Extended Saint-Venant torsion theory and its application to topology optimization of beams under torsion

Abstract

In this dissertation, the new efficient method of calculating the warping function of a beam with a longitudinal discontinuity is proposed. The proposed interface warping function is obtained by extending the classical Saint-Venant torsion theory to a three-dimensional domain. The calculated interface warping functions are employed in the continuum-mechanics based beam formulation to analyze arbitrary shape cross-section beams with longitudinal discontinuities. Compared to the previous work, higher accuracy with fewer degrees of freedom is obtained for beams with geometric and material discontinuities. Using this method, topology optimization of finding the optimal beam cross-section for a given force condition can be formulated. A well-known SIMP method is implemented and the sensitivity is directly derived from the continuum mechanics based beam without further assumption. Through numerical examples, it was confirmed that the proposed method has good convergence behavior with a low computational cost.