Solving slender axisymmetric structures using the boundary element method - Stikan, Rafael Pacheco; de Moura, Leonardo Caputo; Loeffler, Carlos Friedrich; Lara, Luciano de Oliveira Castro (Engineering analysis with boundary elements, 2024)
In addition to the well-known advantages of mesh generation and straightforward data entry, the Boundary Element Method presents high precision for solving axisymmetric problems. However, many axisymmetric industrial problems involve structures that often have thin walls. This characteristic discourages the employment of axisymmetric models comparatively to the three-dimensional elements or other options such as shells and plate models. However, the BEM axisymmetric model is robust due to its mathematical foundation, consisting of a three-dimensional model integrated into the circumferential direction due to the angular symmetry. Thus, the main objective of this work is to show the scope of the BEM in the static solution of slender structures with geometric conformation and loads that do not vary circumferentially. Conversely, the complete formulas for axisymmetric tensors are unavailable in the specialized literature. Therefore, this work presents all tensor components and their spatial derivatives, including corrections of mistakes committed in some references. Quadratic boundary elements were used. Furthermore, in solving the integral singularities involved, the source points were located externally to the domain to simplify the cumbersome mathematical treatment.