Interaction of rock-bolt supports while weak rock reinforcing by means of injection rock bolts

Purpose is to analyze changes in shape and dimensions of a rock mass area, fortified with the help of a polymer, depending upon the density of injection rock bolts as well as the value of initial permeability of enclosing rocks to substantiate optimum process solutions to support roofs within the unstable rocks and protect mine workings against water inflow and gas emission. Methods. Numerical modeling method for coupled processes of rock mass strain and filtration of liquid components of a polymer has been applied. The model is based upon fundamental ideas of mechanics of solids and filtration theory. The problem has been solved using a finite element method. Its solution took into consideration both the initial permeability and the permeability stipulated by mine working driving, injection time of reagents and their polymerization, and effect of po-lymer foaming in the process of mixing of its components. Changes in physicomechanical and filtration characteristics of rock mass during polymer hardening were simulated. It has been taken into consideration that a metal delivery pipe starts operating as a reinforcing support element only after the polymer hardening. Findings. If three and five injection rock bolts are installed within a mine working section then stresses, permeability coefficients, pressure of liquid polymeric composition, and geometry of the fortified area of rock mass have been calculated. It has been shown that rock bolt location is quite important to form a rock-bolt arch. It has been demonstrated for the assumed conditions that if five injection rock bolts are installed within the mine working roof then close interaction between rock-bolt supports takes place; moreover, the integral arch is formed within the mine working roof. Originality. Dependence of change in the polymer reinforced area upon a value of initial permeability of enclosing rocks has been derived. It has been shown that in terms of low values of initial permeability, geometry of rock-bolt supports as well as its size is identified only by means of a value of the unloaded zone around the mine working. In this context, initial permeabi-lity increase results in the enlarged diameter of the reinforced rock mass area in the neighbourhood of the injection rock bolt. Practical implications. The findings are recommended to be applied while improving a method to support the mine working roof and decrease water inflow as well as gas emission from the rocks, being undermined, into the working.

Definitions for Mechanical Engineering Textbook - Volume1 Authors

The objective of this book is to present important definitions from the subjects like Fluid Mechanics & Hydraulic Machines, Engineering Metrology & Measurements, Engineering Thermodynamics, Kinematics of Machinery, Mechanics of Solids, Manufacturing Technology and Automobile Engineering. The purpose of this book is to make students easier to understand the definitions and the students will be benefitted in various examinations.

Acceleration of boundary element calculations for closed domain using nonlinear form functions and CUDA technology

The evolution of computer technologies, as a hardware and a software parts, allows to attain fast and accurate solutions to many applied problems in scientific areas. Acceleration of calculations is broadly used technic that is basically implemented by multithreading and multicore processors. NVidia CUDA technology or simply CUDA opens a way to efficient acceleration of boundary elements method (BEM), that includes many independent stages. The main goal of the paper is implementation and acceleration of indirect boundary element method using three form functions. Calculation of the potentialdistribution inside a closed boundary under the action of the defined boundary condition is considered. In order to accelerate corresponding calculations, they were parallelized at the graphic accelerator using NVidia CUDA technology. The dependences of acceleration of parallel computations as compared with sequential ones were explored for different numbers of boundary elements and computational nodes. A significant acceleration (up to 52 times) calculation of the potential distribution without loss in accuracy is shown. Acceleration of up to 22 times was achieved in calculation of mutual influence matrix for boundary elements. Using CUDA technology allows to attain significant acceleration without loss in accuracy and convergence. So application of CUDA is a good way to parallelizing BEM. Application of developed approach allows to solve problems in different areas of physics such as acoustics, hydromechanics, electrodynamics, mechanics of solids and many other areas, efficiently.

Van der Waals interaction affects wrinkle formation in two-dimensional materials

Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer “bubbles” in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensional crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical “Winkler foundation” model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane.

Monte Carlo method for determination and analysis damage to the power system

The purpose of the work, the results of which are presented within the framework of the article, was to develop algorithms for calculating the damage to a solid or a system of solids based on the Monte Carlo method and the analytical boundary element method. The analytical boundary element method was used to calculate and analyze the stress-strain state of a solid under the distributed surface load. Based on indicators of the stress state, the algorithms for numerically assessing the dangerous volume and integral damage using the Monte Carlo methods, have been developed. Based on the pattern of distribution of stress fields, the technique of determining the area for randomly generating integration nodes is described. General recommendations have been developed for determining the boundaries of a subdomain containing a dangerous volume. Based on the features of the Monte Carlo methods, a numerical assessment of the indicators of damage of continuous media for a different number of integration nodes was carried out. Methods and algorithms were used to calculate the dangerous volume and integral damage in the plane and spatial cases for the two most common laws of the distribution of surface forces in the contact mechanics of solids: in case of contact interaction of two non-conformal bodies (Hertz problem) and when a non deformable rigid stamp is pressed into elastic half-plane or half-space. The scientific novelty of the work is to combine analytical and numerical approaches for the quantitative assessment of damage indicators of the power system. As a result the quantitative indicators of the dangerous volume (in the flat case - the dangerous area) and the integral damage of the half-plane and half-space related to the value of the applied load are obtained.

Advanced Mechanics of Solids

Build on the foundations of elementary mechanics of materials texts with this modern textbook that covers the analysis of stresses and strains in elastic bodies. Discover how all analyses of stress and strain are based on the four pillars of equilibrium, compatibility, stress-strain relations, and boundary conditions. These four principles are discussed and provide a bridge between elementary analyses and more detailed treatments with the theory of elasticity. Using MATLAB® extensively throughout, the author considers three-dimensional stress, strain and stress-strain relations in detail with matrix-vector relations. Based on classroom-proven material, this valuable resource provides a unified approach useful for advanced undergraduate students and graduate students, practicing engineers, and researchers.