We present a finite element formulation based on a weak form of the boundary value problem for fully coupled thermoelasticity. The thermoelastic damping is calculated from the irreversible flow of entropy 11 due to the thermal fluxes that have originated from the volumetric strain variations. Within our weak formulation we define a dissipation function that can be integrated over an oscillation period to evaluate the 13 thermoelastic damping. We show the physical meaning of this dissipation function in the framework of the well-known Biot’s variational principle of thermoelasticity. The coupled finite element equations 15 are derived by considering harmonic small variations of displacement and temperature with respect to the thermodynamic equilibrium state. In the finite element formulation two elements are considered: the first 17 is a new 8-node thermoelastic element based on the Reissner–Mindlin plate theory, which can be used for modeling thin or moderately thick structures, while the second is a standard three-dimensional 20-node 19 iso-parametric thermoelastic element, which is suitable to model massive structures. For the 8-node element the dissipation along the plate thickness has been taken into account by introducing a through21 the-thickness dependence of the temperature shape function. With this assumption the unknowns and the computational effort are minimized. Comparisons with analytical results for thin beams are shown to illustrate the performances of those coupled-field elements
A finite element formulation for thermoelastic damping analysis
Serra, Enrico;Bonaldi, Michele
2009-01-01
Abstract
We present a finite element formulation based on a weak form of the boundary value problem for fully coupled thermoelasticity. The thermoelastic damping is calculated from the irreversible flow of entropy 11 due to the thermal fluxes that have originated from the volumetric strain variations. Within our weak formulation we define a dissipation function that can be integrated over an oscillation period to evaluate the 13 thermoelastic damping. We show the physical meaning of this dissipation function in the framework of the well-known Biot’s variational principle of thermoelasticity. The coupled finite element equations 15 are derived by considering harmonic small variations of displacement and temperature with respect to the thermodynamic equilibrium state. In the finite element formulation two elements are considered: the first 17 is a new 8-node thermoelastic element based on the Reissner–Mindlin plate theory, which can be used for modeling thin or moderately thick structures, while the second is a standard three-dimensional 20-node 19 iso-parametric thermoelastic element, which is suitable to model massive structures. For the 8-node element the dissipation along the plate thickness has been taken into account by introducing a through21 the-thickness dependence of the temperature shape function. With this assumption the unknowns and the computational effort are minimized. Comparisons with analytical results for thin beams are shown to illustrate the performances of those coupled-field elementsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
