global secant relaxation (GSR)-based accelerated constant stiffness iteration scheme is used to carry out the incremental/iterative solution of nonlinear differential quadrature element problems involving plastic collapse of arch structures. The differential quadrature element method (DQEM) uses the extended differential quadrature (EDQ) to discretize the differential equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the arch structures [1,2]. The DQEM can accurately describe the deformation behavior of the plastic deformed arch structures. The accelerated constant stiffness iteration procedure can overcome the possible deficiency of numerical instability caused by local failure existing in the iterative computation [3,4,5]. Moreover this method can efficiently accelerate the convergence rate of the iterative computation. Consequently, the incremental/iterative analysis can be consistently carried out to update the response history up to a near ultimate load stage, which is important for investigating the global failure behavior of a structure under certain external cause. In this paper, procedures of elastic-plastic formulation, DQEM discretization and the GSR based accelerated constant stiffness iteration summarized and presented. Sample problems are solved, and the numerical results of limit strength are also presented.

1

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

2

Chen C.N., "Differential Quadrature Element Analysis Using Extended Differential Quadrature", Comput. Maths. Appls., Vol. 39, pp. 65-79, 1999. doi:10.1016/S0898-1221(00)00047-X

3

Chen C.N., "Efficient and Reliable Accelerated Constant Stiffness Algorithms for The Solution of Non-linear Problems", Intl. J. Numer. Methods Engr., Vol. 35, pp. 481-490, 1992. doi:10.1002/nme.1620350304

4

Chen C.N., "An Acceleration Method in Elastic-plastic Finite Element Computation", Comput. Struct., Vol. 44, pp. 125-132, 1992. doi:10.1016/0045-7949(92)90231-N

5

Chen C.N., "Accelerated Modified Newton-Raphson Iteration-based Finite Element Solution of Structural Problems Involving Nonlinear Deformation Behavior", Commun. Numer. Methods Engr., Vol. 10, pp. 333-338, 1994. doi:10.1002/cnm.1640100408

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