Isogeometric based formulations for the bending analysis of laminated composite structural elements

Abstract

Isogeometric analysis (IGA) is a family of numerical methods to solve boundary value problems. The founding principle of isogeometric methods is aimed at integrating computer aided design (CAD) with nite element method (FEM). In general, CAD platforms employ NURBS (Non Uniform Rational B-Splines) functions to model geometry and the same functions are adopted by isogeometric methods to approximate the unknown eld variables. Apart from their ability to model complex geometries, NURBS functions possess better approximation properties and high inter-element continuity properties. In its earliest days, isogeometric analysis comprised of Galerkin-isogeometric method alone. Galerkin-isogeometric method in essence is NURBS-based isoparametric nite element method. Research e orts in IGA further led to the development of new numerical methods like isogeometric collocation method. Isogeometric collocation o ers the geometric exibility of an isogeometric method and the computational advantage of a collocation scheme. The present thesis focuses on development of new computational approaches based on isogeometric methods for the bending analysis of laminated structural elements, namely, laminated composite plates and beams. A standard primal approach, shear locking free approach and a mixed approach based on isogeometric collocation are developed for the bending analysis of laminated composite plates governed by rst order shear deformation laminated plate (FSDT) theory. Variational asymptotic method (VAM) within the framework of isogeometric analysis is presented for the bending analysis of laminated composite beams