Substructure Generation

This procedure can be used to create the stiffness matrix of a substructure (sometimes also called a superelement) and store it in a file. A substructure consists of selected degrees of freedom of a model. It can be used in a subsequent linear analysis (this option is not available in CalculiX). In such an analysis, only the selected degrees of freedom are addressable, e.g. to apply loads or boundary conditions. The other degrees of freedom have been removed, thereby substantially reducing the size of the stiffness matrix. The retained degrees of freedom kind of constitute a new element (which explains the term superelement).

The stiffness matrix is obtained by successively applying a unit displacement to one of the retained nodes in one global direction while setting all other displacement values in the retained nodes to zero. This yields one column in the stiffness matrix of the superelement. Notice that in order to obtain the correct stiffness matrix only the elements belonging to the superelement should be retained in the input deck. Any other elements will influence the stiffness matrix and lead to a wrong matrix.

The substructure generation is triggered by the procedure card *SUBSTRUCTURE GENERATE. The degrees of freedom which should be retained can be defined by using the *RETAINED NODAL DOFS card. No transformation is allowed, consequently, the degrees of freedom apply to the global Carthesian system. Finally, the storage of the stiffness matrix is governed by the *SUBSTRUCTURE MATRIX OUTPUT card, specifying the name of the file without extension. The extension .mtx is default. The stiffness matrix can be stored in a USER DEFINED format or in a MATRIX format.

If the storage is in USER DEFINED format (OUTPUT FILE=USER DEFINED on the *SUBSTRUCTURE MATRIX OUTPUT card) the output in the .mtx file constitutes the input one needs to use the superelement in ABAQUS. It consists of:

• a *USER ELEMENT card specifying the number of degrees of freedom involved in the substructure (misleadingly defined as “nodes”).
• a list of the nodes. Each node is listed as many times as the number of its degrees of freedom in the substructure.
• for each retained degree of freedom its global direction. The format for the first degree of freedom of the substructure is just the global direction. For the subsequent degrees of freedom it consists of the number of the degree of freedom followed by the global direction
• a *MATRIX,TYPE=STIFFNESS card followed by the upper triangle (including the diagonal) of the stiffness matrix, column by column, and comma separated.

If the storage is in MATRIX format (OUTPUT FILE=MATRIX on the *SUBSTRUCTURE MATRIX OUTPUT card) the resulting file can be used in a *MATRIX ASSEMBLE card for further usage in CalculiX.