Composite and functionally graded materials are used commonly in a broad variety of engineering systems. This work presents theoretical bending analysis of a simply supported heterogeneous rectangular plate containing discrete inclusions of irregular shapes. The commonly used governing equation for a homogeneous plate is generalized by accounting for inclusions of irregular shapes and different mechanical properties embedded within the plate. The heterogeneous plate problem is then solved by representing the spatial distributions of elastic moduli and Poisson’s ratios using Heaviside functions, thereby enabling an exact and efficient modeling of sharp discontinuities in these properties at the plate-inclusion interfaces. A series solution for the displacement field is derived using the integral and differential properties of the Heaviside function. The derivation is an exact generalized approach to handle multi-inclusion configurations with nonuniform properties, in contrast with previously presented approximate techniques such as homogenization and laminate approximation. Results are shown to reduce to the well-known Navier solution under special conditions. Good agreement with independent finite element simulations is also shown. A key finding of this work is that the location and shape of discrete inclusions, particularly their intersection with the high-bending regions of the plate, significantly influence the magnitude and spatial distribution of transverse deflection. Notably, stiff inclusions tend to displace the deflection peak away from themselves, while soft inclusions attract it, and in both cases, proximity to the plate boundaries can reverse these trends due to geometric and support-induced constraints. The technique developed here enables analysis of a number of practical problems comprising heterogeneous composites, as demonstrated through several examples. In addition to extending the state-of-the-art in theoretical analysis of composite structures, this work may also find practical applications in a number of engineering systems where such materials are used commonly.
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