Numerical Modeling of Deformation Processes in Rock Pillars

2014 ◽  
Vol 682 ◽  
pp. 202-205 ◽  
Author(s):  
V.V. Aksenov ◽  
S.V. Lavrikov ◽  
Alexander F. Revuzhenko
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Rock Mass ◽  
Deformation Process ◽  
The Finite Element Method ◽  
Sequential Development ◽  
Deformation Processes ◽  
Rock Pillars ◽  
The Mathematical Model ◽  
Loss Of Strength

The mathematical model of rock mass in the context of its internal structure, anisotropy, loss of strength, elastic energy accumulation and release is considered. The numerical solution to the problem of quasistatic deformation in a rock mass pillar is obtained by the finite element method. The sequential development of softening and residual strength zones is considered. It is shown that if the softening modulus is strong enough then the deformation process becomes unstable.

A Material Selection Method Based on Finite Element Method

2014 ◽  
Vol 887-888 ◽  
pp. 1013-1016
Author(s):  
Sheng Bin Wu ◽  
Xiao Bao Liu
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Material Selection ◽  
Selection Method ◽  
Structure Design ◽  
The Finite Element Method ◽  
The Mathematical Model ◽  
Selection Of ◽  
Element Method

A new method for material selection in structure design based on the theory of the finite element method was presented. The method made material selection and structure design working at the same time. The mathematical model was established based on the finite element method. Finally, the material selection of an excavator's boom was verified, the results show that the proposed method is effective and feasible.

Prediction of Failure Pressures in Pipelines With Corrosion Defects

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
J. Oliveros ◽  
J. L. Alamilla ◽  
E. Astudillo ◽  
O. Flores
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Experimental Tests ◽  
Original Model ◽  
The Finite Element Method ◽  
New Model ◽  
Failure Pressure ◽  
Irregular Geometries ◽  
Corrosion Defects ◽  
The Mathematical Model

The mathematical model to predict failure pressures in corroded pipelines proposed in this work is based on the analysis of the original model by Cronin and Pick. New definitions and interpretations in order to obtain this new model are given. As a consequence of this, the model can be more adequately interpreted and easier to apply under practical conditions. The new model and the finite element method are applied to predict failure pressures for pipelines with corrosion defects of elliptic and irregular geometries, and the predictions are similar. The model is used to predict the failure pressure in actual defects and compared to results of experimental tests and the original model. This study shows that pressures predicted by the model presented here are comparable to those of experimental tests.

Numerical Analysis of Super Drill of Shaft Well Boring Machine in the Stress Field

2012 ◽  
Vol 468-471 ◽  
pp. 2287-2291
Author(s):  
Wei Guo Zhu ◽  
Ya Wang ◽  
Ke Ren Zhang
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Stress Field ◽  
Theoretical Basis ◽  
Material Model ◽  
Element Model ◽  
The Finite Element Method ◽  
Linear Elastic ◽  
Nonlinear Features ◽  
The Mathematical Model

We research the super two-stage rapid drill of shaft well boring machine, taking the mathematical model of the drill in the stress field of shaft bottom as theoretical basis. Taking linear elastic and nonlinear features of element material into consideration, we establish element model in the stress field of shaft bottom and material model of stratum rock. Furthermore, we use the finite element method to numerically simulate the fragment intake effect of the super drills with diameter of 400mm and 800mm respectively. The result can be applied in the field of mine exploiting and tunnel advancement.

Research on the Influencing Factors of Dynamic Characteristics of Electronic Injector

2010 ◽  
Vol 44-47 ◽  
pp. 260-264
Author(s):  
Hui Qiang Liu ◽  
Si Fang Zhao ◽  
Jing Jing Wang
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Electromagnetic Field ◽  
Dynamic Measurement ◽  
Fuel Injector ◽  
The Finite Element Method ◽  
Core Diameter ◽  
Working Principle ◽  
The Mathematical Model

Base on the structure and working principle of electronic fuel injector, according to the related theories of electromagnetic field and flow field, the mathematical model of the electromagnetic force and fuel pressure have been deduced. Then using the finite element method to make a detailed analysis of magnetic permeability, core diameter, the working air gap, winding radius influence on the dynamic characteristic of the injector. According to this analysis, optimize those parameters for a new electronic injector, using the dynamic measurement system for a test, the results show the optimized injector has a better dynamic response than the unoptimized one.

