When implementing semi-analytic method of sensitivity analysis for structures modeled by finite elements, accuracy is improved by considering rigid body modes and applying series expansion technique. Semi-analytic methods are well suited in case that commercial softwares are used for analysis of structures, where analytic differentiation is almost impossible and numerical differentiation is very expensive. But they suffer from inaccuracy problems especially for finite element structures with rotational degrees of freedom.
Considerably accurate sensitivities are obtained by decomposing element displacements into a part containing pure deformations and a part containing pure rigid body motions, and differenting the element stiffness matrix related to the rigid body modes exactly. But the effects are turned out to be only satisfiable. Further improvement of accuracy is achieved by implementing the series expansion of the inverse of the perturbed stiffness matrix of the global structure. Through numerical examples, it is found that series expansion using three terms is enough to get as accurate sensitivities as those from overall finite difference schemes and reliable sensitivities can be obtained in the range of relative difference from $10^{-3}$ to $10^{-6}$
