New Orleans, Louisiana
June 26, 2016
June 26, 2016
August 28, 2016
As part of an elective course in Finite Element Methods (FEM) for senior level and graduate students in mechanical engineering, an ASME standard for flow measurement devices is used to design an orifice plate. Students are given a certain set of flow condition and equipment constraints that they must adhere to. As part of the design process, they are required to evaluate their orifice plate for strength via finite element methods and determine if the plate’s transverse deflections due to uniformly distributed pressure are within set limits.
To design the orifice plate, a symbolic solver (Wolfram Mathematica) is used to solve the governing fourth order differential equation of this problem (plate equation in polar coordinates), with appropriate boundary conditions. Results from the symbolic solver are juxtaposed with results from a GUI/Menu driven FEM package (Altair Hypermesh). Both the symbolic and menu driven solutions are compared with each other and with published empirical relationships.
Governing equations for bending of plates, in polar coordinates (for the orifice plate) are particularly challenging to solve as compared to their rectilinear coordinate counterparts. This is because of numerical stiffness of the equations compounded by the physical stiffness associated with boundary conditions and the need to resolve mathematical singularities for “1/r, for r=0” type terms. This complexity, when reconciled using symbolic solvers allows a better grasp of the esoteric inter-relationships between various terms in the governing equations, which are akin to design variables. This allows students to use this esoteric knowledge to better apply GUI/menu driven solvers for engineering design.
The primary pedagogical goal of this work allows the exertion of importance of governing equation based modeling to improve a "behind the scenes" understanding of GUI/menu driven FEM efforts. Students are made aware of the use of engineering standards and validation of numerical solutions through comparison with analytical or empirical data.
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