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Multi-Layer Curved Beam

Needs["MaterialMinds`curvedBeam`"]

In order to perform the analysis on a multiple layer stack, we need to define the different material properties in the stack. m1 and m2 are lists of material properties.

m1 ={21 10^6,1.2 10^6, 0.8 10^6, .35};
m2 ={1.3 10^6,1.2 10^6, 1. 10^6, .54};

Next, we define what order the layers will be in.

matl = {m2,m1,m2,m1,m2,m1,m2,m1};

The vector of radii is listed here. The lists starts at 1 and ends at 2, with increments of 1/8 in between.

ri=Table[r,{r,1,2,1/8}]

{1, 9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2}

The result of curvedBeamSolve is computed next. The loading here is a pure radial load (no tangential or moment loads present).

result=curvedBeamSolve[matl,ri,{0,1,0}];

We can plot all three components (sigmaT, sigmaR, sigmaRT) over the radial distance r. Note that r is plotted from the first ri shown above (1) to the last ri (2).

Plot[MMStress[result][1][{Pi/4, r}], {r, First[ri], Last[ri]}, PlotRangeAll, AxesLabel ...                                                                                             θ

[Graphics:HTMLFiles/index_4.gif]

⁃Graphics⁃

Plot[MMStress[result][2][{Pi/4, r}], {r, First[ri], Last[ri]}, AxesLabel {"r" ...                                                                                                  r

[Graphics:HTMLFiles/index_7.gif]

⁃Graphics⁃

Moment case looks good from both single and multilayer cases

Plot[MMStress[result][3][{Pi/4, r}], {r, First[ri], Last[ri]}, AxesLabel {"r" ...                                                                                            rθ

[Graphics:HTMLFiles/index_10.gif]

⁃Graphics⁃

Finally, we can plot the model displacement. Arguments here are result from curvedBeamSolve, the upper bound of theta (Pi/2), and the scale factor (2 10^4).

showModelDisplacement[result, Pi/2, 2 10^4]

[Graphics:HTMLFiles/index_13.gif]

⁃Graphics⁃


Created by Mathematica  (March 7, 2004)