Calculating Element Strain Energy

Transcription

1 WORKSHOP PROBLEM 7 Calculating Element Strain Energy Objectives: Procedure: Calculate the element strain energy per mode due to elment stiffness generated from DMIG input 1 Submit the following cantilever beam model consisting of two bar elments This is a planar problem retaining only the 2 and 6 degrees of freedom Review the strain energy output y x 2 Comment out cbar, 11 from the input file for modification and replace the stiffness with the following equivalent DMIG matrix A k2gg=stiff Case Control command is required 3 Write a dmap to calculate the strain energy generated by the DMIG entries 4 Put the strain energy calculation inside a subdmap 5 Use the MESSAGE module to format the strain energy output, mode by mode DMAP Exercise Workbook - Version

2 Hints: The DMIG stiffness matrix is saved as k2jj This datablock needs to be saved inside the SEMG1 module to be retrieved later on The strain energy datablock is called ONRGY1 and is printed inside the SEDRCVR module Other possible useful modules: DBSTORE DBFETCH SMPYAD PARAML 7-2 DMAP Exercise Workbook - Version 75

3 Equivalent DMIG matrix: dmig stiff 6 1 DMIG NAME GJ CJ G1 C1 A1 dmig stiff dmig stiff dmig stiff dmig stiff DMAP Exercise Workbook - Version

4 Input File for Modification: wkshp7dat wkshp7adat - baseline bar model id bar stiff sol 13 time 1 cend title = two bar example spc = 1 disp = all method = 1 ese = all echo = punch begin bulk CBAR CBAR CONM CONM EIGRL 1 2 GRDSET 1345 GRID 1 GRID 2 1 GRID 3 2 GRID MAT PARAM WTMASS 259 PBAR SPC ENDDATA 7-4 DMAP Exercise Workbook - Version 75

5 Solution Input File: soln7dat wkshp7dat replace bar # 11 using dmig id dmig stiff sol 13 diag 8 COMPILE SEMG1 ALTER add*k2jj CALL DBSTORE K2JJ,,,,//// / COMPILE SEDRCVR ALTER OFP*ONRGY1 (1,-1) CALL STRNENRG UG // COMPILE STRNENRG SUBDMAP STRNENRG UG // TYPE PARM,,I,N,NUMMODES,NVALS TYPE PARM,,RS,N,REX TYPE PARM,,RS,Y,TINY DMIG Processing CALL DBFETCH /K2JJ,,,,///// PARAML K2JJ// PRESENCE ////S,N,NOK2JJ IF (NOK2JJ <> -1) THEN matprn k2jj // SMPYAD UG,K2JJ,UG,,,/ESEK2JJ/3////1/// matprn esek2jj// PARAML ESEK2JJ// trailer /1/S,N,NVALS NUMMODES = 1 DO WHILE (NUMMODES <= NVALS) PARAML ESEK2JJ// DMI /NUMMODES/NUMMODES/S,N,REX REX = 5 * REX MESSAGE // MESSAGE // MODE Number /NUMMODES MESSAGE // Strain Energy of DMIG /REX MESSAGE // MESSAGE // NUMMODES = NUMMODES + 1 ENDDO ENDIF NOK2JJ RETURN END cend title = two bar example DMAP Exercise Workbook - Version

6 subtitle = replace one bar with dmig spc = 1 disp = all method = 1 k2gg = stiff ese = all begin bulk cbar conm conm dmig stiff 6 1 DMIG NAME GJ CJ G1 C1 A1 dmig stiff dmig stiff dmig stiff dmig stiff eigrl 1 3 grdset 1345 grid 1 grid 2 1 grid 3 2 grid mat param wtmass 259 pbar spc enddata 7-6 DMAP Exercise Workbook - Version 75

