Компьютерное моделирование процессов и аппаратов пищевой, био- и химической технологии в среде FlexPDE. Дворецкий С.И - 29 стр.

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gyz = dz(V) + dy(W)
gzx = dx(W) + dz(U)
{Напряжения}
Sx = C11*ex + C12*ey + C13*ez
Sy = C12*ex + C22*ey + C23*ez
Sz = C13*ex + C23*ey + C33*ez
Txy = C44*gxy Tyz = C44*gyz Tzx = C44*gzx
{Подсчитываем среднее значение сдвига и поворота}
Vol = Integral(1)
Tx = integral(U)/Vol
{Сдвиг по X}
Ty = integral(V)/Vol {Сдвиг по Y}
Tz = integral(W)/Vol {Сдвиг по Z}
Rz = 0.5*integral(dx(V) – dy(U))/Vol
{Поворот по Z}
Rx = 0.5*integral(dy(W) – dz(V))/Vol {Поворот по X}
Ry = 0.5*integral(dz(U) – dx(W))/Vol
{Поворот по Y}
Up = U – Tx + Rz*y – Ry*z
Vp = V – Ty + Rx*z – Rz*x
Wp = W – Tz + Ry*x – Rx*y
Mx = 0.2*globalmax(magnitude(y,z))/globalmax(magnitude(Vp,Wp))
My = 0.2*globalmax(magnitude(x,z))/globalmax(magnitude(Up,Wp))
Mz = 0.2*globalmax(magnitude(x,y))/globalmax(magnitude(Up,Vp))
Mt=0.4*globalmax(magnitude(x,y,z))/globalmax(magnitude(Up,Vp,Wp))
INITIAL VALUES
U = 1.e-5 V = 1.e-5 W = 1.e-5
EQUATIONS
U: dx(Sx) + dy(Txy) + dz(Tzx) = 0
V: dx(Txy) + dy(Sy) + dz(Tyz) = 0
W: dx(Tzx) + dy(Tyz) + dz(Sz) = 0
EXTRUSION
surface z = 0 surface z = 10
BOUNDARIES
surface 1 value(W)=dist {Зафиксированное основание}
surface 2 load(W)=0
Region 1 {Сталь}
K = 0.11
E = 20e11
nu =0.28
start (R0,0) value(V)=0
arc(center=0,0) angle=360 to finish
MONITORS
contour(Up) on y=high/2 as "X-displacement"
contour(Vp) on x=4*wide/5 as "Y-displacement"
contour(Wp) on y=high/2 as "Z-displacement"
grid(x+Mt*Up,y+Mt*Vp,z+Mt*Wp) as "Shape"
PLOTS
contour(Up) on y=high/2 as "X-displacement"
contour(Vp) on x=4*wide/5 as "Y-displacement"
contour(Wp) on y=high/2 as "Z-displacement"
grid(x+Mt*Up,y+Mt*Vp,z+Mt*Wp) as "Shape"
END
Результаты решения иллюстрирует рис. 16.

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