A Simple and Effective Pipe Elbow Element—Linear Analysis

Abstract

The formulation of a new, simple, and effective displacement-based pipe bend element is presented. The displacement assumptions are axial, torsional, and bending displacements that vary cubically along the axis of the elbow with plane sections remaining plane, and a generalization of the von Karman pipe radial displacement patterns to include the ovalization effects. The amount of ovalization varies cubically along the elbow with full compatibility between elbows. The pipe bend element has been implemented, and the results of various sample analyses are presented, which illustrate the effectiveness of the element.

Numerical analysis of radio-frequency sheath-plasma interactions in the ion cyclotron range of frequencies

“…This means in essence to construct special interpolation functions that are more amenable to capture the desired response. This approach is rather natural to increase the effectiveness of the finite element method for the solution of specific problems, and has been pursued for a long time, like for example in the analysis of wave propagations [67][68][69], global local solutions [70,71], piping analyses [72], the development of beam elements [73], and in fluid flow analyses [74,75]. Such methods have lately also been referred to as partition of unity methods or extended finite element methods, see for example [76][77][78][79].…”

A Simple and Effective Pipe Elbow Element—Interaction Effects

“…In a previous communication, we presented a basic elbow pipe element [1], which we formulated using the displacement-based finite element method. The essential ingredients of the formulation are the specific displacement assumptions used and the stress and strain components included in the evaluation of the strain energy of the element.…”

Computational techniques in structural stability of thin-walled cylindrical shells

“…The first attempt to combine the longitudinal deformation of the tube axis with cross-sectional ovalization was described in the studies of Bathe and Almeida [22], [23] for linear analysis and in a subsequent work of Bathe et al [24], where some nonlinear capabilities were investigated.…”

“…Using (2.86) and (2.87) a dependent variable q can be introduced, that expresses the ratio of the longitudinal uniaxial moduli 22 E over the hoop moduli 11 E . 2 22 11 (1 )…”

“…1). More specifically, the following equations are assumed for the five independent material constants ( 11 A , 22 A , 2 λ , λ and μ ).…”