Module 5 :
Lecture 15 :  Pre-Processor
 


Algorithm for Subroutine READ - INPUT

A typical algorithm for reading the input data can be as follows:

  • Domain Data
    • read the coordinates and of the left and right ends.
    • determine L : .
  • Geometric Data
    • read the geometric transition point .
    • read the areas of cross-section at , and : .
    • calculate the coefficients and in the linear expression for the area for the two parts using equations (14.2) and (14.3).
  • Material Data
    Note that the material transition point is the same as the geometric transition point ( .
    • read the constant Young's moduli E1 and E2 of two parts.
  •  Force Data
    • read the coefficients f0 , f1 and f2 in the quadratic variation of f .
    • read the location ( x p ) and the value ( P 1 ) of the point force.
  • Boundary Data
    First we define the code for the boundary conditions.
    For the Dirichlet boundary condition, code = 1,
    For the Neumann boundary condition, code = 2,
    For the spring boundary condition, code = 3.

Now, the algorithm for the boundary data is as follows :

  • read the code for the boundary condition at .
    If code = 1, read the specified displacement ,
    If code = 2, read the specified force Q,
    If code = 3, read the spring constant and the initial spring deflection .
  • read the code for the boundary condition at .
    If code = 1, read the specified displacement ,
    If code = 2, read the specified force P ,
    If code = 3, read the spring constant and the initial spring deflection .

Note :

  1. and are considered positive if they are along positive x - direction.
  2. Q and P are considered positive if they are tensile.
  3. and are considered positive if they are compressive.
  • Mesh Data
    First we define the lengths l1 , l 2 and l 3 of the three parts as follows :
, , (15.1)

where

(15.2)

There are special cases in which either l1 or l2 or l3 or any two of them are zero. These cases as follows:

If        If  
If       If  
If     
If     

Note that if , then the Young's modulus of part 1 is E1 and that of parts 2 and 3 is E2 . On the other hand, if , then the Young's modulus of parts 1 and 2 is E1 and that of part 3 is E2 . To take care of this situation, we introduce a material code for all the three parts. These codes are matdom _1, matdom _2 and matdom _3. Then, the Young's moduli corresponding to these material codes are as follows.

E = E1 for matdom _1, E = E2 for matdom _3; (15.3)

E = E1 for matdom _2 for ,  
= E2 for matdom _2 for

(15.4)

We assume that the mesh is uniform over all the three parts. Let n1 , n2 , n3 be the number of elements in each part. Now, the algorithm for mesh data is as follows.

  • calculate xmin and xmax using eq. (15.2).
  • calculate l1 , l2 and l3 using eq. (15.1).
  • Assign the Young's modulus for the material code using eq.(15.3)-(15.4).
  • read the number of elements (n1 , n2 , n3 ) for each part
  • read the order of approximation p.