To solve questions 2 and 3, please refer to the following information:
I.2 Truncated Conical Cantilever Beam (Required for all students)
Figure I.2 shows a truncated conical bar of length L and end radii (R, R) that is fixed as a roller/slider boundary at the restrained end (A), while loaded axially by a uniform tension, at the free end (B). In the figure, the x-axis is through the centroidal axis (C.A.) of the bar, which is made of a linearly elastic material with Young's modulus E and Poisson's ratio v.
Refer to the file "Term-Project Case Assignment (2018-02-27)" for the load values you need to work on, and Table I.1 for the material and dimensional data. Finally, the following boundary and loading conditions should be applied, and the mesh size should be chosen:
- Roller/Slider option should be imposed in SolidWorks "Fixtures" to the restrained end face (x = 0), the horizontal (z = 0), and vertical (y = 0) symmetric/central planes.
- A uniform tension of o value should be applied on the free end face (x = L) through the Pressure option of SolidWorksExternal Loads.
- An element size of 0.01m with a tolerance of 0.0005m should be chosen to create the meshes (approximately 215,000 elements) through the Create Mesh option of SolidWorks Mesh.
Report: (minimum items to be included)
1. Show the mesh with loading and restraint B.C.'s. Be sure to include the coordinate system used in the FE simulation.
2. Find the MoM solution of the axial normal stress (σ) distribution.
Hint: Force balance
3. Find the MoM solution of the axial stretching (u).
Note: The governing differential equation and boundary conditions of this axially loaded bar with variable cross-section are:
du(x)/dx = D.E. EA(x) = P(x) = R
B.C. @ fixed end (x = 0): no stretching
