A generic approach for the solution of nonlinear residual equations. II: Homotopy and complex nonlinear eigenvalue method

DOI10.1016/j.cma.2009.09.015zbMath1231.74133OpenAlexW2022841197WikidataQ105651774 ScholiaQ105651774MaRDI QIDQ658702

El Mostafa Daya, Isabelle Charpentier, Massamaesso Bilasse, Yao Koutsawa

Publication date: 8 February 2012

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.2009.09.015

zbMATH Keywords

automatic differentiationhomotopysandwich structuresasymptotic numerical methodcomplex eigenvalue problemsviscoelastic laws

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Vibrations in dynamical problems in solid mechanics (74H45)

Related Items (11)

On higher-order differentiation in nonlinear mechanics ⋮ Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method ⋮ Optimized higher-order automatic differentiation for the Faddeeva function ⋮ Automatic solver for non-linear partial differential equations with implicit local laws: Application to unilateral contact ⋮ A generic approach for the solution of nonlinear residual equations. III: Sensitivity computations ⋮ Towards a full higher order AD-based continuation and bifurcation framework ⋮ Arbogast: Higher order automatic differentiation for special functions with Modular C ⋮ 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 ⋮ Modal analysis of rotating pre-twisted viscoelastic sandwich beams ⋮ Resolvent sampling based Rayleigh-Ritz method for large-scale nonlinear eigenvalue problems

Uses Software

• Diamant toolbox

Cites Work

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• A generic approach for the solution of nonlinear residual equations. I: The Diamant toolbox
• 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
• Iterative algorithms for nonlinear eigenvalue problems. Application to vibrations of viscoelastic shells
• An iterative process based on homotopy and perturbation techniques
• The non-linear perturbation analysis of discrete structural systems
• Finite element analysis of damping the vibrations of laminated composites
• Evaluating Derivatives
• A finite element analysis of viscoelastically damped sandwich plates

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