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A two dimensional model of the deflected configuration of the bottom hole assembly of a drill string is developed in this thesis. The analytical solution of the governing equation of the beam-column problem is treated in matrix form using the transfer matrix method which permits the solution of boundary value problems. A simple, easy to use computer method is developed to solve problems including gravity effects in inclined holes, and multiple stabilizers in straight and curved holes, and the effect of approximating the actual variable compressive axial force with a constant force is studied. Results of the program describe the mechanical behavior of the drill string by solving for the drill string deflection, slope, moment and shear force at any point from the drill bit to the tangency point. From these results, stress and strain at any point, and the resultant force at the bit can easily be computed. Accuracy of the results, for a multiple stabilizers case, is verified by two alternative methods. Simple-beam theory is used to verify the results for the limiting case of a horizontal hole, and the results of the beam-column problem are verified using a computer library, Continuous System Modeling Program (CSMP), which utilizes a Runge-Kutta integration method

Topics: Mechanical engineering
Year: 1986
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