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$                       RIGID FORMAT No. 1, Static Analysis
$           Free Rectangular (QDMEM) Plate with Thermal Loading (1-3-1)
$          Free Rectangular (QDMEM1) Plate with Thermal Loading (1-3-2)
$          Free Rectangular (QDMEM2) Plate with Thermal Loading (1-3-3)
$ 
$ A. Description
$ 
$ Problem 1-3-1 demonstrates the use of thermal loading conditions and
$ temperature-dependent materials. The model, a rectangular plate, is given a
$ temperature gradient which causes internal loads and elastic deflections.
$ Since there are two planes of symmetry, only one-quarter of the structure
$ needs to be modeled. The analysis has been performed using three different
$ NASTRAN membrane plate elements. The two variations of this problem are
$ obtained by replacing the quadrilateral membrane elements, QDMEM, with QDMEM1
$ and QDMEM2 membrane elements to illustrate their application to this type of
$ problem (Problems 1-3-2 and 1-3-3, respectively).
$ 
$ B. Input
$ 
$ The temperature load is constant in the y direction and symmetric about the y-
$ axis. Since membrane elements are used to model the structure, it is necessary
$ to remove all rotational degrees of freedom and translational degrees of
$ freedom normal to the membrane. The symmetric boundary conditions were modeled
$ by constraining the displacements normal to the planes of symmetry. The
$ material used has temperature-dependent elasticity (as defined in Reference
$ 5); therefore, the INPUT module cannot be used for this application. The
$ CNGRNT bulk data card can be used if the congruency is defined in one
$ direction.
$ 
$ 1. Parameters
$ 
$      L =  36.0 in                   (length)
$ 
$      W =  24.0 in                   (width)
$ 
$      t =   0.25 in                  (thickness)
$ 
$                     6      2
$      E =  10.4  x 10  lb/in         (modulus of elasticity at T )
$                                                                o
$      v =   0.3                      (Poisson's ratio)
$                     -6
$  alpha =  12.7  x l0   in/in/deg. F (thermal expansion coefficient)
$ 
$      T  = 75.0  deg. F              (thermal expansion reference temperature)
$       o
$ 
$ 2. Constraints
$ 
$      u  = 0.0 at x = 0.0
$       x
$ 
$      u  = 0.0 at y = 0.0
$       y
$ 
$      u  = theta sub x = theta sub y = theta sub z = 0.0  at all Grids
$       z
$ 
$ 3. Loads
$ 
$ The thermal loading is specified with TEMP Bulk Data cards. Young's modulus is
$ specified as a function of temperature with MATT1 and TABLEM1 cards.
$ 
$ C. Results
$ 
$ There is no theoretical solution to this problem. However, this problem
$ represents a model of a laboratory experiment described in Reference 5.
$ 
$ APPLICABLE REFERENCES
$ 
$ 5. Richard R. Heldenfels and William M. Roberts, "Experimental and Theoretical
$    Determination of Thermal Stresses in a Flat Plate", NACA TN 2769, 1952.
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