*HEADING
: Testing of ESF1 with modal procedures with HPE/HPI/PE/PI loads
Testing only on PIPE21 elements:
 Case A -- 2 ELEMENTS ANGLED AT 90 WITH PE/PI
 Case B -- 2 ELEMENTS PB ANGLED AT 45 WITH HPE/HPI
Loads applied such that HPE/PE magnitude = HPI/PI magnitude
Results (except for *FREQUENCY and OPEN end conditions where ESF1=SF1):
 Case A at both section points:
	ESF1 = SF1 + PeAe - PiAi
	     =  0  + 100*2 - 100*1
	     = 100
 Case B:
   Bottom element section point:
	ESF1 = SF1 + PeAe - PiAi
	     =  0  + 25*2 - 25*1
	     = 25
   Top element section point:
	ESF1 = SF1 + PeAe - PiAi
	     =  0  + 75*2 - 75*1
	     = 75
***********
***********
*NODE,NSET=N_P
*NODE,NSET=N_HP
*ELEMENT,TYPE=PIPE21,ELSET=E_P
*ELEMENT,TYPE=PIPE21,ELSET=E_HP
*ELSET,ELSET=ALL
*BOUNDARY
 101,ENCASTRE
 102,ENCASTRE
 201,ENCASTRE
 202,ENCASTRE
*RESTART,WRITE,FREQ=10
*BEAM SECTION,SECTION=PIPE,MATERIAL=MAT1,ELSET=E_P
 1.0,0.25
*BEAM SECTION,SECTION=PIPE,MATERIAL=MAT1,ELSET=E_HP
 1.0,0.25
**
*MATERIAL,NAME=MAT1
*ELASTIC
 1.E6,
*DENSITY
 1.0,
** 1.0E6
**
** -------------------------------------------
**  STEP 1:   Frequency extraction
** -------------------------------------------
*STEP
 STEP 1: Extract eigenvalues
*FREQUENCY, eigensolver=lanczos
10, ,10000.
*ENDSTEP
** ----------------------------------------------------------
**  STEP 2a:   Steady State Dynamics - Open end conditions
** ----------------------------------------------------------
*STEP,NLGEOM
 STEP 2a: Steady state dynamics procedure, open end, real loads
*steady state dynamics
 0, 10, 2
*MODAL DAMPING
*SELECT EIGENMODES, GENERATE
*DLOAD
  E_P,    PE,      100.0,  1.5957691,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
  E_P,    PI,      100.0,  1.1283792,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*NODE PRINT,TOTAL=YES
 RF,
*EL PRINT
SF1,ESF1
*EL FILE
SF,ESF1
*OUTPUT,FIELD
*ELEMENT OUTPUT
SF,ESF1
*OUTPUT,HISTORY
*ELEMENT OUTPUT,ELSET=ALL
SF1,ESF1
*END STEP
** -------------------------------------------------------------------
**  STEP 2b:   Steady State Dynamics - Open end conditions, Imag loads
** -------------------------------------------------------------------
*STEP,NLGEOM
 STEP 2b: Steady state dynamics procedure, open end, imaginary loads
*steady state dynamics
 0, 10, 2
*MODAL DAMPING
*SELECT EIGENMODES, GENERATE
*DLOAD, LOAD CASE=2
  E_P,    PE,      100.0,  1.5957691,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
  E_P,    PI,      100.0,  1.1283792,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END STEP
** ----------------------------------------------------------
**  STEP 2c:   Steady State Dynamics - Closed end conditions
** ----------------------------------------------------------
*STEP,NLGEOM
 STEP 2c: Steady state dynamics procedure, closed end, real loads
*steady state dynamics
 0, 10, 2
*MODAL DAMPING
*SELECT EIGENMODES, GENERATE
*DLOAD
  E_P,    PE,      100.0,  1.5957691, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
  E_P,    PI,      100.0,  1.1283792, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END STEP
** ---------------------------------------------------------------------
**  STEP 2d:   Steady State Dynamics - Closed end conditions, Imag loads
** ---------------------------------------------------------------------
*STEP,NLGEOM
 STEP 2d: Steady state dynamics procedure, closed end, imaginary loads
*steady state dynamics
 0, 10, 2
*MODAL DAMPING
*SELECT EIGENMODES, GENERATE
*DLOAD, LOAD CASE=2
  E_P,    PE,      100.0,  1.5957691, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
  E_P,    PI,      100.0,  1.1283792, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END STEP
** ------------------------------------------------------------------
**  STEP 3:   Steady State Dynamics, Direct
** ------------------------------------------------------------------
*STEP,INC=1000,NLGEOM
 STEP 3: Steady state dynamics direct procedure
*STEADY STATE DYNAMICS,DIRECT
 10,
*LOAD CASE, NAME=RealOpenEnd
*DLOAD, LOAD CASE=1
  E_P,    PE,      100.0,  1.5957691,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=1
  E_P,    PI,      100.0,  1.1283792,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=1
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=1
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END LOAD CASE
*LOAD CASE, NAME=ImagOpenEnd
*DLOAD, LOAD CASE=2
  E_P,    PE,      100.0,  1.5957691,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
  E_P,    PI,      100.0,  1.1283792,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END LOAD CASE
*LOAD CASE, NAME=RealClosedEnd
*DLOAD, LOAD CASE=1
  E_P,    PE,      100.0,  1.5957691, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=1
