TITLE 'Oscillation of a Glass Plate'

COORDINATES
  cartesian3

SELECT
    modes = 5
    ngrid=10
    errlim = 0.01 		{ 1 percent is good enough }

VARIABLES
    U          {X displacement}
    V           {Y displacement}
    W          {Z displacement}

DEFINITIONS
    E = 2e11
    cm = 0.01
    a = 8 * cm
    b = 5 * cm
    r = 2 * cm
    alpha = 60
    beta = 30
    h= 50 * cm
    nu = 0.31
    rho = 7800
    lam = E*nu/((1-2*nu)*(1+nu))
    mu = E/2/(1+nu)
    S11 = dx(U)
    S22 = dy(V)
    S33 = dz(W)
    S12 = 1/2*(dy(U) + dx(V))
    S23 = 1/2*(dz(V) + dy(W))
    S13 = 1/2*( dx(W) + dz(U))
    T11  = lam*(S11+S22+S33)+2*mu*S11
    T22  = lam*(S11+S22+S33)+2*mu*S22
    T33  = lam*(S11+S22+S33)+2*mu*S33
    T23 = 2*mu*S23
    T13 = 2*mu*S13
    T12 = 2*mu*S12

    Mt = 0.1

INITIAL VALUES
    U = 1.0e-5    V = 1.0e-5    W = 1.0e-5

EQUATIONS
    U:	dx(T11) + dy(T12) + dz(T13) + lambda*rho*U = 0
    V:	dx(T12) + dy(T22) + dz(T23) + lambda*rho*V = 0
    W:	dx(T13) + dy(T23) + dz(T33) + lambda*rho*W = 0

EXTRUSION
    surface "bottom" z = 0
    layer "plate"
    surface "top" z = h

BOUNDARIES
    region 1
    surface  "bottom"  load(U)=0 load(V)=0 load(W)=0
    surface  "top"  load(U)=0 load(V)=0 load(W)=0
    start(0, 0)
        value(U)=0
        value(V)=0
        value(W)=0
        line to (a, 0)
        load(U)=0
        load(V)=0
        load(W)=0
        line to (sqrt(3)+b, 2*sqrt(2))
        line to (sqrt(3), 2*sqrt(2))
        line to close
    start(5, sqrt(2))
        ARC(CENTER=a/2,sqrt(2)) ANGLE=360

MONITORS
    grid(x, y, z)  as "Shape"

PLOTS
    grid(x+Mt*U,y+Mt*V,z+Mt*W)  as "Shape"
    summary
        report lambda
END