PIERS ONLINE, VOL. 4, NO. 2, 2008 231 Improved Isoparameter FEM for Plastic and EM Modeling Chien-Chang Lin 1 , Jianhua Li 1,2 , Ganquan Xie 2 , and Michael Oristaglio 3 1 Department of Mechanical and Automation Engineering, Da-Yeh University, Taiwan 2 GL Geophysical Laboratory, USA 3 Schlumberger Doll Research, USA Abstract— In this paper, we present an improved isoparameter finite element method to calculate the electromagnetic (EM) field and the stress and deformation of the very thin multiple layered plastic hectograph or heliotype plate. The isoparameter element has high accurate to simulate the multiple layered thin plastic plate deformation and EM modeling. The thin multiple layered plastic plate has more advantages than the glass plate in the new LCD screen etc displayer and other industrial engineering applications. 1. INTRODUCTION The laptop and new TV are developed very fast. The LCD is an important screen tool in the laptop and new TV. In the LCD design and application, the traditional glass plate has been used. However the glass plate has fragile and heavier etc. shortcomings. The thin multiple layered plastic plate has more advantages in the new LCD screen etc displayer and other industrial engineering. The advantages of the plastic hectograph plate is its plastic, thin, light, and multiple layered material rigid strength. In the new LCD thin plastic hectograph design, the deformation and stress calculation is necessary. Exact and high resolution of simulation of the above thin multiple layered plastic hectograph plate is challenge in the scientific computation. The FEM is used for this product design. The long and wide of the plastic LCD is 20 cm around, but its thick is only 0.1 μm. If we use the trilinear cubic element scaled by thickness, the 20000 2 nodes are needed for simulation. Therefore, the FEM method needs very large computational cost and inaccurate boundary reflection will degrade the computational accurate of the displacement and stress. In this paper, we present an isoparameter FEM method for the plastic thin plate deformation and EM modeling. As early as in 1972, Xie and Li proposed 3D isoparameter curve element with 20 nodes [1]. In paper [1], the author use a novel method to construct the 20 nodes curve isoparameter element and develop 3D elastic FEM and its software first in China, also author used the 3D isoparameter FEM software to calculate all dams and underground structures displacement and stress of China. In particular, Xie and Li discovered superconvergence of the isoparameter element first of the world that discover has been recognized by Brandts, J. and M. Krizek’s paper “History and Future of Superconvergence in Three Dimensional Finite Element Methods” [2] and Michael Krizek’s paper “Superconvergence Phenomena on Three Dimensional Meshes” [3]. The isoparameter element can be compressed and bended to a singular element automatically. We used these advantages of the isoparameter element for the plastic thin plate deformation and EM modeling simulation. The description plan of this paper is as follows. The introduction is described in Section 1. In Section 2, we present elastic and plastic and EM modeling and its variation. The improved isoparameter element and its properties are presented in Section 3. In Section 4, we describe applications of the improved 3D and 2D isoparameter element. Accomplishment is described in Section 5. The paper will be concluded in Section 6. 2. ELASTIC AND PLASTIC AND EM MODELING 2.1. The Elastic Plastic Variational Principle The elastic and plastic field variation equation is as follows [1, 6–12], Z Ω ε T * (u)D(λ, μ, ε(u))ε(u)dr - Z Ω fudr = min, (1) where ε is the strain, D is the elastic-plastic matrix, λ and μ is Lame coefficient which depends on displacement u and strain ε in the plastic materials. ε(u)=  ∂u ∂x , ∂u ∂y , ∂u ∂z , ∂u ∂y + ∂v ∂x , ∂u ∂z + ∂w ∂x , ∂u ∂y + ∂v ∂x ¶ , (2)