ANALYSIS OF COMPOSITE PLATES WITH MATERIAL UNcERTA N"~"'. IES USING HIGHER ORDER SHEAR DEFORMATION THEORY

Abstract

Laminated FRP (Fiber Reinforced Polymer or Plastic) composites are widely used in many recent civil engineering applications such as roof of buildings, bridge decks, structural panels, beams etc. Using laminated composite materials in construction give many advantages such as high strength / stiffness to weight ratio, sevivability in extreme weather conditions, durability, fatigue resistance and design flexibility (three-dimensional forms molded in place), easy to install in structure replacement. It is anticipated that in coming days composite materials are going to replace the present day traditional construction materials in many applications. However, FRP composite materials are relatively weak in shear compared to extensional rigidity. As such the shear deformation has to be modeled very efficiently in such laminated FRP structures. Moreover, the material properties of these FRP composite structures may vary randomly due to various environmental and other factors related to manufacturing and curing. Some of the main parameters in analysis and design of composite plates are deflections, stresses and natural frequencies which are stochastic processes. However, design engineers prefer a deterministic approach invoking mean of structural responses (deflections, stresses and natural frequencies) and rather empirical factors of safety to account for uncertainty. The present study includes the stochasticity in the deterministic designs by linking the factor of safety (in respect of deflections, stresses and natural frequencies) to the allowable probability of failure through a Monte Carlo simulation on a distributed parameter deterministic model. A parametric study reveals that for a given probability of failure level, the factors of safety are strongly dependent upon the coefficient of variations of the material properties, and only mildly upon geometric parameters. This facilitates development of closed form equations for the upper bounds on factors of safety exclusively in terms of allowable probability of failure and the coefficient of variation of structural responses. In this dissertation, studies have been carried out, for static as well as vibration analysis of laminated composite plates using a higher order shear deformation theory considering uncertainty in the material parameters through different values of coefficient of variations for the material properties. A FORTRAN program is developed to find out the necessary results like deflections/stress values for static problems and natural frequency values for dynamic problems. In this study stochastic approach using Monte-Carlo Simulation is implemented by finding different random realizations each time to run the program so as to get the more rational results for the structural responses such as deflections, stresses and free vibrations. Different types of FRP laminated composite plates have been considered like cross ply, angle ply, all with different ply orientations etc. Studies have been done by taking various parameters such thickness ratios, different boundary conditions, different ply orientations and different coefficients of variations etc. Many results are presented which give useful information on the behavior of composite laminates having material uncertainty.