A Study on Isogeometric Analysis of Laminated Composite Beams

Abstract

A myriad of physical processes in engineering and other science branches is represented using differential equations with boundary conditions. Finding the exact solution for the differential equation is quite challenging in many situations. Thus developing numerical methods for finding solutions for the differential equation is always one of the major problem considered in engineering. A wide variety of numerical methods have evolved over time for solving partial differential equations. Among them the most reliable and widely used method is the finite element method that was introduced in the 1960’s. This was a major development in the numerical analysis field and later on many modified versions of finite element analysis were presented. In this study, an attempt is made to use a better algorithm to produce numerical solutions of composite laminated beams. Although many works have been carried out in this field, it is still a challenge to model curved laminated beams using finite element method accurately. A newly introduced analysis method is used to model both straight composite as well as curved composite beams. The method considered in this study is the Isogeometric analysis which carry many of the advantages of regular finite element method. It has additional benefits of representation of the exact geometry which is not possible in normal finite element method. This work is an attempt to use the isogeometric analysis method to laminated composite beams. The initial part of the study is the analysis of a simple straight laminated composite beam using Isogeometric methods extended later on to the curved beam analysis. Both advantages and limitations are studied and compared with available closed formand 3D finite element solutions