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2.5 Computation of interface and reaction forces

In general, the stresses computed by the finite element method are not contained in one element or another. The stress vectors (normal force, tangential force) along an interface (a line or a surface) infers that the stresses are not in equilibrium on this interface (the action is different from the reaction).

Preprocessor FOINXX constructs the D.S. B of interface and reaction forces obtained by combining the element stress arrays 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, obtained at the same time the solution of the elasticity problem was computed.

Module FOINRE, called by FOINXX computes the interface and reaction forces in all or part of the elements in the mesh. In the case of a two-dimensional problem, structure B resulting from FOINRE is used to visualize the interface and reaction forces via TRMCXX (see part II of this user guide). For the three-dimensional case, structure B resulting from FOINRE is visualized via TRC3XX (see part II as before).

Program FOINRE has the following form:

      SUBROUTINE FOINRE(M,ISTRES,LINDIC,INDIC,NFTAE,NITAE,NFB,NIB,
     +       NFMAIL,NIMAIL,NFNDL1,NINDL1,NFB2,NIB2,NTB2,NOT1,NOT2)
C ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C  AIM : COMPUTE THE INTERFACE AND REACTIONAL FORCES
C  ---   RESTORE HE D.S. AND ADDRESS THE WORK ARRAYS
C ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

where

• M is the work array,
• ISTRES is an option for selecting those elements to be treated, with:

  1

  : select all the elements,

  2

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

  3

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

  4

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

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

  ISTRES = 1

  , the array is not used,

  ISTRES = 2

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

  ISTRES = 3

  , the numbers of the LINDIC elements to treat,

  ISTRES = 4

  , the numbers of the LINDIC sub-domains to treat. The elements which have these sub-domain numbers will then be selected.

• NFTAE, NITAE are the file number and level of D.S. TAE containing the element arrays. NFTAE > 0.
• NFB, NIB are the file number and level of D.S. B containing the displacements (NFB > 0: the file is sequential, NFBE = 0, the D.S. is in main memory),
• NFMAIL, NIMAIL are the file number and level of D.S. MAIL,
• NFNDL1, NINDL1, used if ND = 0, are the the file number and level of elasticity D.S. NDL1 (ND = 0 indicates that the number of degrees of freedom per node is not constant),
• NFB2, NIB2, NTB2 are the file number, the level and number of arrays to be associated to the O.D.S. B which will contain the interface forces of the selected elements (NFB2 0),
• NOT1 is the rank in TAE of element stiffness array,
• NOT2 is the rank in TAE of the element RHS array,

The input files necessary are NFB, NFTAE, NFMAIL and, in certain cases, NFNDL1. The output file is NFB2.

There is no data to input specifically for this module except if NTB2 is non-zero. In this case, the following input is required;

Loop I from 1 to NTB2

• 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.

The output structure, B, is described in [MODULEF User Guide - 2].