The static and dynamic analyses of warping included composite exact conical helix by mixed FEM

The objective of this study is to investigate the combined influence of two important topics on the precision of static and dynamic analyses of non-circular composite helical bars, namely, exact helix geometry and the warping effect. Sometimes a conical helix over logarithmic spiral planar curve is formed by a degenerated plane curve. The most important goal of this study is to determine the range of the geometric parameters in which the degenerated plane curve lacks the precision necessary for the structural analysis of the conical helix compare to using an exact logarithmic spiral function. Another important topic on the precision of the results is the warping of non-circular composite sections. In this study, first, a parametric analysis is carried out in order to determine the maximum influence of warping on the torsional rigidity of non-circular sandwich/composite cross-sections. Then, some benchmark examples are employed to consider the combined influence of the two topics mentioned above. The analysis is performed over a curved mixed finite element formulation based on Timoshenko beam theory by considering the shear influence, rotary inertia and the warping included torsional rigidity. The curved element consists of two nodes and 24 degrees of freedom in total.