A Unified Solution to Linear Beam Bending Problems

AbstractDirectional drilling is a common and essential procedure of major extended reach drilling operations. With the development of directional drilling technologies, the percentage of recoverable oil production has increased. However, its challenges, like real-time bit steering, directional drilling tools selection and control, are main barriers leading to low drilling efficiency and high nonproductive time. The fact inspires this study. Our work aims to contribute to the better understanding of directional drilling, more specifically regarding rotary steerable system (RSS) technology. For instance, finding the solutions of the technological challenges involved in RSSs, such as bit steering control, bit position calculation and bit speed estimation, is the main considerations of our study. Classical definitions from fundamental physics including Newton’s third law, beam bending analysis, bit force analysis, rate of penetration (ROP) modeling are employed to estimate bit position and then conduct RSS control to steer the bit accordingly. The results are illustrated in case study with the consideration of the 2D and 3D wellbore scenarios.

Download Full-text

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

Mathematics and Mechanics of Solids ◽

10.1177/10812865211001533 ◽

2021 ◽

pp. 108128652110015

Author(s):

YL Qu ◽

GY Zhang ◽

YM Fan ◽

F Jin

Keyword(s):

Classical Theory ◽

Couple Stress ◽

Couple Stress Theory ◽

Constitutive Relations ◽

Stress Theory ◽

Isotropic Materials ◽

Flexoelectric Effect ◽

Beam Bending ◽

Gradient Theories ◽

Anisotropic And Isotropic Materials

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

Download Full-text