A three-dimensional continuum approach to the thermoelastodynamics of large-scale structures

Abstract

A three-dimensional (3D) continuum procedure proposed for the evaluation of the temperature field due to solar and environmental exposure in large-scale 3D structures, together with effects on the linear modal properties is here. 3D finite element discretization of the heat equation is employed to compute first, the temperature changes in the structure due to the heat exchanges with the external environment. The heat equation is complemented with nonlinear boundary conditions of the Fourier–Robin type to describe heat transfers by convection, radiation, and solar radiation. The heat exchanges by convection and radiation between the structure and the surrounding air are described once the variation of air temperature with time is known. The solar radiation on the structure is defined through a procedure that requires, as input data, the geometry and the orientation of the irradiated surfaces, the latitude of the location, and the clearness index. The computed thermal fields represent the input data for the nonlinear problem which governs the thermoelastic equilibrium. The linearization of the equations of motion about this equilibrium state yields the eigenvalue problem governing the evolution of the eigenfrequencies due to the slowly time-varying thermal gradients. A nonlinear continuum model based on a linearly elastic constitutive law is employed. The novelty of this work lies in the accurate description of the thermal gradient field, in terms of the actual measurable input data to the heat diffusion problem, as well as the refined mechanical representation of the 3D effects of the thermo-geometric stiffness and the elastic moduli.