PROBLEM mechanical MESH veeder.msh

b = 1 # cylinder radius

h = 0.5 # cylinder height

E = 1 # young modulus (does not matter for the displacement, only for stresses)

nu = 1/3 # poisson ratio

alpha = 1e-5 # temperature expansion coefficient

# temperature distribution as in the original paper

T1 = 1 # maximum temperature

T0 = 0 # reference temperature (where expansion is zero)

T(x,y,z) = T0 + T1*(1-(x^2+y^2)/(b^2))

# boundary conditions (note that the cylinder can still expand on the x-y plane)

BC inf tangential radial

# write vtu output

WRITE_RESULTS

# non-dimensional numerical displacement profiles

v_num(z') = v(0, b, z'*h)/(alpha*T1*b)

w_num(r') = w(0, r'*b, h)/(alpha*T1*b)

########

# reference solution

# coefficients of displacement functions for h/b = 0.5

a00 = 0.66056

a01 = -0.44037

a10 = 0.23356

a02 = -0.06945

a11 = -0.10417

a20 = 0.00288

b00 = -0.01773

b01 = -0.46713

b10 = -0.04618

b02 = +0.10417

b11 = -0.01152

b20 = -0.00086

# coefficients of displacement functions for h/b = 1.0

# a00 = 0.73197

# a01 = -0.48798

# a10 = 0.45680

# a02 = -0.01140

# a11 = -0.06841

# a20 = 0.13611

#

# b00 = 0.26941

# b01 = -0.45680

# b10 = -0.25670

# b02 = 0.03420

# b11 = -0.27222

# b20 = -0.08167

R(r') = r'^2 - 1

Z(z') = z'^2 - 1

v_ref(r',z') = r' * (a00 + a01*R(r') + a10*Z(z') + a02* R(r')^2 + a11 * R(r')*Z(z') + a20 * Z(z')^2)

w_ref(r',z') = z' * (b00 + b01*R(r') + b10*Z(z') + b02* R(r')^2 + b11 * R(r')*Z(z') + b20 * Z(z')^2)

PRINT_FUNCTION FILE veeder_v.dat v_num v_ref(1,z') MIN 0 MAX 1 NSTEPS 50 HEADER

PRINT_FUNCTION FILE veeder_w.dat w_num w_ref(r',1) MIN 0 MAX 1 NSTEPS 50 HEADER