An efficient algorithm for finite-difference modeling of mixed-boundary-value elastic problems

2006 ◽  
Vol 37 (1) ◽  
pp. 41-55 ◽  
Author(s):  
M. Zubaer Hossain ◽  
S. Reaz Ahmed ◽  
M. Wahhaj Uddin
Keyword(s):  
Finite Difference ◽  
Efficient Algorithm ◽  
Mixed Boundary ◽  
Boundary Value

A NEW MATHEMATICAL MODEL FOR FINITE-DIFFERENCE SOLUTION OF THREE-DIMENSIONAL MIXED-BOUNDARY-VALUE ELASTIC PROBLEMS

2005 ◽  
Vol 02 (01) ◽  
pp. 99-126 ◽  
Author(s):  
M. ZUBAER HOSSAIN ◽  
S. REAZ AHMED ◽  
M. WAHHAJ UDDIN
Keyword(s):  
Finite Difference ◽  
Potential Function ◽  
Solid Mechanics ◽  
Present Model ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Computational Time ◽  
Comparison Of The Results

This paper describes a new mathematical formulation, specifically suitable for finite-difference analysis of stresses and displacements of three-dimensional mixed-boundary-value elastic problems. Earlier, mathematical models of elasticity were very deficient in handling three-dimensional practical stress problems. In the present model, a new scheme of reduction of unknowns is used to formulate the three-dimensional problem in terms of a single potential function, defined in terms of the three displacement components. Compared to the conventional models, the present model provides numerical solution of higher accuracy in a shorter period of computational time. The application of the potential function formulation is demonstrated here through a number of classical problems of solid mechanics, and the results are compared with the available solutions in the literature. The comparison of the results establishes the rationality of the present approach.

Finite-difference techniques for a harmonic mixed boundary problem having a reentrant boundary

1971 ◽  
Vol 323 (1553) ◽  
pp. 271-276 ◽  
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Uniform Convergence ◽  
Boundary Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Value Problem ◽  
Mixed Boundary Problem ◽  
Finite Difference Techniques

The proof of uniform convergence of a family of finite-difference solutions to the exact solution is outlined for a harmonic mixed boundary-value problem in a rectangle containing a slit. Finite-difference results in the neighbourhood of the tip of the slit are given for reference.

Sign in / Sign up

Export Citation Format

Share Document