Space-Fractional Truss Element - shape functions and stiffness matrix

<p>The following research data zipped to a .zip file is included.</p> <p>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.</p> <p>The data are described as follows:</p> <ul> <li>The .zip file contains information in the name about the number of nodes of the truss element (m).</li> <li>Formulas for shape functions written in different formats: <ul> <li>Display_Ni.svg shows the formula in a conveniently viewable form;</li> <li>LaTeX_Ni.txt contains a formula written in LaTeX syntax;</li> <li>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);</li> <li>Plot_Ni.svg contains plotted shape functions.</li> </ul> </li> <li>Formulas for the elements of the stiffness matrix written in different formats:<br> <ul> <li>The formula for the elements of the stiffness matrix is as follows,&nbsp;<br>\(K_{ij}=EA\frac{L}{2}\int_{-1}^{1} B_{i}B_{j} d\xi. \)</li> <li>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.</li> </ul> </li> </ul>