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• Finite element formulation for analysis of pipes conveying fluids is developed. • The study presents a mathematically rigorous technique to extract the mode shapes. • Effects of axial compressive force and intermediate flexible supports are studied. • Algorithm based on Hermitian angles between eigenvectors is proposed to trace frequency-velocity plots. A finite element formulation is presented for the natural vibration analysis of pipes conveying fluids. The solution of the resulting quadratic eigenvalue problem generally yields complex eigenvalues and eigenvectors. The present study then develops a robust mathematical procedure that combines the real and imaginary components of the eigenvectors to form physically attainable (i.e., real) mode shapes. The procedure yields a family of solutions that is more general than previously known solutions. The well-known classical mode shape is shown to be recoverable as a special case from the present solution. The study provides new insights on the effects of viscous damping, axial compressive force, and the flexibility of intermediate pipe supports on the response. Additionally, the study develops a novel algorithm based on Hermitian angles between eigenvectors to automate the tracing of mode evolution in the frequency-velocity plots. [ABSTRACT FROM AUTHOR]

A family of shell finite elements is developed for the geometrically nonlinear analysis of pipe bends. The constitutive description follows the Saint-Venant-Kirchhoff model. The first Piola–Kirchhoff stress and the conjugate gradient of the virtual displacement fields are adopted within the framework of the virtual work principle. Three C 1 continuous schemes are used to interpolate the displacement fields in the longitudinal direction while Fourier series are used for circumferential interpolation. Eigenvalue analyses are conducted to assess the ability of the elements to represent rigid body motion. Comparisons with other shell and elbow models demonstrate the accuracy and versatility of the formulation. • Finite elements are formulated for geometric nonlinear analysis of pipe bends. • Solution adopts First Piola–Kirchhoff stress within the virtual work principle. • Eigenvalue analyses assess the ability of elements to capture rigid body motion. • The formulation properly tackles the effect of follower loads (e.g., pressure). • The formulation accurately captures the nonlinear response. [ABSTRACT FROM AUTHOR]

A family of new geometrically nonlinear finite elements is formulated for the simulation of the structural response in the elastic regime of straight pipes with circular cross-sections under various loading conditions. The first Piola–Kirchhoff stress tensor is employed within the principle of virtual work framework in conjunction with a total Lagrangian approach. The Green–Lagrange strain tensor is adopted to capture the finite deformation-small strain effects. The formulations are based on the kinematic assumptions of the thin shell theory and capture the follower effects due to pressure load. Three schemes are proposed to interpolate the displacement fields in the circumferential direction: (1) a Fourier series expansion, (2) a quartic spline interpolation, and (3) a mixed interpolation combining Fourier series and splines. The performance and prediction accuracy of the elements are assessed through comparisons with finite element models based on shell and elbow elements in ABAQUS under various loading conditions. The results demonstrate the ability of the elements to predict the displacement and stress fields. In particular, the element based on Fourier series interpolation is shown to provide accurate predictions. • A geometrically nonlinear finite element is developed for circular cylindrical shells. • The virtual work is expressed in terms of the First Piola–Kirchhoff stress tensor. • Various interpolation schemes are compared. • The formulation captures the follower effect of the pressure. [ABSTRACT FROM AUTHOR]

Evaluating the dynamic behavior of corroded pipelines conveying fluids is essential to guard against resonance and fatigue failures. However, existing solutions for obtaining the dynamic characteristics, such as natural frequencies, lack an updating methodology based on new corrosion inspection data, hindering effective planning for preventing corrosion damages. Thus, this article introduces a novel framework for characterizing the natural frequency of corroded pipelines conveying fluids. The framework simulates fluid-structure parameters using Gaussian random fields, modified using fuzzy membership functions to account for corrosion effects as identified from field inspection. Based on these fuzzy-random fields, piecewise fuzzy-probabilistic formulations are developed for the natural frequency of pipeline systems function of (1) dimensionless fluid-structure parameters to facilitate adaptation for various pipeline systems; (2) a pipeline condition index (PCI) to enable updates with new corrosion inspection data; and (3) a user-defined safety margin to accommodate different safety requirements. Numerical examples are presented, showcasing the ability of the proposed piecewise formulations to estimate the natural frequencies with R2 ranging from 90.8% to 99.8%. • Fuzzy-probabilistic assessment of corroded pipes conveying fluids. • Simulate the uncertainty in corrosion quantification using the fuzzy logic theory. • Model the uncertainty in FSI parameters using the random field theory. • Formulate a pipe condition index via field inspection to estimate corrosion level. • Parametric formulas for natural frequencies of pipes given condition and properties. [ABSTRACT FROM AUTHOR]