This module implements the 3D Linear Bar Element (bar3d) formulation to solve
truss structures for linear static stress-strain analysis.
Input data is imported from a .xls file, where the table of nodes, table of
elements, nodal external loads vector and boundary conditions are stored.
This program calculates the stiffness matrix in local coordinates kL (element
i). Once the transformation matrix associated to the element is obtained, the
stiffness matrix in global coordinates kG is also calculated. The table of
connectivity is automatically generated for the assembly process and then
computes the complete stiffness matrix of the structure. Boundary conditions are
introduced on the .xls sheet in order to remove the singularity of the stiffness
matrix. After solving the matrix system, the nodal displacements vector u0 and
the nodal loads vector P0 (external loads and reactions) are calculated.
Finally, the program returns to the element formulation by transforming the
global displacements into local ones to obtain the bar stresses sigma of the
element and design the each member of the structure. A plot of the deformed and
non deformed structure in static equilibrium is also shown with a sigma11
This program only considers concentrated loads on the nodes. In case there be
distributed loads or thermal loads, they must be calculated separately and then
included into the nodal external loads vector. Flexion and shear effects are not
considered due to the element formulation, which satisfy the hypothesis of the
Finite Element Method (FEM).