Question

New Work University Tandon School of Engineering

Mechanical and Aerospace Engineering Department

Fall 2018 ME - UY 4214: Finite Element Design, Model, and Analysis

Lab Instructor Dr. Dzung Dinh Luong Industry Assistant Professor Room # RH 502B, Mechanical & Aerospace Engineering Department Ph: 646 997 4081, Email: [email protected]

Guideline of the lab assignment report The report may include the following sections: 1. Model

x State any assumption for the simulation model (Ex: 2D behavior, 3D symmetrical model …)

x Describe boundary conditions (constraints, applied forced or displacements) and others (contacts, connections, …).

2. Simulation Result x Show results of your simulation in ANSYS - tables and figures whatever it’s

necessary. (Important: any result needs to be defined clearly, ex: what is the kind of stress? Normal or equivalent stress? …)

x Check the convergence for any result values. Format

x The report must be submitted with the ID on the cover page. x All symbols must be defined clearly. x All tables and figures come with the caption. x The report is submitted with the PDF format; Word or other formats are not

accepted.

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Guidelines

New York University Tandon School of Engineering

Mechanical and Aerospace Engineering Department

Fall 2018 ME - UY 4214: Finite Element Design, Model and Analysis

Lab assignment 3

Note: 1. DO NOT submit the homework unless you have addressed everything. 2. The convergence of results must be checked. 3. Show all steps clearly.

Problem#1 Calculate the first three natural frequencies of a cantilever beam by

1. ANSYS 2. Solving the FEM model manually 3. Analytic solution

The material properties and dimension of the cantilever beam are listed below

Young’s modulus (E) 70 GPa Poisson’s ration (υ) 0.3 Density (ρ) 2700 kg/m3 Length 0.2 m Cross-section (height x width) 0.5 mm x 10 mm

Hint: Review the attached document of the vibration analysis of the beam using FEM in the current folder. Problem#2 Define the mass flow rate fraction of the enter laminar fluid through the bottom into two channels that have the same static pressure. The 2D planar model and other information are described in the following table and figure.

Material Properties Fluid Air Density 1 kg/m3 Viscosity 0.00333 kg/m-s Geometry L 3 m W 1 m Boundary Conditions Ps 0 Velocity profile (import external file)

Re_300.prof

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ASSIGNMENT

Experimental result: The fraction of mass flow rate in the main channel is 0.887 [Ref.1]. References: 1. R.E. Hayes, K. Nandkumar, H. Nasr-El-Din, “Steady Laminar Flow in a 90 Degree Planar

Branch”. Computers and Fluids, Vol 17, pp. 537-553, 1989