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Aircraft structure subjected to elevated temperature presents a challenging design environment as damaging thermal stress can result. Thermal stress in a structural component is typically alleviated by accommodating the thermal expansion. However, very little work has been done that directly addresses the situation where such a prescription for expansion is not possible. When a structural component is failing due to tensile stresses which are thermally induced, the answer to the question of how best to stiffen the structure in this environment is far from trivial. This work demonstrates that conventional stiffening techniques, for example, thickness increase, may actually increase the rate of damage, as well as generate additional load that must be reacted by sub- and surrounding structure. Because flat plates represent a common structural element that is susceptible to developing tensile stresses due to thermally induced out-of-plane deformation, a simple strip model which represents cylindrical bending in a semi-infinite flat plate is chosen as the focus of this work.

Interlaminar stress distribution in smart composite shells using a coupled thermal-piezoelectric-mechanical model is investigated. To maintain local accuracy of stress distributions, the trial displacement field is assumed layerwise higher order and Co continuous through the entire laminate thickness, accommodating zigzag in-plane warping and interlaminar shear stress continuity. The temperature and electrical fields are modeled using higher. order descriptions that can satisfy surface flux boundary conditions at structural surfaces and equipotential conditions at electrode surfaces. These assumptions ensure computational efficiency. A variational principle, addressing the interaction between thermal, piezoelectric, and mechanical fields, is used to derive the governing equations of equilibrium. The proposed theory is used to investigate the cylindrical bending problem of simply supported composite host structures with attached piezoelectric actuators, subject to a combination of mechanical, piezoelectric, and thermal loading. The interlaminar stress distributions under comprehensive loading are presented for different geometries and stacking sequences. The effects of two-way piezoelectric and thermal coupling on the stress distributions are investigated. The significance of the thermal mismatch effect on interlaminar stress distribution is also discussed. The results from present theory are validated with available exact elasticity solutions.

An exact solution is obtained for three-dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and/or bottom surfaces. Suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate, which are then solved by employing the power series method. The exact solution is applicable to both thick and thin plates. Results are presented for two-constituent metal--ceramic functionally graded rectangular plates that have a power law through-the-thickness variation of the volume fractions of the constituents. The effective material properties at a point are estimated by either the Mori--Tanaka or the self-consistent schemes. Exact displacements and stresses at several locations for mechanical and thermal loads are used to assess the accuracy of the classical plate theory, the first-order shear deformation theory, and a third-order shear deformation theory for functionally graded plates. Results are also computed for a functionally graded plate with material properties derived by the Mori--Tanaka method, the self-consistent scheme, and a combination of these two methods.

Thermal buckling of circular plates made of functionally graded material is discussed. The nonlinear equilibrium and linear stability equations are derived using variational formulations. The thermal buckling of solid circular plates under uniform temperature rise, gradient through the thickness, and linear temperature variation along the radius are considered, and the buckling temperatures are derived. The buckling temperatures are derived for simply supported and clamped edges. The results are verified with known results in the literature.

Thermoelastic equilibrium equations for a functionally graded beam are solved in closed-form to obtain the axial stress distribution. The thermoelastic constants of the beam and the temperature were assumed to vary exponentially through the thickness. The Poisson ratio was held constant. The exponential variation of the elastic constants and the temperature allow exact solution for the plane thermoelasticity equations. A simple Euler-Bernoulli-type beam theory is also developed based on the assumption that plane sections remain plane and normal to the beam axis. The stresses were calculated for cases for which the elastic constants vary in the same manner as the temperature and vice versa. The residual thermal stresses are greatly reduced, when the variation of thermoelastic constants are opposite to that of the temperature distribution. When both elastic constants and temperature increase through the thickness in the same direction, they cause a significant raise in thermal stresses. For the case of nearly uniform temperature along the length of the beam, beam theory is adequate in predicting thermal residual stresses.

The application of new approximation tools for thermal structural approximation has been evaluated. The method has been used to calculate the minimum mass design of structures subjected to stress, displacement and temperature constraints. The efficiency of the method is based on the two-point approximation of the function, consideration of coupling between the heat transfer and structural analysis and approximation of the internal forces instead of stresses.

Results demonstrate nonlinear characteristics of the temperature-frequency curves exhibited by the pretwisted composite laminated plates.

Chen and Cheung's reformulated boundary integral equation was extended to solve notch problems in plane elasticity. The resultant heat flow Q and the resultant force -Y + iX were used to formulate the boundary conditions along the notch surface which created singular integral equations with a logarithmic kernel. Three different types of notches were considered to demonstrate the accuracy of the approach.

A study for predicting thermally induced deformations and stresses in eccentrically stiffened composite laminates is conducted. The constitutive relations of a laminated composite stiffener have been derived. Numerical results for an eccentrically stiffened composite laminate subjected to a uniform temperature change within the plane of the plate but having a linear gradient through the thickness has been derived.