A trilinear cylinder (r interpolation) of incompressible Mooney-Rivlin material is inflated to 1kPa.
#Example_531 Inflation and 10% axial extension of a cylinder using r interpol.n
fem
fem define coordinates;r;cylind;example #Define 3 GLOBAL CYLINDRICAL POLAR
# ! coordinates for an UNSYMMETRIC
# ! GEOMETRY, RADIAL INTERPOLATION in r.
# ! Written to file CYLIND.ipcoor.
fem define node;r;;example #4 NODES, 3 COORDINATES, NO VERSION
# ! PROMPTING, 0 DERIVATIVES for all
# ! coordinates. Nodal coordinates (Xj)
# ! are (R,theta,Z): 1=(2,0,0);2=(2,0,1);
# ! 3=(3,0,0); 4=(3,0,1).
fem define base;r;;example #Define 3 BASIS FUNCTIONS. Choose
# ! LAGRANGE/HERMITE for basis function 1
# ! with 3 Xi COORDINATES, a LINEAR LAGRANGE interpolant
# ! and 1 GAUSS POINT each in Xi(1) (circumferential) and
# ! Xi(2) (axial) directions but 3 in Xi(3) (radial).
# ! For basis function 2 (hydrostatic pressure), choose an
# ! AUXILIARY BASIS with 5 AUXILIARY ELEMENT PARAMETERS,
# ! PRESSURE BASIS with 3 Xi coordinates and the same
# ! number of Gauss points as basis function 1. For all 5
# ! parameters choose POLYNOMIAL DEGREE of 0 (ie constant)
# ! in Xi1 and Xi2 directions. For parameters 1;2;3;4;5
# ! choose POLYNOMIAL DEGREE 0;1;2;-1;-2 respectively
# ! (0;1;2 denote a quadratic variation in the hydrostatic
# ! pressure in Xi3 whilst -1;-2 denotes parameters for
# ! Xi3=0;Xi3=1 face pressure bc respectively.) Basis
# ! function 3 describes surfaces and thus has 2 Xi
# ! COORDINATES with LINEAR LAGRANGE interpolant, and 3
# ! Gauss points in Xi(1) and Xi(2) directions.
fem define element;r;;example #1 ELEMENT with 3 Xj COORDINATES. BASIS
# ! FUNCTION 1 describes each coordinate.
# ! GLOBAL NODE # is 1,1,2,2,3,3,4,4.
fem define fibre;d # Set up a default fibre angle (aligned
# ! with xi 1)
fem define element;d fibre
fem define window;r;;example #Define window dimensions in X,Y,Z
# ! directions as (min,max): (-4,4),
# ! (-4,4), (-1,2).
fem draw lines #Make line segments visible on window.
fem define equation;r;;example #Defines equation the same as in the
# ! uniaxial cube extension problem.
fem define material;r;;example #Defines a Mooney-Rivlin material as in
# ! the uniaxial cube extension problem.
fem define initial;r;;example #BOUNDARY PRESSURE INCREMENTS will be
# ! entered and HYDROSTATIC PRESSURE will
# ! be matched across elements with adjacent Xi3 faces
# ! (none in this example). INITIAL DISPLACEMENTS are ALL
# ! ZERO. For equation 2 (theta-direction) fix node 1; for
# ! equation 3 (Z-direction), fix nodes 1,3 and apply 0.1
# ! displacement to nodes 2,4. Pressure bcs are applied
# ! via DEPENDENT VARIABLE/EQUATION 4. For ELEMENT 1 DO NOT
# ! prescribe bcs for parameters 1,2,3; to apply a pressure
# ! of magnitude 1 on Xi3=0 face(inside cylinder) prescribe
# ! an INCREMENT of 1.0 to AUXILIARY VARIABLE 4. To apply
# ! a pressure of magnitude 0 on Xi(3)=1 face (outside
# ! cylinder) prescribe an INCREMENT of 0.0 to AUXILIARY
# ! VARIABLE 5.
fem define solve;r;;example #Defines solution information.
fem solve step 1 #Solve the problem, (should converge
# ! in about 6 iterations).
fem draw lines def dotted #Draw deformed mesh.
fem list strain at 1 ref #List strain information wrt reference
# ! coordinates at 1st gauss point.
fem list stress at 1 ref #List stress information wrt reference
# ! coordinates at 1st gauss point.
fem list elem tot
fem list elem deformed total
#Note that volume is not conserved with quadratic transmural
# hydrostatic pressure and r interpolation (I3 not equal
# to 1). The radial stress at the first Gauss point is
# near the inner radius where the stress should be close
# to the applied pressure (-1) but is quite different.
# At the third Gauss point (display this point by
# repeating the last command and replace the "1" with a
# "3"), near the outer radius, the radial stress should
# be near zero but is again quite different from what is
# expected. Contrast these results with the next
# sample problem.
Name Modified Size
example_531.com 06-Mar-2012 5.2k cylind.ipbase 10-Apr-2000 4.2k cylind.ipcoor 10-Apr-2000 647 cylind.ipelem 10-Apr-2000 409 cylind.ipequa 02-May-2004 2.1k cylind.ipinit 05-Dec-2002 2.4k cylind.ipmate 05-Dec-2002 2.3k cylind.ipnode 10-Apr-2000 1.1k cylind.ipsolv 06-Mar-2012 2.4k cylind.ipsolv.old 13-Apr-2007 2.1k cylind.ipwind 10-Apr-2000 262 test_output_old.com 10-Apr-2000 50
Name Modified Size
examples_5_53_531.tar.gz 07-Mar-2012 8.3k
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