## A Simplified Method of Determining the Elastic State of Thermal Stress in a Thin, Flat Plate of Finite Dimensions |

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Aeronautics and Space Alexander A SIMPLIFIED Alexander Mendelson boundary conditions chordwise displacement closely satisfied everywhere collocation method conditions are satisfied defines the behav desk calculator Dimensionless span coordinate dimensions is derived employs polynomial approxi equation 13 equation that defines Ernest Roberts examples finite dimensions Finite-difference solution flat plate high accuracy integrodifferential equation linear algebraic equa METHOD OF DETERMINING method that employs minimum of labor NASA NASA TN NASA TECHNICAL NOTE National Aeronautics number of stations odd function ordinary differential equations OTS price PARABOLIC THERMAL GRADIENT placements shows plate of finite presented in detail quadrant satisfied identically shear stresses show that solutions shown in figure SIMPLIFIED METHOD solutions of high Space Administration spanwise and chordwise spanwise displacement square plate subjected station collocation strain compatibility condi SUBJECTED TO CHORDWISE system of linear TECHNICAL NOTE D-1740 temperature function THERMAL STRESS thermally loaded tion is reduced tions are closely TN D-1740 ELASTIC