Free vibration analysis of nanocomposite plates reinforced by graded carbon nanotubes based on first-order shear deformation plate theory

AbstractBased on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.</jats:p

Numerical Simulation of MZF Design with Non-planar Hydraulic Fracturing from Multi-lateral Horizontal Wells

In recent years, developments in the oil and gas industry have evolved significantly in advancing the mechanical systems technology to perform hydraulic fracturing. However, further developments will require an in-depth understanding of the impacts of fracture spacing, stress anisotropy, and reservoir characterization. In order to develop a comprehensive and robust completion design for hydraulic fracturing from multi-lateral wellbores with closely spaced fractures, it is important to consider stress shadowing effects. In this work the Cohesive Segments Method is combined with the Phantom Node Method, a combination termed CPNM. This is capable of not only simulating non-planar hydraulic fracture propagation with an unpredictable path, but also simulating the emergence of multiple cohesive cracks within a porous medium. This paper focuses on the “Modified Zipper-Frac” (MZF) design, which has been introduced to design the clusters from multi-lateral wells with the aim of increasing the fracture complexity. Validation of the numerical technique has been performed by comparing the solution for an individual hydraulic fracture with a Khristianovic-Geertsma-de Klerk (KGD) solution. In addition, a study of the development of double fractures has been conducted in the presence of stress shadowing to verify the simulation results. Taking the stress shadowing effects into account, a large number of numerical simulations are conducted using CPNM to investigate the stress anisotropy as well as the in-plane shear stress in the area between the two wells. The main contribution of this work is the detailed investigation of the effects of stress shadowing as a function of the fracture spacing on the horizontal stress contrast, direction of maximum local stress, leak-off flow rate, in-plane shear stress, and pore pressure of the formation