Finite Element Analysis of 2D Heterogeneous Objects Using Material Based Graded Elements

Lokesh Singh1 1GD rungta college of Engineering & Technology, India [email protected] ABSTRACT A heterogeneous object is referred to a solid object made of different constituent materials. The object is made up of finite collection of regions having set of prescribed material classes of continuously or discontinuously varying material properties. These properties have an abrupt or gradual change across the interference of the material regions. Application of heterogeneous material range from bio-material products, aerospace structures, to meta-material with demonstrated performance improvement in structural, mechanical, electronics and or sensing property in these application , the performance goal are achieved because of the capability of varying material properties globally across the spatial domain. In order to take the full advantage of the greatest potential of heterogeneous object, we must go for developing their computer modelling and analysis techniques. Based upon the computerized object model, finite element methods are often used to analyse these objects. In homogeneous objects, such analysis typically involves lengthy analysis model setup time, i.e. material property, mesh construction and mesh refinement, boundary condition setup and so on. It is estimated that analysis model setup takes more than 80% of the overall analysis time. In the context of heterogeneous object analysis, this issue is further exacerbated. In case of heterogeneous objects each and every point in the domain material property is vary (i.e. young modulus and Poisson ratio) so for this type of material for getting exact result we define new type of elements (called as Material Based Graded Element) in the domain with the help of this we can come closer to the exact result and also find the difference. The objective of the paper is to get near to accurate result of heterogeneous object by using Material-Based Graded elements. In this paper we have considered linear and nonlinear material variation with two approaches average and integration approach for 2D and four types of graded element, Average Young’s modulus of domain, Average Young’s modulus of element, Bi-Linear variation of Young’s modulus along X & Y direction, Bi-Non linear variation of Young’s modulus along X & Y direction for 2D .