(Comp.sys.handhelds)
Item: 3183 by jn190068 at longs.LANCE.ColoState.EDU
Author: [Jay Nestle]
  Subj: composite analysis documentation
  Date: Mon May 20 1991

Composite Analysis Code for the hp48sx

Written by:  Jay Nestle
Spring 1991 for CE496v at Colo State Univ

The following remarks contain some fundamentals about the way the
program operates and some basic theory behind it, it is assumed that
the user has some knowledge of Classical Lamination Theory (CLT).

To run the program takes 2 or 3 steps: (3 for thermal effects, can be omitted)

        1)  Run INT1
                the interface program allows you to enter the number
                of new materials and layers, just follow the prompts.
                Variables req'd for Materials are: E1, E2, G12, v21, v12
                (Note: the v21 and v12 are the poisson ratios)
                the 1 and 2 designate the principle material directions,
                i.e. 1 points in the fiber direction, 2 perp to it.
                Variables req'd for the layers are: theta (the material
                orientation measured from the x-axis as CCW is positive)
                ztop, zbottom (see below), alpha1, and alpha2 (the
                coefficients of thermal expansion in the 1 2 directions)

                         _______________________________  -0.01
                        |                               |
                        |       Layer 1                 |
                        |_______________________________| -0.005
                        |                               |
                        |       Layer 2                 |
                 _______|_______________________________|_____\
                |       |                               |     / X
                |       |       Layer 3                 |
                |       |_______________________________| 0.005
                \/ +Z   |                               |
                        |       Layer 4                 |
                        |_______________________________| 0.01
                                    TOP of Laminate

                With this orientation you can see that for layer 1:
                        ztop=-0.005 and zbottom=-0.01
                This is the orientation used in my program.

        2)  After all the materials have been entered and the layer
                values you will be ready to calculate the Q, Qbar
                (reduced stiffness matrix) for each layer, and then
                calculate the ABD matrix for the laminate.  This is
                all done by just pressing CALC.  (note after running
                INT1 like above the Temp Menu is still displayed,
                simply hit VAR to get to the CALC option.)

        3)  If you are considering thermal effects now just press CNTa
                and the program will calculate the alpha vector for the
                entire laminate and the NT vector.  These will be located
                in the LAYERS directory in the ABD directory, which is
                where you will be after pressing CNTa.

        If you have an understanding of CLT you know that you can now solve
        equations (in matrix form) like:

                { N M } = [ABD]{ e K }

        Where { N M } is the vector of stesses and moments and
        { e K } is the vector of strains and curvatures. (e=epsilon, K=kappa)
        [ABD] is the ABD matrix calculated from my program.  Given this
        simply use the built in matrix editor to enter the known, either
        N M or e K and solve for the other, quite fast and simple!

        You could also get the stress of individual layers (sigma=o) from

        {o}=[Qbar]{{e0}+z{K}}

        where o is for the layer likewise z and Qbar.  Qbar is found in the
        individual layers directories corresponding to the layer wanted.

        Note it works quite well to simply name layers as L1, L2, Ln etc.
        this works quite well!

        The {e0} is the vector of midplane strains, typically known or can
        be found above using the ABD calculation.

        I don't have any text references because we didn't use any, this
        theory is well documented and our course was taught from lecture
        only.

        Questions/Comments/Improvements can be send to me at:
        jn190068@longs.lance.ColoState.edu

        I hope someone can use this!! Please feel free to distribute!

jn190068@longs.lance.colostate.edu

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