Analytical stresses of homogeneous and composite laminated non-prismatic beams under layerwise loading

Innovative engineering solutions often require lightweight, stiff structures to meet specific design criteria. Consequently, potential solutions comprise slender structural elements with optimised mass distributions made from a combination from materials often using composite laminates.

Classical beam theory remains utilised to investigate the state of stress of non-prismatic slender structures, although adopted hypotheses are not appropriate for tapered beams, which behave differently from their prismatic counterparts. For example, the bending moment contributes to the shear stress, and specific equilibrium considerations govern layer interfaces and beam surfaces.

Although widely accepted in beam theories, the classical assumption that external loads are reacted uniformly through the cross-section may need refinement to account for load cases where the load is applied to part of the cross-sectional area, e.g. beams subject to partial cross-sectional loading in prestressed concrete structures and partially-immersed slender structures subject to fluid interactions.

The state-of-the-art limitations are addressed in this thesis by deriving a consistent stress recovery method for non-prismatic beams subject to layerwise loading. Analytical solutions are given for homogeneous materials, multilayered media and composite laminates. Cauchy stress equilibrium is invoked considering adequate equilibrium relations, boundary conditions and beam eccentricity effects.

The developed theory is computationally efficient and accurate; hence it could be utilised as a benchmark solution for numerical methods and assessed in the early design stage.