Configuration design sensitivity analysis and optimization of beam structures

A general method for configuration design sensitivity analysis over a three-dimensional beam structure is developed based on a variational formulation of the classical beam in linear elasticity. A sensitivity formula is derived based on a variational equation for the beam structure using the material derivative concept and adjoint variable method. The formulation considers not only the shape variation in a three dimensional direction, which includes translation as well as rotational change of the beam but also the orientation angle variation of the beam's cross section. The sensitivity formula can be evaluated with generally and ease even by employing a piecewise linear design velocity field despite the fact that the bending model is a fourth order differential equation. The design sensitivity analysis is implemented using the post-processing data of a commercial code ANSYS. Several numerical examples are given to show excellent accuracy of the method. Optimization is carried out for a tilted arch bridge and an archgrid structure to show the method's applicability.