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Multi-Layer Curved Beam

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}]

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).

Moment case looks good from both single and multilayer cases

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).

Created by Mathematica  (March 7, 2004)