Mixed methods for viscoelastodynamics and topology optimization
Journal Title: Frattura ed Integrità Strutturale - Year 2014, Vol 8, Issue 29
Abstract
A truly-mixed approach for the analysis of viscoelastic structures and continua is presented. Anadditive decomposition of the stress state into a viscoelastic part and a purely elastic one is introduced alongwith an Hellinger-Reissner variational principle wherein the stress represents the main variable of theformulation whereas the kinematic descriptor (that in the case at hand is the velocity field) acts as Lagrangemultiplier. The resulting problem is a Differential Algebraic Equation (DAE) because of the need to introducestatic Lagrange multipliers to comply with the Cauchy boundary condition on the stress. The associatedeigenvalue problem is known in the literature as constrained eigenvalue problem and poses several difficultiesfor its solution that are addressed in the paper. The second part of the paper proposes a topology optimizationapproach for the rationale design of viscoelastic structures and continua. Details concerning densityinterpolation, compliance problems and eigenvalue-based objectives are given. Worked numerical examples arepresented concerning both the dynamic analysis of viscoelastic structures and their topology optimization.
Authors and Affiliations
Giacomo Maurelli, Nadia Maini, Paolo Venini
Keywords
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- EP ID EP99744
- DOI 10.3221/IGF-ESIS.29.31
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