文档介绍：5 Slab method
Introduction
Plane pression
Plane strain drawing of a sheet
pression
Solution with engineering slab analysis — simplified engineering method
Introduction
Introduction of slab analysis
If the boundary conditions are stated only in terms of stresses, then equilibrium equations and yield criterion equation are sufficient to define the stress distribution.
Solution with equilibrium equations integrated with yield criterion — Engineering method
Slab analysis
Simplified equilibrium equation + simplified yield criterion
Slab method:
slab method entails a force balance on a slab of metal of differential thickness and variations are considered only in one direction. This will produce a ordinary differential equation. Using pertinent boundary conditions, an integration then provides a solution. The procedures of this method are as follows:
Assume homogeneous deformation mode;
Select a slab of differential thickness;
Formulate a ordinary differential equation by force balance in the thickness direction;
Solve the differential equation with the help of yield criterion and pertinent boundary conditions
Introduction
Experiment results in pression
Slab analysis
Photoelastic method
lead
epoxy resin
l/h > 6
c1o:
Introduction
Experiment results in pression
Slab analysis
a1b1:
The shear stress is proportion to normal stress
b1c1:
The shear stress reaches maximum
Assumption:
Plane strain with constant frictional stress
Plane pression
Solution with “engineering method”
The first equation differentiate with y and the second equation differentiate with x,
Slab analysis
From the yield criterion
Then equation (7-1) es,
Plane pression
Solution with “engineering method”
(5-1)
(5-2)
(5-3)
(5-4)
Slab analysis
Substituting the xy in equation(5-4) into the equilibrium equations,
Plane pression
Solution with “engineering method”
(5-5)
(5-6)
Substituting the x,