SUMMARYFinite element solution methods for the incompressible Navier-Stokes equations in primitive variables form are presented. To provide the necessary coupling and enhance stability, a dissipation in the form of a pressure Laplacian is introduced into the continuity equation. The recasting of the problem in terms of pressure and an auxiliary velocity demonstrates how the error introduced by the pressure dissipation can be totally eliminated while retaining its stabilizing properties. The method can also be formally interpreted as a Helmholtz decomposition of the velocity vector.The governing equations are discretized by a Galerkin weighted residual method and, because of the modification to the continuity equation, equal interpolations for all the unknowns are permitted. Newton linearization is used and at each iteration the linear algebraic system is solved by a direct solver.Convergence of the algorithm is shown to be very rapid. Results are presented for two-dimensional flows in various geometries.

A finite element method for the solution of the compressible Navier-Stokes equations, in primitive variables form, is presented in this paper. To provide stability and the necessary coupling, a simple pressure dissipation, in the form of a Laplacian, is introduced into the continuity equation. The equations are discretized by a weak-Galerkin weighted residual method and equal interpolation for all the unknowns is used. Newton linearization is utilized, and at each iteration, the linear algebraic system is solved directly for the velocity components and pressure in a fully coupled manner. Convergence of the algorithm is linear because of the lagging of the solution of the energy equation. Results are presented for two-and three-dimensional subsonic flows in various internal flow geometries. NomenclatureA = domain surface tftea E = total number of elements e = element index H = enthalpy K = global influence matrix k -element influence matrix L = characteristic length L 2 = residual norm, %(R?) M = Mach number TV = finite element shape function n -outward normal to domain boundary p = pressure R = residual of a differential equation R g -gas constant Re = Reynolds number T = temperature V = volume V -velocity vector W = weight function x,y,z = Cartesian coordinates 7 = isentropic exponent A = change in a variable e = pressure dissipation parameter £,i?,f = local element coordinates [i = viscosity p = density $ = general variable Presented as Paper 90-0441 at

Axisymmetric finite element models are developed to simulate static pull test and dynamic drop test of MCB33 (modified conebolt with full dedonding) using ABAQUS. Results from the numerical models are in reasonable agreement with the test results. A parametric study is performed considering various variables (i.e. friction, cone angle, material strength, etc.) to analyze the performance of MCB33. The results demonstrate that friction between the steel and resin, cone angle, and the Poisson's ratio of the resin affect the static and dynamic behaviors of the rockbolt. These parameters can be modified to improve the current design and enhance the overall performance of the rockbolt.

As the depth of mining and underground construction increases, rock failure leading to seismic events and rockbursting is inevitable. Rockbursts can cause fatalities and/or injuries to workers, damage mine infrastructure and/or equipment and disrupt production. To minimise rockburst risk, design measures will be required. As an important line of defence, ground control support systems are used to prevent or minimise rockburst damage to excavations and enhance workplace safety. A new, patented dynamic rockbolt (the Superbolt) that integrates a reinforcement component (SDA) and a yielding component (paddle bolt) has been developed. The paddle bolt's shank can slide freely inside the SDA when the bolt is plastically stretched. If the epoxy resin is not properly mixed and the paddle anchor slides, the SDA acts as a secondary mechanical anchor and holds the paddle in place, allowing yielding of the paddle. This new technology allows a one-pass support system to be installed underground, which will result in significant saving in mining operations. In this paper, finite element models are developed to simulate the dynamic drop tests of the paddle Superbolt using Abaqus. The split-tube and continuous-tube drop tests are simulated, and the results from the numerical simulations are in reasonable agreement with the experimental results. A parametric study is performed based on various parameters (i.e. friction, geometry, material strength, etc.) to analyse the performance of the bolt. The results demonstrate that the quality of epoxy-resin mix, the strength and ductility of the bolt material and the corrugated pipe (SDA) influence the performance of the rockbolt. The parametric study improves understanding of the influence of various parameters on the performance of the Superbolt and aids in improving the design of this ground support technology.