Static analysis of biologically motivated helicoidal/Bouligand laminated composite plates in a non-polynomial axiomatic environment

Abstract

In this work, the flexural behavior of the biologically motivated helicoidal laminated composite plate model is studied analytically by utilizing the inverse hyperbolic shear deformation theory (IHSDT) for the first time. IHSDT uses an inverse hyperbolic function to model the shear strain distribution across the thickness of the plate, effectively capturing non-linear variations and ensuring zero shear stress at the boundaries. This theory does not require shear correction factors unlike other refined theories. The minimum potential energy concept is used to determine the governing differential equations. Further, the Navier’s solution involves getting a solution in closed form by keeping the edges of the plate simply supported. Five different types of helicoidal schemes are considered here such as linear, exponential, recursive, Fibonacci, and semi-circular. The dimensionless stresses and the dimensionless central deflection are computed for various Bouligand laminated composite plate structures with 12, 16, 20, and 32 numbers of layers. Additionally, the stress distribution of helicoidal designs is examined across the thickness of the plate and distinguished with traditional layup quasi-isotropic schemes. This work is also examined with the outcomes found in the existing literature to validate the current mathematical model and solution methodology.