STK_TESTCASE_TRUSS3 provides information about the 'truss3' test case

 CALL: TC = stk_testcase_truss3 ()

    returns a structure TC that describes the 'truss3' test case, borrowed
    from [1, chapter 9].  This structure contains two fields:

     * .constants: all the numerical constants for this problem,

     * .search_domain: an stk_hrect object that specifies the search
       domain of the optimization problem.

 TEST CASE OVERVIEW

    The system considered in this test case is the following 3-bar truss:

                 <---------  D  ----------->
                 <--- w --->
           ------A==========B==============C------
                  \_        |           __/    ^
                    \_      | (2)    __/       |
                      \_    |     __/          L
                   (1)  \_  |  __/   (3)       |
                          \_P_/                v

    Nodes A, B and C are fixed (pin joints).  Node P is submitted to both
    an horizontal load F1 (e.g., wind) and a vertical load F2 (suspended
    load).

    The design variables are the cross-sections a1, a2 and a3 of the three
    bars, and the horizontal position w of the vertical bar.  The
    quantities of interest are the total volume of the structure, the
    mechanical (tensile) stress in the bars, and the displacement of P.
    Various formulations of optimization problems can be considered,
    depending on which quantities are selected as contraints and
    objectives, and whether or not uncertainties are taken into account
    (robust formulations).

 NUMERICAL CONSTANTS

    The numerical values borrowed from [1] have been converted to SI
    units.  The fields of TC.constants are:

     *       .D: truss width [m],
     *       .L: length of the vertical bar [m],
     *       .E: Young's modulus [Pa],

     *   .a_min: minimal cross-section [m^2],
     *   .a_max: maximal cross-section [m^2],
     *   .w_min: minimal value of the position of the vertical bar [m],
     *   .w_max: maximal value of the position of the vertical bar [m],

     * .F1_mean: mean (nominal) value of the horizontal load [N],
     *  .F1_std: standard deviation of the horizontal load [N],
     * .F2_mean: mean (nominal) value of the vertical load [N]
     *  .F2_std: standard deviation of the vertical load [N].

    The standard deviations F1_std and F2_std are used in the formulation
    of robust optimization problems [see 1, chap 11].
    
 NUMERICAL FUNCTIONS

    Two numerical functions are provided to compute the quantities of
    interest of this test case:

     * stk_testfun_truss3_vol: computes the total volume of the structure,

     * stk_testfun_truss3_bb: computes the tensile stress in the bars and
       the displacement of P.

    Both functions have the same syntax:

       V = stk_testfun_truss3_vol (X, CONST)

       Z = stk_testfun_truss3_bb (X, CONST)

    where CONST is a structure containing the necessary numerical
    constants.  To use the constants from [1], pass TC.constants as
    second input argument.

    Both functions accept as first input argument an N x D matrix
    (or data frame) where D is either 4 or 6:

     * columns 1--3: cross-section a1, a2 and a3,

     * column 4: position w of the horizontal bar,

     * column 5-6 (optional): horizontal and vertical loads F1, F2.

    The second function is named 'bb' for 'black box', as it plays the
    role of a (supposedly expensive to evaluate) black box computer model
    for this test case.  The output Z has five columns, corresponding to:

     * columns 1--2: horizontal and vertical displacement y1, y2 of P,

     * columns 3--5: tensile stress sigma_j in bars j = 1, 2 and 3.

 EXAMPLE

     tc = stk_testcase_truss3 ();  n = 5;

     % Draw 5 points uniformly in the 4D input domain ("design space")
     xd = stk_sampling_randunif (n, [], tc.search_domain)

     % Compute the volumes
     v = stk_testfun_truss3_vol (xd, tc.constants)

     % Compute displacements and stresses for nominal loads
     z = stk_testfun_truss3_bb (xd, tc.constants)

     % Draw loads from normal distributions
     F = stk_dataframe (zeros (n, 2), {'F1' 'F2'});
     F(:, 1) = tc.constants.F1_mean + tc.constants.F1_std * randn (n, 1);
     F(:, 2) = tc.constants.F2_mean + tc.constants.F2_std * randn (n, 1);

     % Compute displacements and stresses for the random loads
     x = [xd F]
     z = stk_testfun_truss3_bb (x, tc.constants)

 REFERENCE

  [1] Indraneel Das,  Nonlinear Multicriteria Optimization and Robust
      Optimality.  PhD thesis,  Rice University,  1997.

  [2] Juhani Koski,   Defectiveness of weighting method in multicriterion
      optimization of structures.  Int. J. for Numerical Methods in
      Biomedical Engineering,  1(6):333-337,  1985.

 See also: stk_testfun_truss3_vol, stk_testfun_truss3_bb