Energy analysis of hydraulic fracturing

In this paper, numerical simulations of circular boreholes under internal hydraulic pressure are carried out to investigate the energy transferred to the surrounding rock and the breakdown pressure. The simulations are conducted by using a micromechanical continuum damage model proposed by Golshani et al. (2006). The simulation results suggest that the borehole breakdown pressure and the energy transferred to the surrounding rock are dependent on the mechanical properties of the rock and borehole size. Although the energy transferred to the surrounding rock increases with increasing borehole size, the borehole breakdown pressure decreases

A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems

This paper presents a second-order continuity non-overlapping domain decomposition (DD) technique for numerically solving second-order elliptic problems in two-dimensional space. The proposed DD technique uses integrated Chebyshev polynomials to represent the solution in subdomains. The constants of integration are utilized to impose continuity of the second-order normal derivative of the solution at the interior points of subdomain interfaces. To also achieve a C2 (C squared) function at the intersection of interfaces, two additional unknowns are introduced at each intersection point. Numerical results show that the present DD method yields a higher level of accuracy than conventional DD techniques based on differentiated Chebyshev polynomials

Impact on a water filled cylinder

The computational and experimental results of impact loading a water filled cylinder with a high speed piston are presented. Computational simulation of the impact process is performed by means of DIANA, a commercial finite element software package. In this simulation, water is modeled as a solid with very small shear modulus compared to the bulk modulus of water. The efficiency of the simulated impact is evaluated by the time dependent water pressure in the vicinity of the cylinder. Also, the shock pressure resulting from impact is detected by using a pressure transducer located in the middle of the water tube. Comparison of the computational and experimental results shows that the impact process on a water filled cylinder is well modeled. It is shown that the best way to increase the pressure peaks of the pressure profile curve is to increase the piston’s impact velocity

A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains

In this paper, an integral collocation approach based on Chebyshev polynomials for numerically solving biharmonic equations [N. Mai-Duy, R.I. Tanner, A spectral collocation method based on integrated Chebyshev polynomials for biharmonic boundary-value problems, J. Comput. Appl. Math. 201 (1) (2007) 30–47] is further developed for the case of irregularly shaped domains. The problem domain is embedded in a domain of regular shape, which facilitates the use of tensor product grids. Two relevant important issues, namely the description of the boundary of the domain on a tensor product grid and the imposition of double boundary conditions, are handled effectively by means of integration constants. Several schemes of the integral collocation formulation are proposed, and their performances are numerically investigated through the interpolation of a function and the solution of 1D and 2D biharmonic problems. Results obtained show that they yield spectral accuracy

Monte-Carlo simulation of the durability of glass fibre reinforced composite under environmental stress corrosion

The lifetime distribution of glass fibre subject to permanent environmental stress corrosion is very important for assessing the durability and damage tolerance of composites using glass reinforcement. A mechanical model based on the statistics of flaw spectra during stress corrosion and 3D shear lag model is presented. The proposed approach shows that it is possible to identify the influence of stress corrosion properties on the long term durability of glass fibre reinforced composites (GFRP)

Computation of transient viscous flows using indirect radial basis function networks

In this paper, an indirect/integrated radial-basis-function network (IRBFN) method is further developed to solve transient partial differential equations (PDEs) governing fluid flow problems. Spatial derivatives are discretized using one- and two-dimensional IRBFN interpolation schemes, whereas temporal derivatives are approximated using a method of lines and a finite-difference technique. In the case of moving interface problems, the IRBFN method is combined with the level set method to capture the evolution of the interface. The accuracy of the method is investigated by considering several benchmark test problems, including the classical lid-driven cavity flow. Very accurate results are achieved using relatively low numbers of data points

A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures

This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated. Numerical results and comparative studies with other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and easy to implement

An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis

This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on the boundaries of smoothing cells which leads to very accurate solutions, even with distorted meshes, and possible reduction in computational cost. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings