A mixed-hybrid finite element for three-dimensional isotropic helical beam analysis

Numerical High-Order Model for the Nonlinear Elastic Computation of Helical Structures

“…dφ. Using the Timoshenko and de Saint-Venant hypotheses [3][4][5][6], the components of the displacement vector at a point P in the cross section are written in the Frenet coordinate system as follows:…”

“…Numerical modeling of the linear elastic behavior of helical springs has been studied by many searchers. Taktak et al [3] proposed a mixed hybrid formulation, including shear effects, based on the use of a curvilinear finite element with two nodes and six degrees of freedom per node. Dammak et al [4] have shown that it is possible to obtain the distribution of the various generalized stresses along the middle line of the helical spring with great precision by using a single curvilinear finite element with twelve degrees of freedom.…”

“…The finite element used in our numerical approach is of curvilinear type, defined along the middle line of the structure considered [18,19]. The kinematics adopted in our theoretical formulation takes into account the hypotheses of Timoshenko and de Saint-Venant [3][4][5][6]. The efficiency of the proposed algorithm lies in the reduction of the number of inversions of the tangent matrix compared to the incremental iterative algorithm of Newton-Raphson [20,21].…”

Finite element simulation of creep of spiral strands

“…Consequently this is the reason why the finite element model based on three-dimensional beam elements and the Timoshenko beam theory was developed. The models based on the beam element were applied by Nawrocki and Labrosse [22], Paczelt and Beleznai [25] and Taktak et al [44].…”

The application of the pseudospectral method to the analysis of helical springs of arbitrary shape

“…Choi and Lim formulated two-node and three-node general curved beam elements on the basis of assumed strain fields on Timoshenko's beam theory [4]. Taktak et al [5] and Fakhreddine et al [6] introduced two-node helical spring elements based on the mixed-hybrid formulations.…”