A new finite element for treating plane thermomechanical heterogeneous solids

This study is concerned with the development and implementation of a new nite element which is capable of treating the problem of interacting circular inhomogeneities in heterogeneous solids under mechanical and thermal loadings. The general form of the element, which is constructed from a cell containing 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 be used to treat quite readily the two-dimensional steady-state heat conduction and thermoelastic problems of an elastic circular inclusion embedded in an elastic matrix with di erent thermomechanical properties. Moreover, the devised element may be applied to deal with arbitrarily and periodically located multiple inhomogeneities under general mechanical and thermal loading conditions using a very limited number of elements. The current element also enables the determination of the local and e ective thermoelastic properties of composite materials with relative ease. Three numerical examples are given to demonstrate its versatility, accuracy and e ciency. Copyright