ABSTRACT
Coupled problems in applied mechanics are generally deÞned as those requiring the solution of more than one physical process for adequate representation of the overall system. In reality, most engineering problems fall into this category, although it is still a common practice to perform single-physics analysis for many applications. Coupled phenomena are very prevalent in the areas of ßuid mechanics and heat transfer as is evident from some of the topics from previous chapters. In Chapter 3, coupled problems involving heat conduction and radiation, and heat conduction and chemical reaction were considered. At the beginning of Chapter 5 it was noted that convective heat transfer was a coupled problem since it involved two different physical phenomena, namely, ßuid mechanics and heat transfer within a ßuid. Likewise, the conjugate problem of convective heat transfer in a ßuid adjacent to a heat conducting solid is a type of coupled problem. In the present chapter we are going to revisit coupled problems, though the emphasis will be on problems involving more than one discipline or branch of mechanics. SpeciÞcally, the Þnite element solution of solid mechanics and electromagnetics problems will Þrst be presented. Subsequent sections will describe how these types of solutions may be coupled to ßuid mechanics and heat transfer simulations to provide a more complete analysis.
Boundary value problems describing different types of mechanics may be coupled through a variety of mechanisms and with varying degrees of interaction. Both of these characteristics are difficult to generalize and quantify, and lead to a certain vagueness when discussing coupled problems in generic terms. Before getting to the speciÞc cases of interest here, it is worthwhile to set some terminology and outline some of the complexities that may occur. The partial differential equations describing different phenomena are coupled
when any terms in either equation are functions of the dependent variable or its derivatives from the other equation. This functional dependence may occur directly in source or volume terms, material coefficients, and/or boundary conditions. The dependent variables from one equation may also act more indirectly on the second equation by causing alterations in the geometry of the problem and changes to the temporal behavior of the problem. The degree to which one equation is coupled to
