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 2

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 A long thick-walled cylinder is maintained at a temperature Ti on the inner surface and To on the outer surface. Determine the temperature distribution through the wall thickness. Also determine the tangential stress σt at the inner and outer surfaces and the maximum the radius stress σr. Compare the maximum and minimum values of the tangential and longitudinal stresses.

Material Properties Geometric Properties Loading E = 30 x 106 psi α = 1.435 x 10-5/°F ν = 0.3 k = 8.333e-4 Btu/s-in-°F

a = 0.1875 in b = 0.625 in

Ti = -1°F To = 0°F

Requirements:

¾ Solve problem in 2D and 3D models. ¾ Using the symmetric model for 3D problem (No credit for others) ¾ Provide the temperature at x = 0.2788 in

Hand calculation results: � � psiart 420 V , � � psibrt 194� V and � � psir 87max V (S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems)

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Assignment

Problem#2 (Biomechanical Engineering) The object of this problem is finding the development of the trabecular/cortical bone surrounding the dental implant as depicted in the following figure. The bone development is defined by four strain windows as shown in the below table. Determine the volume percentage of each strain window in the region of interest.

No. Strain Range Description 1 < 200 PH Disuse window: The bone density decreases (bone loss) 2 200 PH - 1000 PH Adapted window: The bone density remains 3 1000 PH - 3000 PH Mild overload window: The bone density increases 4 > 3000 PH Pathologic overload window: The bone damage is permanent

Requirements: ¾ The original research was presented in “Influence of Clinically Relevant Factors on the

Immediate Biomechanical Surrounding for a Series of Dental Implant Designs” by Shunmugasamy, V.S. et al. Review this paper to define the boundary conditions and more information.

¾ Use one cortical bone model with 4 mm thickness. ¾ Set the Young’s modulus of trabecular bone to 4 GPa. ¾ Use the equivalent elastic strain to generate the results.

Hints:

¾ The implant model and the reference paper are attached in the current folder. ¾ In order to calculate the volume percentage of strain result, the following steps should be

used: o Generate the result of the equivalent strain for the region of interest. o Change the parameter in “Display Option” from “Averaged” to “Elemental Mean”

in the detailed view. o Export the equivalent strain result to the excel file. o Use that file to calculate the volume percentage after sorting the equivalent strain

values from smallest to biggest. ¾ Review the article at https://en.wikipedia.org/wiki/Dental_implant for more information

about the dental implant.

4 mm 11 mm