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UCORR

User subroutine to define cross-correlation properties for random response loading.

User subroutine UCORR:

can be used to define the coefficients for the cross-correlation matrix in a random response analysis;
will be called once for the combination of any two degrees of freedom with nonzero prescribed loads for each load case specified as a concentrated or distributed load or once for the combination of any two excitation directions specified as a base motion;
allows correlation coefficients to be defined as a function of nodal coordinates; and
ignores any data specified outside the user subroutine for the associated cross-correlation matrix.

This page discusses:

Cross-Correlation for Base Motion Excitation
Cross-Correlation for Point Loads and Distributed Loads
User Subroutine Interface
Variables to Be Defined
Variables Passed in for Information

Cross-Correlation for Base Motion Excitation

The spatial correlation matrix for base motion excitation is defined by the coefficients $Ψ_{i j}^{I J}$ in user subroutine UCORR, where $i, j$ are excitation directions and J corresponds to the Jth frequency function referenced under load case I.

Cross-Correlation for Point Loads and Distributed Loads

The spatial correlation matrix of the load is defined as follows. Let $F_{(N, i)}^{I}$ be the load applied to degree of freedom i at node N in load case I, through the use of a concentrated or distributed load. Let J correspond to the Jth frequency function referenced under load case I. The spatial correlation matrix used in the random response analysis for this load case is then

$Ψ_{(N, i) (M, j)}^{I J} = C_{(N, i) (M, j)}^{I J} F_{(N, i)}^{I} F_{(M, j)}^{I},$

where $C_{(N, i) (M, j)}^{I J}$ are the coefficients defined in user subroutine UCORR. Typically the load magnitude is given as 1.0; therefore, the load definition is simply selecting the nonzero terms that will appear in $Ψ_{(N, i) (M, j)}^{I J}$ .

User Subroutine Interface

      SUBROUTINE UCORR(PSD,CORRR,CORRI,KSTEP,LCASE,JNODE1,JDOF1,
     1 JNODE2,JDOF2,COOR1,COOR2)
C
      INCLUDE 'ABA_PARAM.INC'
C
      DIMENSION COOR1(3),COOR2(3)
      CHARACTER*80 PSD


      user coding to define CORRR and CORRI


      RETURN
      END

Variables to Be Defined

CORRR: Real part of the cross-correlation scaling factor.
CORRI: Imaginary part of the cross-correlation scaling factor.

Variables Passed in for Information

PSD: User-specified name for the frequency function that references this correlation, left justified.
KSTEP: Step number.
LCASE: Load case number, I.
JNODE1: First node involved, N (not used for base motion excitation).
JDOF1: Degree of freedom i at the first node (for concentrated or distributed load excitation) or global excitation direction i (for base motion excitation).
JNODE2: Second node involved, M (not used for base motion excitation).
JDOF2: Degree of freedom j at the second node (for concentrated or distributed load excitation) or global excitation direction j (for base motion excitation).
COOR1: An array containing the coordinates of the first node (not used for base motion excitation).
COOR2: An array containing the coordinates of the second node (not used for base motion excitation).