The modulus of elasticity and coefficient of thermal expansion are treated throughout this text as constants over the temperature ranges involved. Stresses due to the restriction of thermally induced expansion or contraction of a body are called thermal stresses. It is observed that if a free plate is heated uniformly, normal strains are produced but no thermal stresses. When, however, the plate experiences a nonuniform temperature field, if the displacements are prevented from occurring freely because of the restrictions placed on the boundary even with a uniform temperature, or if the material displays anisotropy even with uniform heating, thermal stresses will occur.
First, reformulation of the stress–strain relationships is accomplished by superposition of the strains caused by stress and by temperature. For homogeneous isotropic materials, a change in temperature produces uniform linear strain in every direction. Then, the stress resultants and the governing equations are developed. Simply supported rectangular plates subject to an arbitrary temperature distribution and with temperature varying over the thickness are discussed. Analogy between thermal and isothermal plate problems is demonstrated for clamped and simple support or free edge conditions. The chapter concludes with a discussion of axisymmetrically heated circular plates.