Design of an Induction Glass Melting Furnace by Means of Mathematical Modelling Using the Finite Element Method

2007 ◽  
Vol 553 ◽  
pp. 124-129 ◽  
Author(s):  
Isaac Arellano ◽  
Gabriel Plascencia ◽  
Elías Carrillo ◽  
Miguel A. Barrón ◽  
Adolfo Sánchez ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Glass Melting ◽  
Melting Furnace ◽  
The Finite Element Method ◽  
Glass Melting Furnace ◽  
High Frequencies ◽  
Harmful Emissions ◽  
The Mathematical Model ◽  
Element Method

In this paper we propose the design of a novel induction furnace for glass melting. The design is based on a mathematical analysis and performed numerically by means of the Finite Element Method. Several induction coils configurations were tested. The results from the mathematical model show that it is possible to melt glass in a furnace whose hearth is no larger than half a metre by using axial induction coils and high frequencies. This furnace configuration may result in increased glass melting rates along with the elimination of harmful emissions.

Model calculations in reconstructions of measured fields

Open Physics ◽  
2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Mihály Makai ◽  
Yuri Orechwa
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Group Theory ◽  
Point Group ◽  
Iterative Solution ◽  
The Finite Element Method ◽  
Technological Systems ◽  
Convergence Problem ◽  
Model Calculations

AbstractThe state of technological systems, such as reactions in a confined volume, are usually monitored with sensors within as well as outside the volume. To achieve the level of precision required by regulators, these data often need to be supplemented with the solution to a mathematical model of the process. The present work addresses an observed, and until now unexplained, convergence problem in the iterative solution in the application of the finite element method to boundary value problems. We use point group theory to clarify the cause of the non-convergence, and give rule problems. We use the appropriate and consistent orders of approximation on the boundary and within the volume so as to avoid non-convergence.

Design and Analysis of a 6-DOF Monolithic Nanopositioning Stage

2010 ◽  
Vol 437 ◽  
pp. 61-65 ◽  
Author(s):  
Ling Li Cheng ◽  
Jian Wei Yu ◽  
Xiao Fen Yu
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Optimization Problem ◽  
Fiber Optic ◽  
Piezoelectric Actuators ◽  
Flexure Hinge ◽  
Constraint Optimization ◽  
The Finite Element Method ◽  
Displacement Sensors ◽  
Final Design

A 6-DOF monolithic nanopositioning stage is developed for three coordinate measuring machines (CMM) with nanometer resolution. The stage consists of a monolithic flexure hinge mechanism, six piezoelectric actuators and six fiber-optic displacement sensors. A mathematical model of the constraint optimization problem is presented. Based on the solution of the optimization problem, the final design of the 6-DOF stage is also presented. The numerical analysis on static and dynamic behavior of the stage is done by using the finite element method. The experimental results of the performance of the 6-DOF stage are presented.

scholarly journals УЗАГАЛЬНЕННЯ МОДЕЛІ ФОЛЬКЕРСЕНА НА ВИПАДОК ОСЬОВОЇ СИМЕТРІЇ

2021 ◽  
pp. 78-89
Author(s):  
К. П. Барахов
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Stress State ◽  
Boundary Conditions ◽  
Classical Model ◽  
The Finite Element Method ◽  
Premature Failure ◽  
One Dimensional ◽  
Element Method

Thin-walled structures may contain defects as cracks and holes that are leftovers of the material the construction, is made of or they occur during the operation as a result of, for example, mechanical damage. The presence of holes in the plate causes a concentration of stresses at the boundary of the holes and ultimately leads to premature failure of the structural element. Repair of local damage of modern aircraft structures can be made by creating overlays that are glued to the main structure. The overlay takes on part of the load, unloading the damaged area. This method of repair provides tightness and aerodynamic efficiency to the structure. The calculation of the stress state of such glued structures is usually performed by using the finite element method. The classic models of the stress state of overlapped joints are one-dimensional. That is, the change of the stress state along only one coordinate is considered. At the same time, the connections of a rectangular form are also considered. The purpose of this work is to create a mathematical model of the stress state of circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. It is assumed that the bending of the plates is absent; the deformation of the plates is even by thickness. The adhesive layer works only on the shift. The main plate and the overlay are considered isotropic. The solution is built on polar coordinates. The stress state of the connection depends only on the radial coordinate, i.e. one-dimensional. The solution is obtained in analytical form. This mathematical model is a generalization of the classical model of the adhesive connection of Volkersen to a circular or annular region and is considered for the first time. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations with respect to the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

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