Computational analysis via MDF of cylindrical shells with bilateral and unilateral contact constraints
Fernando Carlos Scheffer Machado1; McGlennon da Rocha Régis2; Ricardo Azoubel da Mota Silveira3; Christianne de Lyra Nogueira3
1 Instituto Federal de Educação, Ciência e Tecnologia do Sul de Minas Gerais; 2 Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais; 3 Universidade Federal de Ouro Preto
doi:10.20906/CPS/CILAMCE2017-0736
Resumo
The cylindrical shells are widely used as structural elements in buried pipelines, containment structures for tunnels and shafts, and deposits of various materials in the form of silos or tanks. In these applications, the cylindrical shells interact with the medium, in this case soil or rock. This interaction can be considered in two different ways: as a bilateral contact problem (BCP), when the structure and the medium do not lose contact during the deformation process; and as an unilateral contact problem (UCP), when the shell is not completely fixed and may lose contact with the medium for certain loading conditions. Therefore, this work presents a computational study involving cylindrical shells with bilateral and unilateral constraints imposed by the soil or rock medium. The numerical methodology proposed has the following main characteristics: i. the use of the finite difference method to approximate the derivatives of the equilibrium differential equations of the elastic shell-base system; ii. the soil or rock medium is approximated by Winkler's model; iii. the use of optimization algorithms for solving the BC and UC problems. In the case of BCP, the contact region between the bodies Sc (shell-medium) is known a priori, and its solution can be obtained directly if the assumptions of small displacements and elastic material are considered. In the case of UCP, the main challenge is the definition of the contact region between the bodies, Sc, which is unknown a priori. In one of the proposed formulations, the interaction shell-medium is calculated considering directly the unilateral contact constraints and solving a linear complementarity problem (LCP). In another approach, the contact area is initially approximate and, by Newton-Raphson's method, is made the correction of the foundation contribution. Examples are presented in order to verify the efficiency of the numerical strategies proposed for solving this class of contact problem.
Palavras-chave: cylindrical shell; interaction shell-medium; unilateral contact problem; finite difference method; linear complementarity problem