A variational-difference method for solving the axisymmetric problem of elasticity theory in terms of stress functions

1970 ◽  
Vol 2 (10) ◽  
pp. 1015-1017
Author(s):  
A. L. Kvitka ◽  
V. Z. Filippov
Keyword(s):  
Elasticity Theory ◽  
Difference Method ◽  
Axisymmetric Problem ◽  
Stress Functions ◽  
Variational Difference Method

Variational-difference method in the problem of the vibrations of laminated plates

1992 ◽  
Vol 28 (8) ◽  
pp. 506-511 ◽  
Author(s):  
V. G. Piskunov ◽  
Yu. M. Fedorenko ◽  
A. E. Stepanova
Keyword(s):  
Difference Method ◽  
Laminated Plates ◽  
Variational Difference Method

Design of thick slabs by the variational-difference method

1991 ◽  
Vol 27 (6) ◽  
pp. 558-563
Author(s):  
V. I. Akimova ◽  
N. A. Shul'ga
Keyword(s):  
Difference Method ◽  
Variational Difference Method

Numerical Solution of Axisymmetric Problem for an Elastic Footing

2012 ◽  
Vol 170-173 ◽  
pp. 115-120
Author(s):  
Jia Zhang ◽  
Xing Min Hou ◽  
Li Xiang Wu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Axisymmetric Problem ◽  
Numerical Solutions ◽  
Hankel Transform ◽  
Substitution Method ◽  
Function Calculation ◽  
Boussinesq’S Equation ◽  
Elastic Mechanics

Based on formulas of elastic mechanics, the axisymmetric problem applied to an elastic footing is analyzed. Using Hankel transform and finite difference method, the arbitrary points’ displacement and stress solutions of the axisymmetric elastic footing problem is obtained. Compared with recursive substitution method and transfer matrix method, this method is simple because it avoids complex formulas and exponential function calculation. The half space model is more flexible to simulate an actual footing. The numerical solutions are compared with Boussinesq’s Equation and results show that finite difference method is applicable to solve axisymmetric elastic footing problem. But in the application of finite difference method, there are a few factors that could cause calculation errors. Effective measures are needed to obtain exact solutions.

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