nslfem-spring1d

nslfem-spring1d is a simple C++ implementation of the Finite Element Method (FEM) applied to simple one-dimensional assemblages of linear spring elements as described in the second chapter "Introduction to the Stiffness (Displacement) Method" of the book "A First Course in the Finite Element Method, Third Edition" by Darul L. Logan.

Installation

Download

Clone the sources of nslfem-spring1d from github.com:

git clone https://github.com/newskylabs/nslfem-spring1d.git

Building

Change into the base directory of the source tree and type make to build the executable:

cd nslfem-spring1d
make

Examples

To run all examples use make examples:

make examples

The examples can also be run one by one either with

make example-2-1
make example-2-2
make example-2-3 
make example-2-4

or by using the executable together with the respective example file:

bin/nslfem-spring1d input-files/example-2-1.fem
bin/nslfem-spring1d input-files/example-2-2.fem
bin/nslfem-spring1d input-files/example-2-3.fem
bin/nslfem-spring1d input-files/example-2-4.fem

Unit tests

In order to run the unit tests the boost unit test framework has to be installed and the environment variable BOOST_ROOT has to be defined. On my system boost is installed in /usr/local (the header fieles are in /usr/local/include/boost; the libs are in /usr/local/lib) and BOOST_ROOT is defined in my bash profile as

export BOOST_ROOT=/usr/local

To run the unit tests use

make test

Cleaning up

You can remove the program binaries and object files by typing

make clean

To also remove the binaries use

make cleanall

Examples

The following examples have been taken from the the second chapter "Introduction to the Stiffness (Displacement) Method" of the book "A First Course in the Finite Element Method, Third Edition" by Darul L. Logan:

Example 2.1

The input file input-files/example-2-1.fem:

/**
  Dietrich Bollmann, Kamakura, 2015/01/01

  Example 2.1, page 40.
  "A First Course in the Finite element Method, third edition"
  by Daryl L. Logan
*/

// Nodes:
// node <tag> (d <displacement>)? (f <force>)?

node 1  d 0
node 2  d 0
node 3
node 4       f 5000

// Spring elements:
// spring <tag>  <node 1> <node 2>  <spring constant>

spring 1  1 3  1000
spring 2  3 4  2000
spring 3  4 2  3000

// fin.

Running the example:

$ bin/nslfem-spring1d input-files/example-2-1.fem 

FEM: Spring Assemblage (1D)

Input files: 

  - input-files/example-2-1.fem

Global displacements:

  - node 1: 0
  - node 2: 0
  - node 3: 0.909091
  - node 4: 1.36364

Global forces:

  - node 1: -909.091
  - node 2: -4090.91
  - node 3: 0
  - node 4: 5000

Local forces at each element:

  - element 1: (-909.091, 909.091)
  - element 2: (-909.091, 909.091)
  - element 3: (4090.91, -4090.91)

fin.

Example 2.2

The input file input-files/example-2-2.fem:

/**
  Dietrich Bollmann, Kamakura, 2015/01/01

  Example 2.2, page 43.
  "A First Course in the Finite element Method, third edition"
  by Daryl L. Logan
*/

// Nodes:
// node <tag> (d <displacement>)? (f <force>)?

node 1  d 0
node 2
node 3
node 4
node 5  d 0.02

// Spring elements:
// spring <tag>  <node 1> <node 2>  <spring constant>

spring 1  1 2  200
spring 2  2 3  200
spring 3  3 4  200
spring 4  4 5  200

// fin.

Running the example:

$ bin/nslfem-spring1d input-files/example-2-2.fem 

FEM: Spring Assemblage (1D)

Input files: 

  - input-files/example-2-2.fem

Global displacements:

  - node 1: 0
  - node 2: 0.005
  - node 3: 0.01
  - node 4: 0.015
  - node 5: 0.02

Global forces:

  - node 1: -1
  - node 2: 0
  - node 3: 0
  - node 4: 0
  - node 5: 1

Local forces at each element:

  - element 1: (-1, 1)
  - element 2: (-1, 1)
  - element 3: (-1, 1)
  - element 4: (-1, 1)

fin.

Example 2.3

The input file input-files/example-2-3.fem:

/**
  Dietrich Bollmann, Kamakura, 2015/01/01

  Example 2.3, page 46.
  "A First Course in the Finite element Method, third edition"
  by Daryl L. Logan
*/

// Nodes:
// node <tag> (d <displacement>)? (f <force>)?

node 1  d 0
node 2       f 6   // Force: P = 6
node 3  d 0
node 4  d 0

// Spring elements:
// spring <tag>  <node 1> <node 2>  <spring constant>

spring 1  1 2  1   // Spring constant:  k1 = 1
spring 2  2 3  2   // Spring constant:  k2 = 2
spring 3  2 4  3   // Spring constant:  k3 = 3

// fin.

Running the example:

$ bin/nslfem-spring1d input-files/example-2-3.fem 

FEM: Spring Assemblage (1D)

Input files: 

  - input-files/example-2-3.fem

Global displacements:

  - node 1: 0
  - node 2: 1
  - node 3: 0
  - node 4: 0

Global forces:

  - node 1: -1
  - node 2: 6
  - node 3: -2
  - node 4: -3

Local forces at each element:

  - element 1: (-1, 1)
  - element 2: (2, -2)
  - element 3: (3, -3)

fin.

Example 2.4

The input file input-files/example-2-4.fem:

/**
  Dietrich Bollmann, Kamakura, 2015/01/01

  Example 2.4, page 54.
  "A First Course in the Finite element Method, third edition"
  by Daryl L. Logan
*/

// Nodes:
// node <tag> (d <displacement>)? (f <force>)?

node 1  d 0
node 2       f 1000

// Spring elements:
// spring <tag>  <node 1> <node 2>  <spring constant>

spring 1  1 2  500

// fin.

Running the example:

$ bin/nslfem-spring1d input-files/example-2-4.fem 

FEM: Spring Assemblage (1D)

Input files: 

  - input-files/example-2-4.fem

Global displacements:

  - node 1: 0
  - node 2: 2

Global forces:

  - node 1: -1000
  - node 2: 1000

Local forces at each element:

  - element 1: (-1000, 1000)

fin.

Comments etc.

If you have any comments, please drop me a message!

fin.

Copyright (c) 2015 Dietrich Bollmann