Variational Inequality Formulation Method for Unconfined Seepage in 3D Fracture Network

2013 ◽  
Vol 405-408 ◽  
pp. 2084-2088
Author(s):  
Wei Sheng Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Rock Mass ◽  
Variational Inequality ◽  
Numerical Stability ◽  
Fracture Network ◽  
The Finite Element Method ◽  
3 Dimensional ◽  
3D Fracture Network

A variational inequality formulation method to define the free surface of fracture network was given, related formulas were deduced and the Finite Element Method was used to solve the equations. By computing, the following conclusions were gotten, that is the variational inequality formulation method to solve unconfined seepage in 3 dimensional fracture network of rock mass is possible, and had a better numerical stability and much less mesh-depenciency.

Finite Element Analysis to a Kind of Elliptic Variational Inequality

2012 ◽  
Vol 557-559 ◽  
pp. 2126-2129
Author(s):  
Jun Hui Zhu ◽  
Chun Rui Cheng ◽  
Guang Pu Lou
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Variational Inequality ◽  
Error Estimate ◽  
Finite Element Methods ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Nonlinear Materials ◽  
Elliptic Variational Inequality

Finite element methods for the elliptic variational inequality of the second kind deduced from friction problems or nonlinear materials in elasticity have been discussed. In this paper, the finite element method with numerical integration for the second type elliptic variational inequality is considered and an error estimate is proved.

scholarly journals MATHEMATICAL MODELING OF NON-STATIONARY ELASTIC WAVES STRESSES UNDER A CONCENTRATED VERTICAL EXPOSURE IN THE FORM OF DELTA FUNCTIONS ON THE SURFACE OF THE HALF-PLANE (LAMB PROBLEM)

2019 ◽  
Vol 15 (2) ◽  
pp. 111-124
Author(s):  
Vyacheslav Musayev
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Boundary Conditions ◽  
Half Plane ◽  
Rayleigh Waves ◽  
The Finite Element Method ◽  
Initial And Boundary Conditions ◽  
Element Method

The problem of numerical simulation of longitudinal, transverse and surface waves on the free surface of an elastic half-plane is considered. The change of the elastic contour stress on the free surface of the half­plane is given. To solve the two-dimensional unsteady dynamic problem of the mathematical theory of elasticity with initial and boundary conditions, we use the finite element method in displacements. Using the finite element method in displacements, a linear problem with initial and boundary conditions resulted in a linear Cauchy prob­lem. Some information on the numerical simulation of elastic stress waves in an elastic half-plane under concen­trated wave action in the form of a Delta function is given. The amplitude of the surface Rayleigh waves is sig­nificantly greater than the amplitudes of longitudinal, transverse and other waves with concentrated vertical ac­tion in the form of a triangular pulse on the surface of the elastic half-plane. After the surface Rayleigh waves there is a dynamic process in the form of standing waves.

An Approach to the Problem of Vibration: Structural Modification by Optimizing Density Distribution

1994 ◽  
Author(s):  
Yoshiko Kawabe ◽  
Shinobu Yoshida
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Density Distribution ◽  
Dynamic Characteristics ◽  
Material Properties ◽  
Structural Modification ◽  
Variable Density ◽  
The Finite Element Method ◽  
3 Dimensional ◽  
Mode A

Abstract This paper proposes a basic method for designing light and rigid structures that maximize the natural frequency of the structure for a designated mode. A design variable ‘density’ is introduced into the finite element method and is related to the material properties of a 3-dimensional solid element. Thus, a structure is expressed as a density distribution inside its occupiable domain, and the optimal structure is obtained by searching for the most suitable density distribution. The dynamic characteristics of the structure are improved by repeatedly modifying its density distribution.

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