Processor

Using the data supplied by the pre-processor, this part of the code calculates the element stiffness matrices and element force vectors for all the elements and assembles them into the global stiffness matrix and global force vector. Next, the boundary conditions are applied. Finally, the resulting algebraic equations are solved to obtain the global vector of the nodal displacements. Thus, the processor can be divided into the following 4 steps :

(i) Calculation of element stiffness matrix and element force vector :
(Subroutine ELEMK)

This subroutine has already been discussed in Lecture 13.

(ii) Assembly of element stiffness matrices and element force vectors into global stiffness matrix and global force vector (Subroutine ASSEMBLE ) :

The algorithm for the assembly procedure was discussed in Lecture 6. The subroutine will be discussed in Lecture 16 (subroutine ASSEMBLE).

(iii) Application of point force and boundary conditions :
(Subroutine POINT- FORCE and BOUNDARY)

The algorithm for applying the Dirichlet (i.e., specification of the axial displacement), or the Neumann (i.e., specification of the axial force) or the spring (i.e., the bar end connected by a spring) boundary condition at either end of the bar was discussed in Lecture 7. The subroutines POINT-FORCE and BOUNDARY will be discussed in Lecture 16. Note that the application of the boundary condition modifies the global stiffness matrix as well as the global force vector. Application of the point force modifies the global right side vector only.

(iv) Solving the algebraic equations to find the global vector of the nodal displacements :

There are many methods available for solving a set of algebraic equations. The Gauss elimination method is the simplest. But, it takes a lot of computational time if the number (n) of equations is very large. The computational time is of the order of n³. The Crout's and Cholesky's factorization methods take less time. Algorithm for these methods will be discussed in Lecture 16. Since, the routines based on these methods are available in literature [ ], they will not be discussed.