Introduction¶

CALFEM is a MATLAB toolbox for finite element applications. This manual concerns mainly the finite element functions, but it also contains descriptions of some often-used MATLAB functions.

The finite element analysis can be carried out either interactively or in a batch-oriented fashion. In the interactive mode, the functions are evaluated one by one in the MATLAB command window. In the batch-oriented mode, a sequence of functions is written in a file named .m file and evaluated by writing the file name in the command window. The batch-oriented mode is a more flexible way of performing finite element analysis because the .m file can be written in an ordinary editor. This way of using CALFEM is recommended because it gives a structured organization of the functions. Changes and reruns are also easily executed in the batch-oriented mode.

A command line typically consists of functions for vector and matrix operations, calls to functions in the CALFEM finite element library, or commands for workspace operations. An example of a command line for a matrix operation is:

C = A + B'

where the two-by-two matrices A and B are added together, and the result is stored in matrix C. The matrix B' is the transpose of B. In MATLAB, the transpose operator is denoted by a single quote '.

An example of a call to the element library is:

Ke = spring1e(ep)

where the two-by-two element stiffness matrix \({\mathbf{K}}^e\) for a spring element is computed and stored in the variable Ke. The input argument is given within parentheses ( ) after the name of the function and is in this case ep, containing the spring stiffness \(k\). Some functions have multiple input arguments and/or multiple output arguments. For example:

[L, X] = eigen(K, M)

computes the eigenvalues and eigenvectors of a pair of matrices K and M. The output variables, the eigenvalues \(\lambda\), stored in the vector L and the corresponding eigenvectors stored in the matrix X are surrounded by brackets [ ] and separated by commas. The input arguments are given inside the parentheses ( ) and also separated by commas.

The statement:

help function

provides information about the purpose and syntax for the specified function.

The available functions are organized in groups as follows. Each group is described in a separate chapter.