1. adding the module solver containing the MPM solution to the motion…

…s equation. 2. Improvements in documentation.

README.md

@@ -1,6 +1,6 @@
 # MPM-Py
 
-A Material Point Method implementation using Python: MPM-Py.
+A Material Point Method implementation using Python: MPM-Py. This program uses objected-oriented programming paradigm to represent and modeling the elements and its interaction in the material point method context.
 
 ## Installation
 
@@ -10,47 +10,62 @@ git clone https://github.com/fabricix/MPM-Py.git
 
 ## Documentation
 
-To create the documentation, run:
+To create the documentation, install pdoc:
 
 ```bash
-pdoc --html modules
+pip3 install pdoc3
 ```
-
-To read the documentation, open
+And then run
 
 ```bash
-/html/modules/index.html
+pdoc --html -c latex_math=True modules/
 ```
 
+To read the documentation, open the file `/html/modules/index.html` using a web browser.
+
 ## Requirements
 
 * Python 3.7.4 or superior
 
 * Matplotlib 3.3.4 or superior
 
-
 ## Running tests and examples
 
+In the folders `verification_problems` and `tests` there are examples showing and testing the functionalities of the program.
+
 ### Mesh test
 
+The file `tests/mesh-test.py` tests the mesh generations module by plotting the mesh and showing the number of elements, nodes and material points. 
+
+Run this example as:
+
 ```bash
 python mesh-test.py
 ```
 
 ### Interpolation function test
 
+The file `tests/interpolation_functions_test.py` shows the interpolation functions and its derivates over an one 1D element.
+
+Run this example as:
 ```bash
 python interpolation-functions-test.py
 ```
 
-### Single mass bar vibration problem
+### Single mass vibration problem
+
+In this verification problem a single mass vibration is analyzed numerically and then the numerical solution is compared with the analytical one.
 
+Run this example as:
 ```bash
 python mpm-single-mass-bar-vibration.py
 ```
 
 ### Continuum bar vibration problem
 
+In this verification problem a continuum bar vibration is analyzed numerically and then the numerical solution is compared with the analytical one.
+
+Run this example as:
 ```bash
 python mpm-continuum-bar-vibration.py
-```
+```

modules/element.py

@@ -1,39 +1,38 @@
 #!/usr/bin/env python3
 # -*- coding: utf-8 -*-
-"""
-Purpose
--------
-Defines classes for finite elements representation
 
-Data
-----
-Created on Tue Mar 16 08:29:59 2021
+"""
 
-Author
-------
-Fabricio Fernandez, <[email protected]>
+Represent a finite element
 
 """
 class bar_1D:
-    """
-    Class to create 1D bar element with 2 nodes
-
-    Attributes
-    ----------
-    eid : int
-    	Element identification
-    n1 : node type
-    	Node 1 (left)
-    n2 : node type
-    	Node 2 (right)
-    L : float
-    	Element length
-    particles : list
-    	List of particles in element
-    """
-    def __init__(self):
-        self.eid = 0 # element id 
-        self.n1 = 0  # node 1
-        self.n2 = 0  # node 2
-        self.L = 0   # element length
-        self.particles = [] # particles in element
+
+	"""
+	Represent an 1D finite element with 2 nodes
+
+	Attributes
+	----------
+
+	eid : int
+		Element identification
+
+	n1 : node
+		Node 1 (left)
+
+	n2 : node
+		Node 2 (right)
+
+	L : float
+		Element length
+
+	particles : list
+		List of particles in the element
+	"""
+
+	def __init__(self):
+		self.eid = 0 # element id 
+		self.n1 = 0  # node 1 (left)
+		self.n2 = 0  # node 2 (right)
+		self.L = 0   # element length
+		self.particles = [] # list of particles in element

modules/integration.py

@@ -1,29 +1,36 @@
 #!/usr/bin/env python3
 # -*- coding: utf-8 -*-
+
 """
-Purpose
--------
-Defines nodal integration functions
 
-Data
-----
-Created on Tue Mar 16 16:17:03 2021
+Defines nodal integration functions. 
+This functions in general have the objective to advance in time, or adding quantities at the nodes.
 
-Author
-------
-Fabricio Fernandez, <[email protected]>
 """
 
 def total_force_in_nodes(msh):
     """
     Calculate total forces in nodes
+    
+    Arguments
+    ---------
+    msh: mesh
+        a mesh object
     """
     for node in msh.nodes:
             node.f_tot = node.f_int + node.f_ext
 
 def momentum_in_nodes(msh,dt):
     """
     Calculate momentum in nodes
+
+    Arguments
+    ---------
+    msh: mesh
+        a mesh object
+
+    dt: float
+        time step
     """
     for inode in msh.nodes:
         inode.momentum += inode.f_tot*dt