Análise de tensões térmicas auto-equilibradas em chapas planas retangulares isotrópicas

Abstract

In the present work it is presented a methodology to determine the self-balanced thermal stresses and thermal strains in isotropic rectangular flat plates that are under plane stress state and three-dimensional state. The consideration of some basic simplifying assumptions resulted in the condition of self-balanced thermal stress, where the resulting efforts are null. Thus, there are determined expressions, in polynomial terms, to the self-balanced thermal stresses and thermal strains acting on the plates for the two cases. The plates are free of external loads at their ends and are subjected to nonlinear temperature distributions. The temperature distributions were obtained by solving two problems of heat conduction. The proposed methodology was to approach these nonlinear temperature distributions by polynomials approximations. Thus, the stress and strain fields were completely determined by the polynomial coefficients of the approximate polynomial temperature field through the use of the expressions obtained in polynomial terms. The results obtained by this method were compared with the results obtained by the finite element method. The comparison of approximate analytical results and the results obtained by the finite element method showed high level of agreement to locations away from the free ends of the plates. Thus, there are determined certain expressions that satisfactorily represent the stress and strain fields to distant points of the free ends of the plates, that is, in regions where the basic simplifying assumptions are met.