A Mixed-Approach Analysis of Deformations in Pipe Bends. Part 2. Three-Dimensional Bending with Internal Pressure

2007

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The notion of the dynamic flexibility factor of a pipe bend to be used in problems on the calculation of harmonic vibrations of pipelines is formulated. Based on the Vlasov semi-momentless theory, simplifying hypotheses are introduced that make it possible to reduce the problem statement to the solution of the quartic differential equation. Using the results of the dynamic analysis for toroidal shells, the procedure for taking into account the increased flexibility of pipe bends under dynamic loading has been developed. The expression for the flexibility factor is derived as a function of both the geometrical parameters of the bend and the vibration frequency. The efficiency of the derived expression for the flexibility factor is illustrated by a great number of examples.

Section: Dynamic Analysis Of a Straight Pipementioning

confidence: 82%

“…The quantity K is related to the ovalization of the cross section [1,2]. In dynamic processes, the ovalization of the cross section should depend on local forces of inertia in the cross-sectional plane, since the ring deformation depends on the inertia forces induced by displacements of the points in the cross section.…”

Section: Introductionmentioning

confidence: 99%

Calculation of natural and forced vibrations of a piping system. Part 2. Dynamic stiffness of a pipe bend

2007

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“…The experience in the solution of the Karman problem shows that the N ϕ values connected with ovalization (loading with a bending moment) have the order of magnitude α σ k h z 2 [26,27]. Therefore, they are much smaller than the forces N x , which are comparable to the quantity k h z σ according to (26).…”

Section: Idea Of Solution Of the Problemmentioning

confidence: 94%

“…In this case, the results of solving the Saint Venant problem for pipe bends are utilized [26][27][28], and the analytical method of solution developed is an alternative to an original numerical procedure based on the iterative application of the initialparameter method [29]. Let us determine during solution the lowest necessary level of complexity which preserves its accuracy.…”

mentioning

confidence: 99%

Analytical solution of the Brazier problem for thin-wall pipes with initial cross-sectional shape imperfection in the case of action of pressure

2008

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An analytical method is proposed for the solution of geometrically nonlinear Brazier problem for thin-mall pipes with initial cross-sectional shape imperfection in the case of action of pressure. Geometrical equations relating displacement components to strains and equilibrium equations taking into account change in the curvature of pipe cross section and axis have been derived. A solution in a first approximation for dimensionless flexibility parameter is presented, the exactness of which is illustrated by numerous examples. For the case of joint action of external bending moment and pressure, a limit curve of the critical moment value as a function of pressure value has been obtained.

“…We will seek the solution by assuming the curvature parameter α = → R B 0. The geometrical and physical notations will be as specified earlier in [1,2].…”

mentioning

confidence: 99%

Classical Approach to Analyzing the Influence of Edge Boundary Conditions on Stresses and Flexibility of Pipe Elastic Bend

2005

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A new analytical method is proposed for the analysis of boundary effect in a pipe bend portion loaded by bending moment combined with internal pressure. The proposed method is based on the simplifying hypotheses, which make possible to represent all deformation-and force-related parameters in terms of the tangential displacement assumed in the form of the Fourier series expansion by the circumferential coordinate. A set of quadric differential equations by axial coordinate containing unknown displacement expansion coefficients is derived. We obtained an analytical approximate solution for a pipe bend portion and precise solution for a straight pipe, which are expressed via Krylov functions. We formulate the application procedure for the method of initial parameter, where the values of tangential and longitudinal displacements, axial and tangential forces are used as boundary conditions. We present the equations relating the above-mentioned parameters in the initial and end sections of the pipe bend portion. The results obtained are compared with the available published data.