FE ANALYSIS OF LAMINATED SHELLS INCLUDING FAILURE AND RELIABILITY BASED ON HOZT

Abstract

The use of Fibre reinforced polymer (FRP) laminated composites and sandwich structures are increasing rapidly in civil and other engineering applications. The material (FRP) has high specific strengthlstiffness and light weight properties. which are very useful for weight sensitive structural applications. Different forms of shell configurations are used for the construction of aesthetically elegant as well as large span structures. The self weight of the shell structures may be substantially reduced by using high strength FRP composites/sandwich laminates. Though the initial cost of FRP composite shell structures may be high at present but the cost of maintenance and the cost of supporting structures will be reduced; and the life cycle cost should be lesser than the same structures made of conventional materials. However, FRP materials are relatively weak in shear compared to extensional strength and also there is a possibility of the occurrence of inter-layer slips resulting from high inter-laminar stresses due to their layered configurations. Therefore, the shear deformation of these laminated structures should be properly incorporated in the analysis. Based on some 3D elasticity studies, it is observed that the in-plane displacements of laminated composite/sandwich structures should be higher order zigzag in nature which also retains the possibility of discontinuities of shear strain at the layer interfaces. This discontinuity may be negligible for laminated composites with layers made of same materials but it is quite significant in case of sandwich structures having layers with wide variation of material properties. Conventionally, plate or shell like structures are analyzed as a 2D structures as it is computationally more elegant compared to a 3D analysis without any significant compromise in the accuracy. In the category of 2D analysis, the Classical Lamination Theory (CLT) does not consider the shear deformation in the formulation and therefore, it is not suitable for the accurate analysis of FRP laminated structures. The First order Shear Deformation Theory (FSDT) includes the effect of shear deformation in a simple manner by assuming constant shear strainlstress across the laminate thickness. The FSDT requires a shear correction factor to compensate for the actual variation of shear stress across the thickness but still it is unable to predict the actual variation of transverse shear stresses across the thickness. The Higher order Shear Deformation Theory (HSDT) considers a higher order global variation of the in-plane displacements which help to omit the need of shear correction factor. The HSDT gives reasonably good results for laminated composites having same material properties across the 4 V ABSTRACT thickness but it is unable to predict the actual behavior of laminated sandwich structures having large variations of the material properties of core and face layers. The Higher Order Zigzag Theory (HOZT) overcomes the limitations of HSDT and ensures the continuity of transverse shear stress at the layer interfaces giving piecewise higher order zigzag variation of the in-plane displacements as observed in a sandwich structure. Finite element method (FEM) has been successfully used for decades in the analysis of structures having different geometry, boundary conditions, loadings etc. FEM is, therefore, considered as a versatile numerical tool for solving problenis related to different forms of structures. Although HSDT and HOZT are quite elegant 2D theories for the analysis of composite/sandwich laminates but a problem is faced during the finite element implementation as these refined shell theories (HSDT and HOZT) demand C' continuity of the transverse displacement. The requirement of C' continuity imposes additional constraint in the transverse displacement as the displacement as well as its derivatives should be continuous at the element interfaces. Therefore, the use of C' continuous element is not encouraged in practical applications and it is desirable to circumvent the problem of C' continuity by using suitable Co Finite element formulation. In a practical situation, a shell structure may have a skew geometry in plan other than usual regular geometry. It may also contain some opening in the form of cutouts to facilitate lighting/ventilation or maintenance etc. It is observed that only few research papers are available in the literature based on FSDT for laminated shell structures having these features and no results are available for these cases based on the refined shell theories (HSDT and HOZT). Failure analysis is an essential step for suitable design of composites/sandwich laminates. Different failure criteria are being used to study the behavior of laminated structures on the basis of first/last ply failure loads. Most of the results of failure analyses available in the literatures are based on FSDT. Therefore, there is a genuine requirement of results on failure analyses of laminated structures using refined 2D shear deformation theories such as HSDT and HOZT. It is expected that the results based on these refined (HSDT and HOZT) theories will be more accurate to the correct results as compared to the results based on FSDT. FRP laminated composite/sandwich structures are also characterized by inherent uncertainties in their material properties. Hence, an efficient reliability analysis of sandwich and composite structures becomes inevitable for assessing appropriate design load ranges for these structures. vi ABSTRACT In the present thesis, a 2D CO Finite element model has been developed for the analysis of laminated composites/sandwich shells based on refined shear deformation theories (HSDT and HOZT). All the three radius of curvatures including the cross curvature have been incorporated in the present formulation. The present FE model has been applied to solve the problems of laminated shells having different geometry (e.g., cylindrical, spherical, conical, hypar etc.) including skew shells and shells with cutouts. Static, free vibration and forced vibration analyses of laminated composites/sandwich structures are done to generate results for different cases. The results based on the present model are compared with the results of published literature works to study the convergence and accuracy of the proposed 2D FE model. For laminated composite shell structures, the results are generated based on both HSDT and HOZT whereas for laminated sandwich structures most of the results are based on HOZT. The first ply failure analyses of laminated composite/sandwich structures have been conducted in the present study based on HSDT and HOZT by using different failure criteria and the improvement of the present results compared to those obtained by FSDT are discussed. The reliability analyses of laminated composite/sandwich shell structures have also been done by applying Monte Carlo simulation (MCS) and Response surface method (RSM) within the framework of the present FE model based on HSDT and l-IOZT. Sensitivity analysis of basic random variables (BRVs) has been done to predict the failure loads corresponding to variations of a single BRV. Many new results are generated for different problems of laminated shells which should be useful for practical design and future research.