An alternative numerical solution of 90⁰/0⁰/90⁰ cross-ply laminated composite plate using displacement potential approach

ABSTRACT

Conventional loading with a composite plate has a very small moment of inertia due to its low height, and it was solved by shear deformation and other approaches. In the present study, a thin cross-ply 90⁰/0⁰/90⁰ laminated composite plate is erected to increase its height, which increases its moment of inertia with load; increased moments of inertia of the plate increase its load-carrying capacity in a real structure. Finite difference solutions of a cross-ply 90⁰/0⁰/90⁰ laminated plate made of T-300 carbon/epoxy are obtained using displacement potential approach. The plate behaves like a cantilever beam; one end of the plate is rigidly fixed and a uniformly distributed load is applied on its top span. The displacement potential approach is extended using the lamination theory of composite materials and plane stress concept. The different equivalent displacement, strain, and stress components at different sections of the plate with its deformed shape are discussed. Using the concept of the classical theory of laminations, different stress components along the lamina and inter-laminar regions are obtained. Besides to verify the reliability and soundness of the present numerical approach, the solutions of the present problem are compared with those of the finite element method.

KEYWORDS:

• Displacement potential approach
• finite difference (FD)
• finite element method (FEM)
• inter-laminar stress
• laminated composite plate
• layerwise stress