A new finite element for treating plane thermomechanical heterogeneous solids

This study is concerned with the development and implementation of a new fi nite element which is capable of treating the problem of interacting circul ar inhomogeneities in heterogeneous solids under mechanical:and thermal loa dings. The general form of the element,which is constructed from a cell con taining a single circular inhomogeneity in a surrounding matrix, is derived explicitly using the complex potentials of Muskhelishvili and the Laurent series expansion method. The newly proposed eight-noded plane element can b e used to treat quite readily the two-dimensional steady-state heat conduct ion and thermoelastic problems of an elastic circular inclusion embedded in an elastic matrix with different thermomechanical properties. Moreover, th e devised element may be applied to deal with arbitrarily and periodically located multiple inhomogeneities under general mechanical and thermal loadi ng conditions using a very limited number of elements. The current element also enables the determination of the local and effective thermoelastic pro perties of composite materials with relative ease. Three numerical examples are given to demonstrate its versatility, accuracy and efficiency. Copyrig ht (C) 1999 John Wiley & Sons. Ltd.