Transient heat transfer analysis by the boundary integral equation method

A description is presented of the first results of an exploratory study concerning an employment of the boundary integral equation method in transient analysis problems. The reported investigation is restricted to the consideration of two-dimensional conduction phenomena in classical thermoelasticity problems, taking into account isotropic conduction relations. The quasi-static case is considered, while coupling strain rates are neglected. The integral relation is discussed, taking into account the theory of distribution described by Schwartz (1966), and the utilization of the properties of a convolution product. The expression of kernels and kernel properties are considered along with the boundary integral equation. A description of the numerical treatment is provided, giving attention to questions of general process organization, assumptions for a simplified study, problems of time integration, and aspects of space integration. The described mathematical techniques are employed in an application to structure analysis.