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A generic approach for the solution of nonlinear residual equations. I: The Diamant toolbox. (English) Zbl 1228.74029
Summary: Sufficiently smooth nonlinear PDE problems may be addressed through the higher order derivative computations of the so-called Asymptotic Numerical Method (ANM). In this paper, we theoretically discuss the generic solution of nonlinear residual equations. We then propose a Matlab implementation of the ANM based on Automatic Differentiation which allows for significant improvements in genericity and ease of use. The Diamant toolbox we construct is applied to the study of the geometrical nonlinear behavior of a laminated glass beam. Numerical results and experimental performances demonstrate the efficiency of the Diamant tool.

MSC:
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74E30 Composite and mixture properties
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