3 Solving Shared-Node Systems

Many problems encountered in FEM analysis place the entries of the known and unknown vectors at the nodes-the vertices of the domain. Elements provide linear relationships between the known and unknown node values, and the entire matrix expresses the combination of all these element relations.

For example, in a structural statics problem, we know the net force at each node, , and seek the displacements of each node, . Elements provide the relationship, often called a stiffness matrix , between a nodes' displacments and its net forces:

We normally label the known vector (in the example, the forces), the unknown vector (in the example, the displacments), and the matrix :

IFEM provides two routines for solving problems of this type. The first routine, IFEM_Solve_shared, solves for the entire vector based on the known values of the vector. The second, IFEM_Solve_shared_bc, allows certain entries in the vector to be given specific values before the problem is solved, creating values for the vector.