Stepped Euler-Bernoulli Beam

Analytical solution for an Euler-Bernoulli beam with changing bending stiffness with fixed or pinned ends.

Stepped-Euler-Bernoulli-Beam

Inhomogeneous bending stiffness in Euler-Bernoulli beam modelled with singularity functions.

The live script examples.mlx contains examples for the functions oneFieldBeam.mlx and twoFieldBeam.mlx.

The live function oneFieldBeam.mlx calculates the displacement, rotation, curvature and bending moment for a single-span beam with changing bending stiffness. You can choose between pinned and fixed ends.

The live function twoFieldBeam.mlx calculates the displacement, rotation, curvature and bending moment for a two-span beam (continuous beam) with changing bending stiffness. You can choose between pinned and fixed ends.

The live functions uses singularity functions to implement the changing bending stiffness in the beam. Also the load and support forces are modelled with singularity functions. See reference for detailed explanation.

Reference

Static, Vibration Analysis and Sensitivity Analysis of Stepped Beams Using Singularity Functions by Peng Cheng, Carla Davila and Gene Hou.

Acknowledgement

This work is part of the ZEBBRA project, which is funded by the Federal Ministry of Education and Research.