Postprocessing - The Boundary Element Method with Programming - page 235

DuDeta(2)= Dot_Product (Dni(:,2),u(:,2))
DuDeta(3)= Dot_Product (Dni(:,2),u(:,3))
CosT= DOT_Product (Vxsi,Veta)
SinT= ABS ( DOT_Product (V2,Veta))
DxsiDx= 1/Jxsi
DxsiDy= -CosT /(Jxsi*SinT)
DetaDx= 0.0
DetaDy= 1/(Jeta*SinT)
! Strains
Strain(1)= Dot_product (DuDxsi,v1)*DxsiDx
Strain(2)= Dot_product (DuDxsi,v2)*DxsiDy&
+ Dot_product (DuDeta,v2)*DetaDy
Strain(3)= Dot_product (DuDxsi,v1)*DxsiDy&
+ Dot_product (DuDeta,v1)*DetaDy&
+ Dot_product (DuDxsi,v2)*DxsiDx
tn= Dot_Product(v3,trac_GP)
ts1= Dot_Product (v1,trac_GP)
ts2= Dot_Product (v2,trac_GP)
! Compute stresses in local directions
C1= E/(1.0-ny**2) ; C2= ny/(1.0-ny) ; G=E/(2*(1.0+ny))
Stress(1)= C1*(Strain(1)+ny*strain(2))+ C2*tn
Stress(2)= C1*(Strain(2)+ny*strain(1))+ C2*tn
Stress(3)= tn
Stress(4)= G*Strain(3)
Stress(5)= ts2
Stress(6)= ts1
DEALLOCATE (Strain)
END IF
! Transformation of local stresses in global stresses
CALL Stress_Transformation(v1,v2,v3,Stress,Cdim)
RETURN
End SUBROUTINE BStress

9.3 COMPUTATION OF INTERNAL RESULTS

For the computation of results which are not on the boundary the integral equation for
the temperature/potential and the displacement is used.

9.3.1 Potential problems

To compute temperature/potential at a point P a we rewrite equation (5.20)

³ ³

u P t Q U P , Q dS Q u Q T P , Q dS Q

(9.25)

a a a

S S

Flows at P a in x-, y-and z-directions are given by