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Deformation and failure analysis of laminated composites by isogeometric elements formulation

Aydın, Cansın Bade
The finite element method (FEM) is the most widely used technique for solution ofengineering problems. In classical finite element analysis (FEA) procedure, the exactgeometry generated in computer aided design software is regenerated to have an anal-ysis suitable model, then this model is used for solution. Isogeometric analysis (IGA)is a computational approach which eliminates the modification phase of the actualgeometry in FEA. Instead, IGA employs the same mathematical model which definesthe geometry in the computer graphics software for defining the solution field. One ofthe most general basis functions used for representing the geometry mathematically isNon-Uniform Rational B-Splines (NURBS). NURBS are more comprehensive formof B-spline functions which are parametric piecewise polynomials. They allow flex-ible and accurate design, control of continuity with ease, and with its rational formenabling representation of conic sections which is not possible by using B-splines.The main advantage of isogeometric approach is to analyze the complex shaped partsby eliminating the error due to inaccurate representation of geometry in the finite el-ement method. In addition, since spline-based functions with higher continuity areused, better accuracy is acquired.v The aim of this thesis is, through the use of isogeometric plate elements, to analyzethe deformation, to determine the strain and stress distribution and to predict the firstply failure by using different failure criteria of laminated composite materials, andto present the applicability of IGA for anisotropic materials. For this purpose, anopen source code written for isotropic materials is modified to analyze laminatedcomposites and various failure criteria are embedded to the code. A number of caseswith various ply orientations and thicknesses, under different loading and boundaryconditions are analyzed and their results are compared with the results obtained bythe solutions of FEM.