Matrix Analysis of Three Dimensional Bar Structures MABS3D

This program is an extension of MABS2D to three-dimensional space (3D).

Description

Input data is the Microsoft Excel® file, where the table of nodes, table of elements, nodal external loads vector and boundary conditions are stored.
After running the mabs3d.m file on the Command Window, the program calculates the stiffness matrix in local coordinates kiL (element i). Once the transformation matrix associated to the element is obtained, the stiffness matrix in global coordinates kiG 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 Excel® 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 sigmai of the element i 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 contourplot.
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. All the elements satisfy the hypothesis of the Finite Element Method (FEM).

Enhancements respect to MABS2D:

- Possible to analyze three dimensional structures (3D)
- Contourplot of normal stress distribution (sigma11)
- Possible to use an amplification factor to view the deformed structure
- Algorithm more robust and optimized

• MATLAB release: MATLAB 7.6 (R2008a)