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

DOI10.1016/j.cma.2008.09.003zbMath1228.74029OpenAlexW2046195570WikidataQ105651799 ScholiaQ105651799MaRDI QIDQ653648

Mohammed Cherkaoui, Isabelle Charpentier, El Mostafa Daya, Yao Koutsawa

Publication date: 19 December 2011

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2008.09.003

zbMATH Keywords

automatic differentiationlaminated glassgeometrical nonlinearitiesasymptotic numerical methodDiamant

Mathematics Subject Classification ID

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

Related Items (10)

On higher-order differentiation in nonlinear mechanics ⋮ Sensitivities of effective properties computed using micromechanics differential schemes and high-order Taylor series: application to piezo-polymer composites ⋮ Automatic solver for non-linear partial differential equations with implicit local laws: Application to unilateral contact ⋮ Various refined theories applied to damped viscoelastic beams and circular rings ⋮ A generic approach for the solution of nonlinear residual equations. II: Homotopy and complex nonlinear eigenvalue method ⋮ A generic approach for the solution of nonlinear residual equations. III: Sensitivity computations ⋮ Topology optimization of frequency dependent viscoelastic structures via a level-set method ⋮ Simulation of instabilities in thin nanostructures by a perturbation approach ⋮ Sensitivity computations in higher order continuation methods ⋮ A unified three-dimensional method for vibration analysis of the frequency-dependent sandwich shallow shells with general boundary conditions

Uses Software

• ADOL-C
• Matlab
• ADMAT
• Diamant toolbox
• MAD

Cites Work

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• Static and free vibration analysis of laminated glass beam on viscoelastic supports
• Sensitivity of solutions computed through the asymptotic numerical method
• Automatic differentiation with the asymptotic method of numerical type: the diamond approach
• Asymptotic numerical method for problems coupling several nonlinearities.
• The non-linear perturbation analysis of discrete structural systems
• Automatic Differentiation for MATLAB Programs
• A path-following technique via an asymptotic-numerical method
• An efficient overloaded implementation of forward mode automatic differentiation in MATLAB
• Fast higher-order derivative tensors with Rapsodia
• Solving Ordinary Differential Equations Using Taylor Series
• Méthodes asymptotiques numériques pour la plasticité
• Asymptotic Numerical Method for Nonlinear Constitutive Laws
• Algorithm 755: ADOL-C
• An asymptotic‐numerical method to compute the postbuckling behaviour of elastic plates and shells

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