Thermo-elastic analysis of multilayered plates and shells based on 1D and 3D heat conduction problems

Three Dimensional Coupling between Elastic and Thermal Fields in the Static Analysis of Multilayered Composite Shells

“…The first part of this section shows three preliminary validation results to verify the developed general three-dimensional exact coupled thermo-elastic shell theory. Comparisons with [21] are performed to define the appropriate order of expansion N for the exponential matrix in Eq. ( 27) and the correct number of artificial layers M for the exact definition of constant curvature terms related to shell geometry.…”

“…Tables 4-14 present four different acronyms used to indicate the different models compared in this section: 3D-u-θ means the 3D full coupled thermo-elastic model where the displacements (indicated as u) and the sovra-temperature profile (indicated as θ ) are fully coupled and they must be considered as primary unknowns of the problem. 3D() is the general indication of the 3D uncoupled thermoelastic models presented by Brischetto et al in [21], where the arguments inside the parentheses denote the variable separately solved and the used Fourier heat conduction relation. Specifically, 3D(θ c , 3D) indicates the 3D uncoupled model where the three-dimensional Fourier heat conduction relation is separately solved to calculate θ c , 3D(θ c , 1D) denotes the 3D uncoupled model where the onedimensional Fourier heat conduction relation is separately solved to calculate θ c and 3D(θ a ) denotes the "a priori" assumed linear temperature evaluation.…”

“…The proposed three-dimensional methodology is able to consider plate and shell geometries by means of a generic and unique theory where several structures can be analysed by means of the same tool. The innovative point with respect to the similar 3D model proposed by Brischetto et al in [21] is the full coupling considered for the elastic and thermal fields. Therefore, the primary variables of the model are the three displacement components and the scalar temperature profile.…”

“…Eq. ( 5) is the 3D Fourier heat conduction equation in steady-state conditions specifically written for spherical shells and already presented by Brischetto et al in [21]. In a full coupled thermoelastic problem, the three-dimensional Fourier heat conduction relation is directly coupled with the three-dimensional equilibrium relations.…”

“…Exact solutions for thermal stress investigations of composite multilayered plates were developed in [20]. Brischetto et al [21,22] developed a 3D uncoupled thermo-elastic model for composite and functionally graded shells and plates having the temperature evaluation defined via the three-dimensional Fourier heat conduction relation. Monge et al [23] proposed a 3D semi-analytical thermo-mechanical model where the Differential Quadrature Method (DQM) was employed for the derivatives in the thickness direction analogous to the 3D pure elastic shell theory in [24] and [25].…”