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2.6 Computing the stresses (D.S. TAE)

Preprocessor STREXX constructs a D.S. TAE containing the stresses by combining the array containing the element stresses of D.S. TAE, set up at the same time as the element matrices and right-hand-sides, with D.S. B containing the displacements, constructed at the same time the solution to the elasticity problem was computed.

All the finite elements in elasticity are possible.

Module STRESS, called by STREXX calculates the stresses in each element at the barycentre or at the numerical integration points (see technical files) and, in addition, can print the stresses of all or part of the elements in the mesh. For a two-dimensional problem (the visualization of the three-dimensional case has not been implemented), structure TAE resulting from STRESS is used to visualize the stresses (see TRSTXX in part II of this user guide).

Program STRESS has the following form:

      SUBROUTINE STRESS(M,XM,ISTRES,LINDIC,INDIC,NFBE,NIBE,NFBT,NIBT,
     +                  NFTAE,NITAE,NFNDL1,NINDL1,NFNDL2,NINDL2,
     +                  NFMAIL,NIMAIL,NFTAES,NITAES,NTTAES)
C   ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C   MODULE  STRESS : COMPUTE THE STRESSES DURING THE SOLUTION OF AN
C   --------------   ELASTICITY PROBLEM FROM THE ELEMENT STRESSES
C                    AND THE SOLUTION
C   ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

where

• M and XM represent the work array,
• ISTRES is the stress print option. ISTRES is set to IJK where:

  I = 1

  : print all the elements,

  I = 2

  : print the elements lying between numbers N1 and N2 given in INDIC,

  I = 3

  : print the LINDIC elements whose numbers are given in INDIC,

  I = 4

  : print the elements whose sub-domain numbers (LINDIC numbers) are given in INDIC,

  J = 1

  , if the principal stresses should be printed, 0 if not,

  K = 1

  , if the principal directions should be printed (I forced to equal 1), 0 if not,

• LINDIC, a function of I, is the length of array INDIC,
• INDIC, a function of I, is the following array:

  I = 1

  , the array is not used,

  I = 2

  , length 2, the array contains the number of the first and last element to print,

  I = 3

  , the number of the LINDIC elements to print,

  I = 4

  , the number of the LINDIC sub-domains to treat. Stresses of all the elements with these sub-domain numbers will be selected.

• NFBE, NIBE are the file number and the level of D.S. B containing the displacements (NFBE > 0: the file is sequential, NFBE = 0, the D.S. is in main memory, NFBE < 0, the file is in direct access),
• NFBT, NIBT, the same for the D.S. B containing the temperatures (thermoelastic case),
• NFTAE, NITAE are the file number and the level of D.S. TAE containing the element arrays (including the element stresses) NFTAE > 0,
• NFNDL1, NINDL1, used if ND = 0, are the file number and the level of the elasticity D.S. NDL1 (ND = 0 indicates that the number of degrees of freedom per node is not constant),
• NFNDL2, NINDL2, used if ND = 0, are the file number and the level of the thermal D.S. NDL1,
• NFMAIL, NIMAIL are the file number and the level of D.S. MAIL,
• NFTAES, NITAES, NTTAES are the file number, the level and the number of arrays to be associated with the O.D.S TAE which contains the stresses element by element (NFTAES > 0).

The input files necessary are NFBE, NFTAE, NFMAIL and, in certain cases, NFBT, NFNDL1 and NFNDL2. The output file is NFTAES.

There is no input data required specifically for this module except in the case where NTTAES is non-zero. In this case, the following data is required:

Loop I from 1 to NTTAES

• name of array I in 4 characters,
• array type (1 = integer, 2 = real single precision, 4 = character, 5 = real double precision, ...),
• number of words in this array,
• variables in this array,
• comments pertaining to the contents of array I in 10 words of 4 characters.

Note that depending on ISTRES, the computation of eigenvalues and eigenvectors is either performed or not. Subroutine VPM2DD computes the eigenvalues and eigenvectors for the two-dimensional case. VAM3DD computes the eigenvalues whereas VPM3DD computes the eigenvectors for the three-dimensional case.

The TAE structure resulting from module STRESS contains the informations corresponding to the stresses of all the elements in the mesh. Module COMTAE is employed to select certain elements only and to construct the corresponding D.S. TAE.

    

      SUBROUTINE COMTAE(M,ISTRES,INDIC,LINDIC,NFTAE,NITAE,NFTAES,NITAES)
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C  MODULE COMTAE : COMPRESS D.S. TAES ( RESULTING FROM STRESS )
C  -------------   ONLY THE ELEMENTS OF INDIC AND ISTRES ARE RETAINED
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

where:

• M represent the work array,
• ISTRES is the stress print option. ISTRES is set to I00 where:

  I = 1

  : select all the elements,

  I = 2

  : select the elements lying between numbers N1 and N2 given in INDIC,

  I = 3

  : select the LINDIC elements whose numbers are given in INDIC,

  I = 4

  : select the elements whose sub-domain numbers (LINDIC numbers) are given in INDIC,

• INDIC, a function of I, is the following array:

  I = 1

  , the array is not used,

  I = 2

  , length 2, the array contains the number of the first and last element to select,

  I = 3

  , the number of the LINDIC elements to select,

  I = 4

  , the number of the LINDIC sub-domains to treat. Stresses of all the elements with these sub-domain numbers will be selected.

• LINDIC, a function of I, is the length of array INDIC,
• NFTAE, NITAE are the file number and the level of D.S. TAE resulting from STRESS,
• NFTAES, NITAES are the file number and the level of O.D.S. TAE containing the stresses of the selected elements
  (NFTAES > 0 and NFTAES NFTAE).

The input file required is NFTAE. The output file is NFTAES.

There is no input data required specifically for this module.