  E_P,    PI,      100.0,  1.1283792, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=1
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=1
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END LOAD CASE
*LOAD CASE, NAME=ImagClosedEnd
*DLOAD, LOAD CASE=2
  E_P,    PE,      100.0,  1.5957691, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
  E_P,    PI,      100.0,  1.1283792, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END LOAD CASE
*END STEP
** ------------------------------------------------------------------
**  STEP 4a:   Steady State Dynamics, SUBSPACE - Open, Real
** ------------------------------------------------------------------
*STEP,INC=1000,NLGEOM
 STEP 4a: Steady state dynamics subspace procedure, open end, real load
*STEADY STATE DYNAMICS,SUBSPACE PROJECTION
 10,
*DLOAD
  E_P,    PE,      100.0,  1.5957691,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
  E_P,    PI,      100.0,  1.1283792,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END STEP
** ------------------------------------------------------------------
**  STEP 4b:   Steady State Dynamics, SUBSPACE - Open, Imag
** ------------------------------------------------------------------
*STEP,INC=1000,NLGEOM
 STEP 4b: Steady state dynamics subspace procedure, open end, imag load
*STEADY STATE DYNAMICS,SUBSPACE PROJECTION
 10,
*DLOAD, LOAD CASE=2
  E_P,    PE,      100.0,  1.5957691,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
  E_P,    PI,      100.0,  1.1283792,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END STEP
** ------------------------------------------------------------------
**  STEP 4c:   Steady State Dynamics, Subspace - Closed, Real
** ------------------------------------------------------------------
*STEP,INC=1000,NLGEOM
 STEP 4c: Steady state dynamics subspace procedure, closed end, real load
*STEADY STATE DYNAMICS,SUBSPACE PROJECTION
 10,
*DLOAD
  E_P,    PE,      100.0,  1.5957691, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
  E_P,    PI,      100.0,  1.1283792, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END STEP
** ------------------------------------------------------------------
**  STEP 4d:   Steady State Dynamics, Subspace - Closed, Imag
** ------------------------------------------------------------------
*STEP,INC=1000,NLGEOM
 STEP 4d: Steady state dynamics subspace procedure, closed end, imag load
*STEADY STATE DYNAMICS,SUBSPACE PROJECTION
 10,
*DLOAD, LOAD CASE=2
  E_P,    PE,      100.0,  1.5957691, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
  E_P,    PI,      100.0,  1.1283792, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD, LOAD CASE=2
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END STEP
** ----------------------------------------------------
**     STEP 5a: Modal Dynamics - Open end conditions
** ----------------------------------------------------
*STEP,NLGEOM
 STEP 5a: Modal Dynamics procedure, open end
*MODAL DYNAMIC
 .1,.4
*DLOAD
  E_P,    PE,      100.0,  1.5957691,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
  E_P,    PI,      100.0,  1.1283792,  OPEN
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792,  OPEN
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*NODE PRINT,TOTAL=YES,FREQ=10
 RF,
*EL PRINT,FREQ=10
SF1,ESF1
*EL FILE,FREQ=10
SF,ESF1
*END STEP
** ----------------------------------------------------
**     STEP 5b: Modal Dynamics - Closed end conditions
** ----------------------------------------------------
*STEP,NLGEOM
 STEP 5b: Modal Dynamics procedure, closed end
*MODAL DYNAMIC
 .1,.4
*DLOAD
  E_P,    PE,      100.0,  1.5957691, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
  E_P,    PI,      100.0,  1.1283792, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*END STEP
** -------------------------------------------
**  STEP 6: Dynamic procedure for comparision
**          to modal dynamics procedure -
**          Closed end condition only
** -------------------------------------------
*STEP,INC=1000,NLGEOM
 STEP 6: Dynamic pressure test using modal dynamic procedure
*DYNAMIC
 .1,.4
*DLOAD
  E_P,    PE,      100.0,  1.5957691, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
  E_P,    PI,      100.0,  1.1283792, CLOSE
**el,PE/PI, amag0, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPE,      100.0,      185.4,      114.6,  1.5957691, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*DLOAD
 E_HP,   HPI,      100.0,      185.4,      114.6,  1.1283792, CLOSE
**el,HPE/HPI, amag0, z-p0, z-p, diam, CLOSE/OPEN
*NODE PRINT,TOTAL=YES,FREQ=10
 RF,
*EL PRINT,FREQ=10
SF1,ESF1
*EL FILE,FREQ=10
SF,ESF1
*OUTPUT,FIELD
*ELEMENT OUTPUT
SF,ESF1
*OUTPUT,HISTORY
*ELEMENT OUTPUT,ELSET=ALL
SF1,ESF1
*END STEP