7 Partial Output with CBAR,11: Compare the results obtained in the f6 file with the results below: R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO ORDER MASS STIFFNESS E E E+1 1E E E E E+2 1E E+6 E L E M E N T S T R A I N E N E R G I E S ELEMENT-TYPE = BAR * TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM = E+5 MODE 1 TOTAL ENERGY OF ALL ELEMENTS IN SET -1 = E+5 * ELEMENT-ID STRAIN-ENERGY PERCENT OF TOTAL STRAIN-ENERGY-DENSITY E E E E+3 1 TWO BAR EXAMPLE TYPE = BAR SUBTOTAL E+5 1 E L E M E N T S T R A I N E N E R G I E S ELEMENT-TYPE = BAR * TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM = E+6 MODE 2 TOTAL ENERGY OF ALL ELEMENTS IN SET -1 = E+6 * ELEMENT-ID STRAIN-ENERGY PERCENT OF TOTAL STRAIN-ENERGY-DENSITY E E E E+5 1 TWO BAR EXAMPLE TYPE = BAR SUBTOTAL E+6 1 DMAP Exercise Workbook - Version

8 Partial Output where CBAR,11 Replaced with DMIG: Compare the results obtained in the f6 file with the results below: R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO ORDER MASS STIFFNESS E E E+1 1E E E E E+2 1E E+6 MATRIX K2JJ (GINO NAME 11 ) IS A DB PREC 24 COLUMN X 24 SYMMETRC MATRIX COLUMNS 1 THRU 1 ARE NULL COLUMN 2 S 2 THRU ) 29988D+4 D+ D+ D D+5 D D+4 D+ D+ D+ 12) 14994D+5 COLUMNS 3 THRU 5 ARE NULL COLUMN 6 S 2 THRU ) 14994D+5 D+ D+ D+ 9996D+5 D D+5 D+ D+ D+ 12) 4998D+5 COLUMNS 7 THRU 7 ARE NULL COLUMN 8 S 2 THRU ) D+4 D+ D+ D D+5 D D+4 D+ D+ D+ 12) D+5 COLUMNS 9 THRU 11 ARE NULL COLUMN 12 S 2 THRU ) 14994D+5 D+ D+ D+ 4998D+5 D D+5 D+ D+ D+ 12) 9996D+5 COLUMNS 13 THRU 24 ARE NULL THE NUMBER OF NON-ZERO TERMS IN THE DENSEST COLUMN = 4 THE DENSITY OF THIS MATRIX IS 278 PERCENT 1 TWO BAR EXAMPLE REPLACE ONE BAR WITH DMIG MATRIX ESEK2JJ (GINO NAME 11 ) IS A DB PREC 2 COLUMN X 2 SQUARE MATRIX COLUMN 1 S 1 THRU ) 19667D D+5 COLUMN 2 S 1 THRU DMAP Exercise Workbook - Version 75

9 1) -3247D D+6 THE NUMBER OF NON-ZERO TERMS IN THE DENSEST COLUMN = 2 THE DENSITY OF THIS MATRIX IS 1 PERCENT ^^^ ^^^MODE NUMBER 1 ^^^STRAIN ENERGY OF DMIG E+4 ^^^ ^^^ ^^^ ^^^MODE NUMBER 2 ^^^STRAIN ENERGY OF DMIG E+6 ^^^ ^^^ TWO BAR EXAMPLE P REPLACE ONE BAR WITH DMIG E L E M E N T S T R A I N E N E R G I E S ELEMENT-TYPE = BAR * TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM = E+4 MODE 1 TOTAL ENERGY OF ALL ELEMENTS IN SET -1 = E+4 * ELEMENT-ID STRAIN-ENERGY PERCENT OF TOTAL STRAIN-ENERGY-DENSITY E E+3 1 TWO BAR EXAMPLE REPLACE ONE BAR WITH DMIG TYPE = BAR SUBTOTAL E+4 1 E L E M E N T S T R A I N E N E R G I E S ELEMENT-TYPE = BAR * TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM = E+6 MODE 2 TOTAL ENERGY OF ALL ELEMENTS IN SET -1 = E+6 * ELEMENT-ID STRAIN-ENERGY PERCENT OF TOTAL STRAIN-ENERGY-DENSITY E E+5 TYPE = BAR SUBTOTAL E+6 1 DMAP Exercise Workbook - Version