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Solution techniques for nonlinear equilibrium equations
(2008) Torkamani, Morteza A.M.; Sönmez, Mustafa
Methodologies for solving nonlinear equilibrium equations are reviewed in this article. Two basic numerical procedures, the pure incremental and the direct iteration methods, are briefly discussed. Then the most frequently used increment-iterative methods are presented and their limitations are discussed. These techniques are the Newton-Raphson and the displacement control method. One of the advanced nonlinear solution procedures, generalized displacement control method, is outlined, and its algorithm is also presented. The generalized displacement method shows that it is a robust numerical technique for solving nonlinear structural problems which may include softening, stiffening behavior and in the bifurcation vicinity of critical points. The elstica problem which is a classic highly geometrically nonlinear problem is presented to show the versatility of the generalized displacement control method for the solution of highly nonlinear problems. © 2008 ASCE.