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Tables of Stress and Strain--the Elastic Torsion Problem--in a CAS

G. Keady
Paul Abbott
Organization: University of Western Australia
Department: Physics
URL: http://www.uwa.edu.au/people/paul.c.abbott
Journal / Anthology

Proceedings of the 2nd Australian Engineering Mathematics Conference
Year: 1996
Page range: 387-392

The torsion function u of a plane domain D is a function which is zero on the boundary of the domain and whose Laplacian is minus one at every point inside the domain. The torsional rigidity S is the integral of u over D, and is known to engineers as a measure of the resistance to twisting for a long bar of cross-section D. Various Computer Algebra Systems (CAS) are providing (in add-ons, Packs, Packages,...) tables of engineering data. One example is the tabulation of torsion functions and torsional rigidities of different cross-sections D. The CAS are excellent tools for computing and manipulating closed-form solutions. Progress at implementing in Mathematica [1] some closed-formtorsion functions is described. It remains true that, for most cross-sections, there will be no closed-form solution. Such cases can be solved numerically. We describe possible implementations involving external C/Fortran code called via MathLink[1] from Mathematica.

*Engineering > Mechanical and Structural Engineering