Quasi-static and dynamic response of viscoelastic helical rods

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

“…The Laplace transform approach has been employed by several researchers [12][13][14] in conjunction with the finite element method. Chen [12] successfully analyzed viscoelastic Timoshenko beams by converting the time dependent and convolution form of the finite element equations into a set of algebraic equations in s space.…”

“…As in the work by Chen [12], the finite element formulations require numerical inversion from the Laplace-Carson domain back to the time domain. Temel et al [14] studied the viscoelastic deformation of cylindrical helical rods using the Timoshenko beam hypotheses. Solutions obtained in the Laplace domain were transformed to the time domain through Durbin's inverse Laplace transform method.…”

The Effects of Viscous Bulk Compressibility for Noncylindrical Helices

“…The viscoelastic behaviors of straight and circular bars were examined extensively [3][4][5][6][7][8][9], however, few studies exist in literature that investigates the viscoelastic behavior of helicoidal bars [10][11][12][13]. Within these studies the works that takes helicoidal bars having noncircular cross section into account are even more rare.…”

Mixed FE analysis of viscoelastic cylindrical helixes

“…The theoretical foundations for viscoelasticity are well established by many researches, among them, Fung 1965, Malvern 1969, Flügge 1975and Christensen 1982 can be referred. The Laplace transform approach (Chen 1995, Aköz and Kadıo÷lu 1999, Temel et al 2004, Argeso et al 2011a) have been used in the solution of the various viscoelastic structural elements. In this study, a mixed finite element formulation based on the Timoshenko beam theory is used for dynamic analysis of viscoelastic cylindrical helixes with circular and square cross section.…”