Multiphase circular inhomogeneities in isotropic laminated plates

Abstract

This work is concerned with a circular inhomogeneity bonded to an infinite matrix though N concentric circular interphase layers within the context of Kirchhoff theory for isotropic laminated plates. An elegant and effective procedure is proposed to obtain the stress resultant fields within the internal inhomogeneity and the surrounding matrix under thermomechanical loadings. The boundary value problem is finally reduced to two coupled linear algebraic equations and four coupled linear algebraic equations that determine the six real coefficients of the stress resultant field in the inhomogeneity. In particular, the average stress resultants within the inhomogeneity can be directly determined from these six real coefficients. The other six unknown real coefficients, which control the stress resultant field in the surrounding matrix, can then be simply obtained. The effect of the N interphase layers on the stress resultant field is demonstrated by their influence on these 12 real coefficients. The obtained solution is further applied to the design of neutral and harmonic circular elastic inhomogeneities with a single interphase layer.