I would like to calculate the forces involved with physical constructions and I am looking for a tool that can do this for me. It would be great if the tool had a programming interface as I would like to use it for automated design.
There are a number of Finite Element Analysis packages available both commercially and as open-source software. Often you can integrate these directly into your CAD software. See http://en.wikipedia.org/wiki/List_of_finite_element_software_packages.