Week 2 Challenge- MATLAB Module for an Element Stiffness Matrix

MATLAB function module to accept the input:

MATLAB File name: InputCheck.m

A function is created and saved in operating folder. These functions will gets input from user using syntax “input”.

Node vector:

For node vector, user need to input node vector as a matrix at any number of row and 2 number of columns. If the column number is greater than 2 then error message appears. Only after perfect values of node vector is given as input, program will execute next phase of line.

Constants:

Then inputs for Young’s modulus, Area and load along Y axis get from user. These values checked for single element then final values are outputted.

RESULT:

Node_Cord =

         0         0

    6.9840    4.0000

   11.0000         0

Constants =

       20000

         200

         100

CALCULATE LENGTH AND ORIENTAION:

MATLAB File name: ElementLength.m

Functions is created to find length and orientation of elements. For this functions Node coordinate is given as input. Each element are designated with 2 nodes. Using trigonometry functions, length and angle between this node are found. These values are then exported to output of the functions.

RESULT:

a =

    8.0484

    5.6682

   11.0000

b =

   29.8014

   44.8856

  180.0000

STIFFNESS MATRIX:

MATLAB File name: StiffnessMatrix.m

Using Constants,length and angle as an input stiffness matrix is derived. Stiffness matrix formula is:

[ST_MAT]=(E*A/L)*(Cos²θ CosθSinθ -Cos²θ  -CosθSinθ; CosθSinθ Sin²θ -CosθSinθ -Sin²θ;

-Cos²θ -CosθSinθ Cos²θ  CosθSinθ; -CosθSinθ -Sin²θ CosθSinθ Sin²θ)

RESULT:

Stiffness matrix =

    1.7068    2.5602   -1.7068   -2.5602

    2.5602    3.8402   -2.5602   -3.8402

   -1.7068   -2.5602    1.7068    2.5602

   -2.5602   -3.8402    2.5602    3.8402

GLOBAL STIFFNESS MATRIX:

MATLAB File name: DofOfMat.m

MATLAB File name:   Main.m

To derive global stiffness matrix, 4*4 matrix converted into 6*6 matrix. For this separate function is used. Degree of Freedom is calculated for 3 matrixes. Position for 3 matrix are determined. Stiffness matrix with 4*4 and relevant DOF is input for function to obtain 6*6 matrix.

After finding all stiffness matrix, matrix are added and Global stiffness matrix is derived.

RESULT:

Dof of Matrix:

    0.8534    1.2801   -0.8534   -1.2801         0         0

    1.2801    1.9201   -1.2801   -1.9201         0         0

   -0.8534   -1.2801    0.8534    1.2801         0         0

   -1.2801   -1.9201    1.2801    1.9201         0         0

         0         0         0         0         0         0

         0         0         0         0         0         0

MAIN:

285338.491726958     128007.737590438     -85338.4917269583    -128007.737590438     -200000           0

128007.737590438     192011.606385656     -128007.737590438    -192011.606385656     0          0

-85338.4917269583    -128007.737590438    203189.621924716            245858.867788195     -117851.130197758    -117851.130197758

-128007.737590438    -192011.606385656    245858.867788195            309862.736583414     -117851.130197758    -117851.130197758

-200000           0          -117851.130197758    -117851.130197758            317851.130197758     117851.130197758

0          0          -117851.130197758    -117851.130197758    117851.130197758            117851.130197758