Análise estática não-linear de cascas conoidais - Morais, Danielly Luz Araújo de (2017)
In the analytical study of conoidal shallow shells, one has the difficulty in analytically representing their displacement fields. In this way a numerical analysis, such as the Finite Element Method (MEF), has been used in the study of this type of structure. In this work, a static analysis of conoidal shallow shells from curved parabolic or cylindrical edges of linear, homogeneous and isotropic elastic material is performed, subjected to a transversal uniformly load distributed along the surface. With the thin-plate formulation derived from Kirchhoff's hypotheses and the theory developed by Marguerre for thin shells, the non-linear equilibrium equations that govern the behavior of the conoidal shell were determined, considering that this is a plate with an initial displacement. A linear parametric analysis of the critical loads and of buckling modes through the MEF is performed using ABAQUS 6.11® program, varying the contour and height conditions of the curved edges. Analytically, a complexity of the components of the buckling mode displacement fields of a given geometry is evaluated by its decomposition into double Fourier series. With the non-linear analysis via MEF, the non-linear equilibrium trajectories of the displacements are obtained and the first non-linear loading limit points are obtained. Nonlinear parabolic or cylindrical geometric parabolic geometry trajectories with describable supports at their four edges are also compared, evaluating how the geometric non-linearities influence the modes of the displacement fields during loading. Finally, a non-linear parametric analysis of the influence of the variation of the curved edge heights on the equilibrium trajectories of the membrane stresses and resulting from internal moments of the conoidal shell is carried out. It is verified, with this work, that linear analyzes can underestimate, or overestimate, the nonlinear behavior of the conoid. As the parametric analysis influences the behavior of the conoid in front of the load, either in the linear analysis, resulting in different critical loads and modes of buckling, or in the nonlinear analysis, resulting in differentiated limits loads and nonlinear equilibrium trajectories of the displacements and membrane stresses and moments.