Module 5 :
Lecture 14 : One - dimensional Finite Element Code
 


Pre- Processor

Function of the pre-processor is to read specifications of the problem, to create data about the mesh, numerical integration and shape functions and supply all these data to the processor. Thus, the pre-processor part of the code can be subdivided into the following 3 steps :

 

  1. Read input data (Subroutine READ-INPUT) :

In this part, the data about the domain geometry, material, forces, boundary conditions and mesh (i.e., the number of elements, order of approximation etc.) are read. Algorithm for this subroutine will be discussed in Lecture 15.

  1. Make the mesh (Subroutine MAKE-MESH) :

In this part, the mesh is made. The mesh is made piecewise uniform. At the same time, care is taken to place nodes at the point of application of point load as well as at the point of change in geometric and/or material properties. This subroutine creates the coordinate vector and the connectivity matrix C( i,j ). Further, the element at the end of which the point load is applied is also identified. Algorithm for this subroutine will be discussed in Lecture 15.

  1. Create the data about integration points and shape functions (Subroutine SHAPEALL) :

In this part, using the order of approximation, the linear variation of and the quadratic variation of , the maximum degree of the two integrands (of and ) is obtained first. The number of Gauss points is then determined from equation (12.29). Next, the data about the coordinates of the Gauss points and the corresponding weights are obtained. Finally, the shape functions and their derivatives at all the Gauss points are obtained. The subroutine which does all these operations (i.e., the subroutine SHAPEALL) has already been discussed in Lecture 12. This subroutine calls two other subroutines : (i) INTEG-PNTS and (ii) SHAPE. The subroutine INTEG-PNTS, which has been discussed in Lecture 11, generates the Gauss point coordinates and the corresponding weights only up to . Further, the subroutine SHAPE, which has been discussed in Lecture 12, calculates the shape functions and their derivatives for the given value of only upto p =   4 .