Third order thermomechanically coupled laminated plate: 2D nonlinear modeling, minimal reduction, and transient/post-buckled dynamics under different thermal excitations

Avoiding/inducing dynamic buckling in a thermomechanically coupled plate: a local and global analysis of slow/fast response

“…Modelling and the nonlinear dynamics of composite plates in a thermomechanical framework have been the subject of some recent studies aimed at unveiling the possible need to account for the actually coupled behaviour occurring in the multiphysics environment which characterizes their applications in several fields of mechanical, aerospace and civil engineering [1][2][3]. Indeed, most of the previous studies dealing with the nonlinear dynamics of structural models were concerned with partially coupled, or even uncoupled, analyses, in which the interaction phenomena between mechanical and thermal variables are neglected; the problem is addressed by simply referring to a thermal environment and assuming the temperature distribution, or at least independently solving the heat conduction problem and then the mechanical equations of dynamic equilibrium with known terms involving temperature effects (see, for example, [4][5][6][7][8][9][10][11][12]).…”

“…Pursuing coupled analyses of composite plates in a coherent and controllable framework has recently required developing a unified formulation of the thermomechanical problem [1,3], based on the Tonti approach to physical theories [19], in which displacement and temperature variables are dealt with at the same time, within a mathematically inseparable context [20] that is certainly more involved than the uncoupled one from the computational point of view.…”

“…Modelling and the nonlinear dynamics of composite plates in a thermomechanical framework have been the subject of some recent studies aimed at unveiling the possible need to account for the actually coupled behaviour occurring in the multiphysics environment which characterizes their applications in several fields of mechanical, aerospace and civil engineering [1][2][3]. Indeed, most of the previous studies dealing with the nonlinear dynamics of structural models were concerned with partially coupled, or even uncoupled, analyses, in which the interaction phenomena between mechanical 2018 The Author(s) Published by the Royal Society.…”

Nonlinear dynamics of a third-order reduced model of thermomechanically coupled plate under different thermal excitations

“…The present numerical study is in-line with the investigation performed in [29], however considering a minimal model which is much more refined than the CTC one used therein, in both mechanical and thermal aspects, while being equivalent in computational terms. Indeed, the new reduced model accounts for third-order shear deformability and a consistently assumed cubic variation of the temperature along the thickness, which still allow to end up to one mechanical and two thermal generalized variables and three corresponding ordinary differential equations (ODEs) [2]. The model is named TTC just for being based on a Third-order theory with Thermomechanical Coupling, instead of the Classical theory with Thermomechanical Coupling in the background of CTC.…”

A Reduced Model of a Thermo-Elastic Nonlinear Circular Plate

“…The bifurcation analysis has been based on a large number of degrees of freedom which caused numerical complications, comparing with reduced low dimensional models. In recent publications [10], [11] The analysis performed for circular plate at elevated temperature and selected variants of external excitation has been presented in [6,12]. The exact thermomechanical model of the circular plate described by PDEs presented has been reduced to one degree of freedom system.…”