Question

Matlab assignment.

The objectives of this project are (1) to introduce the students to scripting applied to solution of mechanical engineering problems and (2) to create a Matlab script that allows the computation of principal stresses and strains starting from a generic state of stress and that automates the drawing of 3D Mohr circles

Assignment

1) Read from input a stress tensor (3D);

2) For any state of 3D stress compute the principal stress values (σ1, σ2, σ3) with σ1 > σ2 > σ3;

3) Calculate the maximum shear stress (radius of the three circles);

4) Draws the correspondent Mohr circles;

5) Given the principal stresses (computed at point 2) use the Hooke’s law to calculate the correspondent principal strains;

6) Create a flowchart correspondent to this code (Points 1 to 5).

Answer 1

function []=mohrs(StressState, option, angle)
%MOHRS Draws a Mohr's circle.
%   MOHRS([SIGMAX,SIGMAY,TAUXY],OPTION,ANGLE) Calculates principle stresses,
%   maximum shear, and normal and shear stress on a requested plane.  All of
%   these are presented graphically on a Mohr's circle diagram that can be
%   easily printed out.
%
%   SIGMAX:  Normal stress in the X direction.
%   SIGMAY:  Normal stress in the Y direction.
%   TAUXY:   Shear on the X-Y plane.
%   Together these three are gathered as the STRESSSTATE.

sx=StressState(1);
sy=StressState(2);
txy=StressState(3);
center=mean([sx,sy]);
[PrincipleStresses, IPShearMax, ShearMax]=pristress(StressState, option);
PP=ppstress(StressState)';
radius=IPShearMax;
clf
showcirc(radius,[center,0],'r');
hold on
showcirc(PrincipleStresses(1)/2,[PrincipleStresses(1)/2,0],'r--');
showcirc(PrincipleStresses(2)/2,[PrincipleStresses(2)/2,0],'r--');
showcirc(PrincipleStresses(3)/2,[PrincipleStresses(3)/2,0],'r--');
axis ('equal')
edges=axis;
le=edges(1);
hs=(edges(2)-edges(1))/2;
plot ([edges(1)-0.1*edges(1) edges(2)+0.1*edges(2)],[0 0],'b')
plot ([0,0],[edges(3) edges(4)],'b')
plot (center,0,'ro')
plot ([sx,sy],[-txy,txy],'k')
colA=strvcat('Center:','Maximum In Plane Shear:','Maximum Total Shear:');
colA=strvcat(colA,'Principle Stresses:','Principle Planes:');
colB=strvcat(num2str(center,4),num2str(IPShearMax,4),num2str(ShearMax,4));
colB=strvcat(colB,num2str(PrincipleStresses,4),num2str(RD(PP),4));
if nargin==3
  AngleToHorPlane=atan2(txy,(sy-center));
  AngleToRequestPlane=AngleToHorPlane + 2*angle;
  rn=center + radius * cos(AngleToRequestPlane);
  rs=radius * sin(AngleToRequestPlane);
  plot ([center,rn],[0,rs],'r',rn,rs,'rd')
  colA=strvcat(colA,'At angle:','**Normal Stress:','**Shear Stress:');
  colB=strvcat(colB,num2str(RD(angle),4),num2str(rn,4),num2str(rs,4));
end
axis ('equal')
colA=strvcat(colA,'Negative shear causes CCW rotation of element.');
colB=strvcat(colB,' ');
expandaxis (30, 30)
titleblock(colA,colB);
xlabel ('Normal Stress')
ylabel ('Shear Stress')
title (strcat('Mohrs circle:   ',option))
text (sx,-txy,'V')
text (sy,txy,'H')
hold off