Space-Fractional Truss Element - shape functions and stiffness matrix

The following research data zipped to a .zip file is included.

Data refers to formulas for shape functions (\(N_{i}\)) and stiffness matrix components (\(K_{ij}\)) for a non-local truss element formulated in terms of fractional calculus (space-Fractional Truss Element) and the finite element method.

The data are described as follows:

The .zip file contains information in the name about the number of nodes of the truss element (m).

Formulas for shape functions written in different formats:

Display_Ni.svg shows the formula in a conveniently viewable form;

LaTeX_Ni.txt contains a formula written in LaTeX syntax;

Sym_Ni.txt contains a formula written in symbolic form, allowing loading into a calculation program (e.g., by loading a file and using the sympify() function);

Plot_Ni.svg contains plotted shape functions.

Formulas for the elements of the stiffness matrix written in different formats:

The formula for the elements of the stiffness matrix is as follows, \(K_{ij}=EA\frac{L}{2}\int_{-1}^{1} B_{i}B_{j} d\xi. \)

In the files, the formulas for \(B_{i} \) and the product of \(B_{i}B_{j} \) are written - in different formats, with naming analogous to that described for the shape functions.