Abstract:
This research addresses a new analysis of the elastic field of laminated composite structures
under the influence of discrete stiffeners at the bounding surfaces. In this work, theory of
elasticity, a new potential function, constitutive relations for composite materials, special
lamination theory and finite-difference computational algorithm are integrated to develop a
new computational scheme for stress analysis of laminated composite structures. Specific
contribution are follows:
A new mathematical formulation is developed for the analysis of structural components
of laminated composites with mixed and changeable boundary conditions. In this formulation,
the displacement components of plane elasticity are expressed in terms of a single
potential function, which satisfies one of the equilibrium equations automatically. The remaining
equilibrium equation is transformed into a fourth order partial differential equation
of the unknown potential function. Thus the mixed boundary value plane elasticity problem
is reduced to the solution of a single fourth order partial differential equation. The finite
difference technique is used to develop an efficient computational algorithm based on the
potential function formulation.
A general computer program is developed based on the finite difference computational
algorithm, which is capable of dealing with almost all the special cases of composite material,
namely orthotropic and anisotropic lamina, angle-ply and cross-ply symmetric laminates,
symmetric balanced laminates, etc., with mixed and changeable physical conditions at
the surfaces of the structural composites.
The application of the computational scheme is investigated to stress analysis of disxxi
NOMENCLATURE xxii
cretely stiffened panels of laminated composites. A number of practical problems of interest
are solved and results are presented in the form of graphs. The problem includes symmetric
and antisymmetric discretely stiffened laminated cantilever under shear loading, a laminated
panel with periodic axial stiffeners subjected to eccentric loading and a laminated cantilever
panel with discrete variable stiffeners.
Finally, in an attempt to validate the new computational method, the potential function
solutions are compared with both analytical and numerical solutions obtained by standard
computational method. For this purpose, finite element solutions are obtained using the
commercial FEM software, SAP2000. For all the problems, both the numerical solutions are
found to be in excellent agreement with each other, which in turn, establishes the suitability
and appropriateness of the present potential function computational scheme.
