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Using Finite Element Methods to Calculate the Deflection of an Orifice Plate Subject to Uniform Pressure Distribution

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2016 ASEE Annual Conference & Exposition


New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

August 28, 2016





Conference Session

Computer Modeling/CAD in Mechanical Engineering

Tagged Division

Mechanical Engineering

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Paper Authors


Aneet Dharmavaram Narendranath Michigan Technological University

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Dr.Aneet Dharmavaram Narendranath is currently a Lecturer at Michigan Technological University (Michigan Tech). He received a PhD in Mechanical Engineering-Engineering mechanics in 2013. Subsequently, he worked as a visiting assistant professor at Michigan Tech from 2013-2014 and then as an Engineer at the French Nuclear Commission (CEA) in France until 2015. His research interests are mathematical modeling of fluid physics. His pedagogical interests are development of mathematically oriented coures in mechanical engineering.

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Prathamesh Prashant Deshpande Michigan Technological University

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Prathamesh Deshpande is pursuing his Doctor of Philosophy in Mechanical Engineering from Michigan Technological University, Houghton, MI, USA. He received his undergraduate degree in Mechanical Engineering in 2013 from Savitribai Phule Pune University (previously University of Pune), Pune, India.
During the academic year 2014-2015, Prathamesh was granted his Master of Science degree from Michigan Technological University with a Report option. His report was on the computational study of a non-cylindrical, non-comformable CNG tank mounting on a pickup truck frame using finite element methods.
He is currently serving as a Graduate Teaching Assistant under Dr. Aneet Narendranath for a senior level introductory finite element method course. The major duties as an assistant involve guiding senior students in gaining computational knowledge of the applications of the finite element methods in solving simple engineering problems.

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Madhu Kolati Michigan Technological University

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Mr. Madhu Kolati is currently pursuing his doctoral studies in the field of acoustic meta-materials at Michigan Technological University. His academic and research interests are in the areas of Solid mechanics, Finite Element Methods, Elastodynamics and Phononic Crystals. Prior to joining Michigan Tech, he worked as a Design Engineer at Caterpillar Inc.

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Datta Sandesh Manjunath Michigan Technological University

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Mr. Datta Sandesh Manjunath, is currently pursuing his Masters in Mechanical Engineering at Michigan Technological University. He has graduated from Amrita Vishwa Vidyapeetham, India with a B.Tech degree in Mechanical Engineering. He is currently doing his report, on Impact analysis of a pick up truck having a non-cylindrical, non-conformable CNG Tank using Finite Element Modelling. His academic and research interests are in the areas of Solid Mechanics, Composite Materials and Finite Element Methods. He also works as a Student Coach in the Engineering Learning Center. After graduation he seeks to work as a Product Development Engineer in a reputed firm.

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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.

Dharmavaram Narendranath, A., & Deshpande, P. P., & Kolati, M., & Manjunath, D. S. (2016, June), Using Finite Element Methods to Calculate the Deflection of an Orifice Plate Subject to Uniform Pressure Distribution Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.27146

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