An overview of layerwise theories for composite laminates and structures: Development, numerical implementation and application

Over the past decades, a vast number of theories for numerical modeling of laminated composite plates and shells has been developed by various researchers and for diverse reasons. Three-dimensional elasticity theory, equivalent single-layer theories, zig-zag theories and layerwise theories are notable examples. In general, computing 3D elasticity solutions require huge computational time, the ESL theories cannot furnish satisfying results for thick laminates or laminates with distinct properties between layers, and the zig-zag theories cannot directly obtain the transverse stress fields from the constitutive model. The layerwise theory treats each layer individually and C-z(0) continuity is satisfied from the beginning; therefore, it yields results comparable to 3D elasticity solutions. These attributes and advantages have driven the prosperity of layerwise theories for analysis of composite laminates and structures. The main aim of this review is to provide the recent development of layerwise theories, their numerical implementation, and application in the analysis of composite laminated structures. The main conclusions and possible future research trends are presented. We expect this review will provide a clear picture of layerwise theory for modeling of composite laminated structures and serve as a useful resource and guide to researchers who intend to extend their work into these research areas.