Abstract: The static and dynamic analyses of hyperboloidal helix having the closed and the open square box sections are investigated via the mixed finite element formulation based on Timoshenko beam theory. Frenet triad is considered as local coordinate systems for helix geometry. Helix domain is discretized with a two-noded curved element and linear shape functions are used. Each node of the curved element has 12 degrees of freedom, namely, three translations, three rotations, two shear forces, one axial force, two bending moments and one torque. Finite element matrices are derived by using exact nodal values of curvatures and arc length and it is interpolated linearly throughout the element axial length. The torsional moments of inertia for close and open square box sections are obtained by finite element solution of St. Venant torsion formulation. With the proposed method, the torsional rigidity of simply and multiply connected cross-sections can be also calculated in same manner. The influence of the close and the open square box cross-sections on the static and dynamic analyses of hyperboloidal helix is investigated. The benchmark problems are represented for the literature.
Abstract: In this study, the free vibration analysis of conical helicoidal rods with two different elliptically oriented cross sections is investigated and the results are compared by the circular cross-section keeping the net area for all cases equal to each other. Problems are solved by using the mixed finite element formulation. Element matrices based on Timoshenko beam theory are employed. The finite element matrices are derived by directly inserting the analytical expressions (arc length, curvature, and torsion) defining helix geometry into the formulation. Helicoidal rod domain is discretized by a two-noded curvilinear element. Each node of the element has 12 DOFs, namely, three translations, three rotations, two shear forces, one axial force, two bending moments and one torque. A parametric study is performed to investigate the influence of elliptical cross sectional geometry and its orientation over the natural frequencies of the conical type helicoidal rod.
Abstract: In this study, the dynamic analysis of viscoelastic plates with variable thickness is examined. The solutions of dynamic response of viscoelastic thin plates with variable thickness have been obtained by using the functional analysis method in the conjunction with the Gâteaux differential. The four-node serendipity element with four degrees of freedom such as deflection, bending, and twisting moments at each node is used. Additionally, boundary condition terms are included in the functional by using a systematic way. In viscoelastic modeling, Three-parameter Kelvin solid model is employed. The solutions obtained in the Laplace-Carson domain are transformed to the real time domain by using MDOP, Dubner & Abate, and Durbin inverse transform techniques. To test the performance of the proposed mixed finite element formulation, numerical examples are treated.