Object-oriented approach to solving beam deflection problems using FEniCS
Bonnie Chan (bc32569) Derek Hornung (deh2434) Brian Tran (bat2285)
Overall Objective:
Create a user-friendly program that can solve beam deflection problems based on user inputs of loading, cross-section geometries, and boundary conditions.
Packages to be used:
FEniCS
numpy
matplotlib
Inputs:
Loading
Point
Uniform
Variable distributed (in the works)
Beam or ball valve handle type (standard)
Boundary conditions
Clamped-Free
Clamped-Clamped
Clamped-Rotating
Rotating-Rotating
Outputs:
Location and value of minimum safety factor
Location and value of maximum stress
Location and value of maximum deflection
Heat map of stress
Heat map of of deformation
Deformed 3D scatter plot
Useful links:
https://www.encyclopediaofmath.org/index.php/Lam%C3%A9_constants
https://www.efunda.com/math/areas/IbeamIndex.cfm
https://fenicsproject.org/pub/tutorial/pdf/fenics-tutorial-vol1.pdf
Misc:
x is the axial direction, y is the horizontal transverse direction, and z is the vertical (gravity-affected) transverse direction
Input format for BeamProblem:
BeamProblem('Material', Cross Section Object(Cross Section dimensions), Length, Number of Elements, Boundary conditions, Load)
Outputs from beamProblem(....).solution():
{'Coordinates': numpy array of coordinates,
'Displacement Magnitudes': numpy array of displacement magnitudes,
'Displacement Vectors': numpy array of displacement vectors,
'Stress Magnitudes': numpy array of stress magnitudes}
Loading input to beamProblem must be specified as:
For uniform loads:
load('uniform', body_force = (x value, y value, z value)) where the units for the x, y, or z values are in N/m^3
For no loading (except gravity)
None
For point loads:
load('point', location = (x coordinate, y coordinate, z coordinate), magnitude = (x value, y value, z value), direction = (x,y,z))
Location and magnitude are in meters and Newtons/m^3, respectively
Direction vector gets scaled automatically.