Análise de estruturas axissimétricas de parede delgada via método dos elementos finitos

Abstract

Many usual structures such as reservoirs, roof domes, pressure vessels and silos have both axisymmetric shape and loading. Due to its extensive use, it is necessary to know the structural behavior of this type of element in its various forms of application loading conditions. Classical theories provide solutions, in principle analytical, for geometric and load profiles by solving complex differential equations. Thus, in some cases, the analytic resolution becomes exhaustive, while in other cases this solution does not exist. The application of the Finite Element Method (FEM) appears as a viable alternative for the study of such structures, provided that the numerical models adopted accurately represent their real behavior. This study focuses on the mechanical behavior, through the FEM, of axisymmetric structures of different shapes subject to conditions of connection, supports and revolution loads. The structural analysis is done by means of a computational program elaborated by the author. There are presented elements of isolated shells, cylindrical reservoirs with flat bottom, conical or flat with flap without roof, a complete reservoir with ring of stiffness and roof dome and finally a study of the approach of Hannah for spherical domes and he usual simplifications in projects is realized. The results of the first examples show that the computational program used in the analyzes presents satisfactory results when compared to the analytical results. In the examples where the elastic base is applied, great influence of the soil stiffness in the distribution of stresses is observed in both the bottom plate and the wall of the reservoir. The use of the conical base, commonly used to facilitate cleaning, causes a reduction in bending moments and an increase in radial stress and displacements. The results show that, up to 30 centimeters in length, the addition of a flap to the bottom plate causes a reduction in the stresses, bending moments and maximum displacements of the reservoir, but for longer flap lengths, the moments and stresses in the elements increase and make it unfeasible. Finally, for the example studied, it is found that the Hannah’s simplification method provides a good approximation for structural analysis of thin spherical domes, although it maximizes normal stresses and minimizes bending displacements and moments. Therefore, the main contribution of the work is the implementation of a computational formulation that allows a more comprehensive analysis of thin structures of revolution subjected to axissimetric loading.