| dc.description.abstract | In aerospace applications, use of laminates made of composite materials as face sheets in sandwich panels are on the rise. These composite laminates have low transverse shear and transverse normal moduli compared to the in-plane moduli. It is also seen that the corresponding transverse strength values are very low compared to the in-plane strength leading to delaminations. Further, in sandwich structures, the core is subjected to significant transverse shear stresses. Therefore the interlaminar stresses (i.e., transverse shear and normal) can govern the design of sandwich structures. As a consequence, the first step in achieving efficient designs is to develop the ability to reliably estimate interlaminar stresses.
Stress analysis of the composite sandwich structures can be carried out using 3-D finite elements for each layer. Owing to the enormous computational time and resource requirements for such a model, this process of analysis is rendered inefficient. On the other hand, existing plate/shell finite elements, when appropriately chosen, can help quickly predict the 2-D displacements with reasonable accuracy. However, their ability to calculate the thickness-wise distributions of interlaminar shear and normal stresses and 3-D displacements remains as a research goal. Frequently, incremental refinements are offered over existing solutions. In this scenario, an asymptotically correct dimensional reduction from 3-D to 2-D, if possible, would serve to benchmark any ongoing research. The employment of a mathematical technique called the Variational Asymptotic Method (VAM) ensures the asymptotical correctness for this purpose.
In plates and sandwich structures, it is typically possible to identify (purely from the defined material distributions and geometry) certain parameters as small compared to others. These characteristics are invoked by VAM to derive an asymptotically correct theory. Hence, the 3-D problem of plates is automatically decomposed into two separate problems (namely 1-D+2-D), which then exchange relevant information between each other in both ways. The through-the-thickness analysis of the plate, which is a 1-D analysis, provides asymptotic closed form solutions for the 2-D stiffness as well as the recovery relations (3-D warping field and displacements in terms of standard plate variables). This is followed by a 2-D plate analysis using the results of the 1-D analysis. Finally, the recovery relations regenerate all the required 3-D results. Thus, this method of developing reduced models involves neither ad hoc kinematic assumptions nor any need for shear correction factors as post-processing or curve-fitting measures. The results are most general and can be made as accurate as desired, while the procedure is computationally efficient.
In the present work, an asymptotically correct plate theory is formulated for composite sandwich structures. In developing this theory, in addition to the small parameters (such as small strains, small thickness-to-wavelength ratios etc.,) pertaining to the general plate theory, additional small parameters characterizing (and specific to) sandwich structures (viz., smallness of the thickness of facial layers com-pared to that of the core and smallness of elastic material stiffness of the core in relation to that of the facesheets) are used in the formulation. The present approach also satisfies the interlaminar displacement continuity and transverse equilibrium requirements as demanded by the exact 3-D formulation. Based on the derived theory, numerical codes are developed in-house. The results are obtained for a typical sandwich panel subjected to mechanical loading. The 3-D displacements, inter-laminar normal and shear stress distributions are obtained. The results are compared with 3-D elasticity solutions as well as with the results obtained using 3-D finite elements in MSC NASTRAN®. The results show good agreement in spite of the major reduction in computational effort. The formulation is then extended for thermo-elastic deformations of a sandwich panel.
This thesis is organized chronologically in terms of the objectives accomplished during the current research. The thesis is organized into six chapters. A brief organization of the thesis is presented below.
Chapter-1 briefly reviews the motivation for the stress analysis of sandwich structures with composite facesheets. It provides a literature survey on the stress analysis of composite laminates and sandwich plate structures. The drawbacks of the existing anlaytical approaches as opposed to that of the VAM are brought out. Finally, it concludes by listing the main contributions of this research.
Chapter-2 is dedicated to an overview of the 3-D elasticity formulation of composite sandwich structures. It starts with the 3-D description of a material point on a structural plate in the undeformed and deformed configurations. Further, the development of the associated 3-D strain field is also described. It ends with the formulation of the potential energy of the sandwich plate structure.
Chapter-3 develops the asymptotically correct theory for composite sandwich plate structure. The mathematical description of VAM and the procedure involved in developing the dimensionally reduciable structural models from 3-D elasticity functional is first described. The 1-D through-the-thickness analysis procedure followed in developing the 2-D plate model of the composite sandwich structure is then presented. Finally, the recovery relations (which are one of the important results from 1-D through-the-thickness analysis) to extract 3-D responses of the structure are obtained.
The developed formulation is applied to various problems listed in chapter
4. The first section of this chapter presents the validation study of the present formulation with available 3-D elasticity solutions. Here, composite sandwich plates for various length to depth ratios are correlated with available 3-D elasticity solutions as given in [23]. Lastly, the distributions of 3-D strains, stresses and displacements along the thickness for various loadings of a typical sandwich plate structure are correlated with corresponding solutions using well established 3-D finite elements of MSC NASTRAN® commerical FE software.
The developed and validated formulation of composite sandwich structure for mechanical loading is extended for thermo-elastic deformations. The first sections of this chapter describes the seamless inclusion of thermo-elastic strains into the 3-D elasticity formulation. This is followed by the 1-D through-the-thickness analysis in developing the 2-D plate model. Finally, it concludes with the validation of the present formulation for a very general thermal loading (having variation in all the three co-ordinate axes) by correlating the results from the present theory with that of the corresponding solutions of 3-D finite elements of MSC NASTRAN® FE commercial software.
Chapter-6 summarises the conclusions of this thesis and recommendations for future work. | en_US |
