Eventos Anais de eventos
CONEM 2022
XI Congresso Nacional de Engenharia Mecânica - CONEM 2022
On the Use of Green's Theorem for the Calculation of Geometric and Inertia Properties of Plane Shapes
Submission Author:
Matheus Basílio Rodrigues Fernandes , SP
Co-Authors:
Matheus Basílio Rodrigues Fernandes, Rubens Gonçalves Salsa Junior, Thiago de Paula Sales, Domingos Rade
Presenter: Thiago de Paula Sales
doi://10.26678/ABCM.CONEM2022.CON22-0618
Abstract
Research on undergraduate engineering education has increasingly focused on the systematic integration of engineering disciplines and advanced mathematics, since it is commonly found in related studies that teaching the mathematics curriculum emphasizing its underlying applications is a key factor in promoting a multidisciplinary and conceptual understanding of mathematical concepts. In this context, this work proposes the use of Green's Theorem as a tool capable of exploring the interdisciplinarity between vector calculus and different engineering disciplines, such as statics and dynamics of rigid bodies. More specifically, it is shown how Green's Theorem can be applied to obtain geometric properties (or inertia properties, for materials with constant surface density) of planar shapes, such as area (mass), centroid (center of mass), second moment of area (moment of inertia), and product moment of area (or product of inertia). For polygonal shapes, the predicted values of the geometric/inertia properties are found to coincide with the analytical ones. For shapes with curvilinear boundaries, the obtained expressions generate approximate values, which converge to the analytical results as the contour discretization is refined. The applicability of this methodology is illustrated through the dynamical analysis of a planar mechanism using the Newton-Euler equations. This application also reveals that orbits obtained with respect to an inertial reference frame or with respect to a body-fixed reference frame are the same.
Keywords
Engineering education, Green's theorem, Planar rigid body dynamics
