Análise mecânica da costela e da caixa torácica humana: implementação pelo método de elementos finitos (MEF)

Abstract

Since the 20th century, with the development of technique and numerical techniques for solving partial differential equations, works with the aim of predicting the mechanical behaviour of the human thorax have been developed. This part of the human body is crucial, as it protects vital organs such as the heart and lungs, futhermore, deformities such as pectus carinatum, often mechanically corrected, can appear during adolescence. Thus, the present work has to develop and evaluate the use of beam elements for a structural simulation, with the development of differential equations by the theory of Continuum Mechanics and geometry symmetrization through the Timoshenko beam theory, solving them by variational methods and arriving at stiffness matrices for two shape functions. The evaluation of the elements was made by comparing the numerical solutions with experimental results present in papers already developed, showing compatibility for a cortical and trabecular area ratio of 0.15, as expected. For this value, rib ring 4 has a maximum force of approximately 50 N for a displacement of 25 mm for the first element and 22 mm for the second, both with the appearance of a force of approximately 6 N in the normal direction, not observed in other rings such as rib 5, also in agreement with the experimental data. In the case of deformities of the type pectus carinatum, a total deformation of approximately 15 mm was observed for an pressure of initial correction of 60 kPa (8.7 psi, approximately), also close to the experimental results. Thus, the present study proved to be promising for an analysis of the mechanical behavior of the human thorax, which can be used and improved for consistent analysis of phenomena that involve it.