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The present study introduces an improved framework to analyze the longitudinal, shear, and peel stresses in the single stepped-lap joints under tensile loading based on a four-parameter viscoelastic model. To model the viscoelastic behavior of adhesive, the standard linear solid model is used. The governing differential equations are derived in the Laplace domain and are simultaneously solved and transformed using the Gaver–Stehfest inverse Laplace method. It was found that a rise in the butt thickness reduces the shear stress and increases the peel stresses. Moreover, an increase in the adhesive thickness reduces the longitudinal stress. [ABSTRACT FROM AUTHOR]

This paper aims to develop a viscoelastic analytical model for adhesively bonded single stepped-lap joints subjected to tensile loading. The adherends are aluminum alloy A6063 and modeled as Timoshenko elastic beams and the adhesive is epoxy type B. A three-parameter fractional viscoelastic foundation (3PFVF) model is proposed to express the governing stresses in the joint and the fractional Zener model is used to model the viscoelastic behavior of the adhesive layer. The proposed 3PFVF model makes it possible to have different peel stresses between the two interfaces of adhesive and adherends. The governing differential equations are derived in the Laplace domain, and then solved and transformed simultaneously in the time domain using the Gaver-Stehfest inverse Laplace transform method. The finite element simulation with ANSYS is applied to validate the proposed method. The results show that a simple fractional viscoelastic model, which has a short differential equation, offers the same results as the classical viscoelastic models, which have higher and more complex differential equations. Moreover, the results show that the maximum shear and peel stresses in the single stepped-lap joints are about 20% less than single-lap joints. [ABSTRACT FROM AUTHOR]

Modeling and simulation of gas-liquid two-phase flow in under-balanced drilling (UBD) operation is very important in order to accurately predict the bottom-hole pressure (BHP) and other parameters of two-phase flow. In this paper one-dimensional form of steady-state two-fluid model in the Eulerian frame of reference is used to simulate the two-phase flow in the UBD operation. Simulation is performed to calculate the parameters such as pressure, volume fraction and velocities of two phases at different flow regimes, namely bubbly, slug and churn turbulent flow. The governing equations along with appropriate constitutive relations form a system of coupled ordinary differential equations (ODEs) which are solved using the well-known iterative Newton method. The effect of gas and liquid injection flow rates and also the choke pressure on the wellbore pressures, particularly on the BHP are investigated numerically. In order to validate the results of the current two-fluid model, they are compared with the actual field data and also with the results of the WELLFLO software using different mechanistic models. The comparisons show that the two-fluid model can accurately predict the BHP and other two-phase flow parameters. [ABSTRACT FROM AUTHOR]