Diamant toolbox

A generic approach for the solution of nonlinear residual equations. I: The Diamant toolbox. 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.


References in zbMATH (referenced in 12 articles )

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  1. Delgado, G.; Hamdaoui, M.: Topology optimization of frequency dependent viscoelastic structures via a level-set method (2019)
  2. Yang, Chuanmeng; Jin, Guoyong; Zhang, Yantao; Liu, Zhigang: A unified three-dimensional method for vibration analysis of the frequency-dependent sandwich shallow shells with general boundary conditions (2019)
  3. Filippi, Matteo; Carrera, Erasmo: Various refined theories applied to damped viscoelastic beams and circular rings (2017)
  4. Charpentier, Isabelle; Lampoh, Komlanvi: Sensitivity computations in higher order continuation methods (2016)
  5. Cong, Y.; Yvonnet, J.; Zahrouni, H.: Simulation of instabilities in thin nanostructures by a perturbation approach (2014)
  6. Charpentier, I.: On higher-order differentiation in nonlinear mechanics (2012)
  7. Lampoh, Komlanvi; Charpentier, Isabelle; Daya, El Mostafa: A generic approach for the solution of nonlinear residual equations. III: Sensitivity computations (2011)
  8. Koutsawa, Yao; Belouettar, Salim; Makradi, Ahmed; Nasser, Houssein: Sensitivities of effective properties computed using micromechanics differential schemes and high-order Taylor series: application to piezo-polymer composites (2010)
  9. Bilasse, Massamaesso; Charpentier, Isabelle; Daya, El Mostafa; Koutsawa, Yao: A generic approach for the solution of nonlinear residual equations. II: Homotopy and complex nonlinear eigenvalue method (2009)
  10. Charpentier, Isabelle: Sensitivity of solutions computed through the asymptotic numerical method (2008)
  11. Charpentier, Isabelle; dal Cappello, Claude; Utke, Jean: Efficient higher-order derivatives of the hypergeometric function (2008)
  12. Koutsawa, Yao; Charpentier, Isabelle; Daya, El Mostafa; Cherkaoui, Mohammed: A generic approach for the solution of nonlinear residual equations. I: The Diamant toolbox (2008)