*HEADING
: TESTING ESF1 WITH AMPLITUDE CARD, BEAM GENERAL SECTION
          AND STOKES WAVES WHERE SECTION POINT CHANGES FROM DRY TO WET
 CASE A -- 1 ELEMENT WITH PB AND PARTIAL SUBMERGENCE SUCH THAT SECTION
           POINT IS ABOVE MWL (BUT NOT NECESSARILY BELOW IWL FOR
           DYNAMIC CASE) WITH INTERNAL FLUID FILLING ENTIRE ELEMENT [PIPE21]
 CASE B -- 1 ELEMENT WITH PB AND PARTIAL SUBMERGENCE SUCH THAT SECTION
           POINT IS ABOVE MWL (BUT NOT NECESSARILY BELOW IWL FOR
           DYNAMIC CASE) WITH INTERNAL FLUID FILLING ONLY BOTTOM 1/4
           OF ELEMENT [B22]
 CASE C -- SAME AS CASE A WITH AMPLITUDE CARD
 CASE D -- SAME AS CASE B WITH AMPLITUDE CARD AND BEAM GENERAL SECTION
 CASE E -- 1 ELEMENT WITH BOTTOM AT SECTION POINT AT TSB LOAD (THIS IS FOR
           DETERMINING PRESSURE FOR USE IN HAND CALCULATIONS) [B21].
           SUM OF REACTION FORCES EQUALS (-) BUOYANCY LOAD.  BUOYANCY LOAD
           TIMES C.S. AREA EQUALS PRESSURE AT THAT ELEVATION.  SINCE
           C.S. IS SET TO ONE, PRESSURE IS (-) SUM OF REACTION FORCES.
**
EXACT SOLUTION: ESF1 = SF1 + P_e*A_e - P_i*A_i
                     =  0  - RF3_CASE_E - rho_i*g*h_i*A_i
WHERE h_i and A_i ARE TAKEN AT SECTION POINT.  SINCE ALL NODES ARE
FIXED, SF1 = 0.  FOR CASES B and D, INTERNAL PRESSURE AT SECTION POINT
IS ZERO SINCE FLUID LEVEL INSIDE IS BELOW SECTION POINT (P_i=0).
**
RESULTS AT MAX BUOYANCY LOAD
 CASE A:  + 2343 - 5058 = -2715           AT MAX BUOYANCY LOAD
 CASE B:  + 2343 -    0 =  2343           AT MAX BUOYANCY LOAD
 CASE C:  0.5*(+ 2343 - 5058) = -1357.5   AT MAX BUOYANCY LOAD
 CASE D:  0.5*(+ 2343 -    0) =  1171.5   AT MAX BUOYANCY LOAD
***********
***********
** Aqua parameters:
**
**   Water depth    - 1000
**   Seabed         - 100
**   Still water    - 1100
**   Steady current - (0,0,0) No steady current
**   Density        - 2.0
**   Gravity const  - 32.2
**
*AQUA
 100., 1100., 32.2, 2.0
 0., 0., 0., 0.
 0., 0., 0., 1100.
***********
***********
** Wave parameters (Stokes):
**
**     Wave height    - 100
**     Wave period    - 15
**     Phase angle    - 0
**     Wave direction - (1,0,0)
**
*WAVE,TYPE=STOKES
 100,15.,0., 1.,0.,0.
***********
***********
*NODE,NSET=A
 101,0.,1010.
 102,0.,1210.
*NODE,NSET=B
 201,0.,1010.
 202,0.,1210.
*NODE,NSET=C
 301,0.,1010.
 302,0.,1210.
*NODE,NSET=D
 401,0.,1010.
 402,0.,1210.
*NODE,NSET=E
 501,0.,1110.
 502,0.,1210.
*ELEMENT,TYPE=PIPE21,ELSET=A
 101,101,102
*ELEMENT,TYPE=B21,ELSET=B
 201,201,202
*ELEMENT,TYPE=PIPE21,ELSET=C
 301,301,302
*ELEMENT,TYPE=B21,ELSET=D
 401,401,402
*ELEMENT,TYPE=B21,ELSET=E
 501,501,502
*NSET,NSET=N_PB
 A,B,C,D
*BOUNDARY
 N_PB,1,2
 N_PB,6,6
 501,1,2
 501,6,6
*RESTART,WRITE,FREQ=10
*BEAM SECTION,SECTION=PIPE,MATERIAL=MAT1,ELSET=A 
 1.0,0.25
*BEAM SECTION,SECTION=PIPE,MATERIAL=MAT1,ELSET=B
 1.0,0.25
*BEAM SECTION,SECTION=PIPE,MATERIAL=MAT1,ELSET=C
 1.0,0.25
*BEAM GENERAL SECTION,SECTION=PIPE,ELSET=D
 1.0,0.25

 1.E6,0.5E6
*BEAM SECTION,SECTION=PIPE,MATERIAL=MAT1,ELSET=E
 1.0,0.25
*MATERIAL,NAME=MAT1
*ELASTIC
 1.E6,
*DENSITY
 1.0E6, 
*AMPLITUDE,NAME=AMP
0.,0.5,15.,0.5
** ----------------------------------------------------------------------
**     Dynamic test for buoyancy loads with fluid inside pipe
** ----------------------------------------------------------------------
*STEP,NLGEOM,INC=1000
 Dynamic buoyancy load with fluid inside pipe
*DYNAMIC,DIRECT
.2,15.
*DLOAD
  A ,PB, 1.0  , 1.1283792                   , 2.   , 1. , 1210.
  B ,PB, 1.0  , 1.1283792                   , 2.   , 1. , 1060.
*DLOAD,AMP=AMP
  C ,PB, 1.0  , 1.1283792                   , 2.   , 1. , 1210.
  D ,PB, 1.0  , 1.1283792                   , 2.   , 1. , 1060.
**el,PB, amag0, D_e (2/sqrt(pi) = area of 1), pho_i, D_i, Free_surface_i
*CLOAD
  501, TSB,  1.0, 1.0, 0.,-1.,0.
**node,TSB,amag0,area,  normal
*EL PRINT
 SF1,ESF1
*NODE PRINT
 U,A
 RF, 
*NODE FILE,FREQ=10
 RF, 
*ENERGY FILE,FREQ=10
*EL FILE,FREQ=10
SF,ESF1
*END STEP