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Thermal stresses in rectangular plates
Authors:K T Sundara Raja Iyengar and K Chandrashekhara
Institution:(1) Indian Institute of Science, Bangalore, India
Abstract:Summary A method of determining the thermal stresses in a flat rectangular isotropic plate of constant thickness with arbitrary temperature distribution in the plane of the plate and with no variation in temperature through the thickness is presented. The thermal stress have been obtained in terms of Fourier series and integrals that satisfy the differential equation and the boundary conditions. Several examples have been presented to show the application of the method.Nomenclature x, y rectangular coordinates - sgr x, sgry direct stresses - tau xy shear stress - ø Airy's stress function - E Young's modulus of elasticity - agr coefficient of thermal expansion - T temperature - xdtri 2 Laplace operator: 
$$ - \left( {\frac{{\partial ^2 }}{{\partial x^2 }} + \frac{{\partial ^2 }}{{\partial y^2 }}} \right)$$
- xdtri 4 biharmonic operator 
$$\left( {\frac{{\partial ^4 }}{{\partial x^4 }} + 2\frac{{\partial ^4 }}{{\partial x^2 \partial y^2 }} + \frac{{\partial ^4 }}{{\partial y^4 }}} \right)$$
- 2a length of the plate - 2b width of the plate - a/b aspect ratio - a mr, bms, cnr, dns Fourier coefficients defined in equation (6) - agr m=mpgr/a m=1, 2, 3, ... beta n=npgr/2a n=1, 3, 5, ... - gamma r=rpgr/b r=1, 2, 3, ... delta s=spgr/2b s=1, 3, 5, ... - A m, Bm, Cn, Dn, Er, Fr, Gs, Hs Fourier coefficients - K rand L s Fourier coefficients defined in equation (20) - sgrinfin direct stress at infinity - T 1(x, y) temperature distribution symmetrical in x and y - T 2(x, y) temperature distribution symmetrical in x and antisymmetrical in y - T 3(x, y) temperature distribution antisymmetrical in x and symmetrical in y - T 4(x, y) temperature distribution antisymmetrical in x and y
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