#!/usr/bin/env python
# coding: utf-8

# # Homework 5
# 
# ## Problem 1 (150 points)
# 
# Consider a slightly asymmetric wellbore in an otherwise symmetric and homogenous medium in which the interior wellbore pressure $p_0$ is held constant.  Assuming steady-state, plane-strain and *undrained* conditions, compute the displacements and pressures on the given mesh.  The mesh information is provided in the following files with short descriptions of thier contents.
# 
# [coords.csv](http://johnfoster.pge.utexas.edu/PGE383-AdvGeomechanics/files/coords.csv) - the geometric node locations for all nodes.  They are listed in $x,y$ pairs with each line corresponding to a global node index starting with 1 and proceding in sequence.
# 
# [connect.csv](http://johnfoster.pge.utexas.edu/PGE383-AdvGeomechanics/files/connect.csv) - the connectivity arrays.  Each line contains the global node numbers of an element with local node numbering as specified in the schematic. For the pressue interpolates, only use the first 4 which will coorespond to the corners of the element.
# 
# [nodeset1.csv](http://johnfoster.pge.utexas.edu/PGE383-AdvGeomechanics/files/nodeset1.csv) - the nodes on the interior boundary.  Use these nodes to specify the interior pressure, $p_0$.
# 
# [nodeset2.csv](http://johnfoster.pge.utexas.edu/PGE383-AdvGeomechanics/files/nodeset2.csv) - the nodes on the exterior boundary.  Use these nodes to specify the far-field pressure, $p_{\infty}$.
# 
# [nodeset3.csv](http://johnfoster.pge.utexas.edu/PGE383-AdvGeomechanics/files/nodeset3.csv) - the nodes on the horizontal symmetric boundary (indicated in blue in the schematic).
# 
# [nodeset4.csv](http://johnfoster.pge.utexas.edu/PGE383-AdvGeomechanics/files/nodeset4.csv) - the nodes on the horizontal symmetric boundary (indicated in red in the schematic).
# 
# Assume zero fluid compressibility, i.e. $1/M = 0$ and the following dimensionless properties $\alpha = 1, \nu = 0.3, \mu = 1$ for Biot's coefficient, Poisson's ratio, and shear modulus, respectively.  Apply an interior pressue $p_0=5$ and a constant far-field pressure $p_{\infty}=1$.  Assume the far field boundary is stress-free as well.  Create plots of the stress fields for $\sigma_{xx}$, $\sigma_{yy}$, and $\sigma_{xy}$ as well as the pressures.

# <img src="images/assignment5.png">