11 th International Research/Expert Conference “Trends in the Development of Machinery and Associated Technology” TMT 2007, Hammamet, Tunisia, 05-09 September, 2007. FINITE ELEMENT ANALYSIS OF PLASTIC YIELDING IN AN ANISOTROPIC PLATE WITH A HOLE USING REFINED PLATE THEORY Tasneem Pervez, Rafiq A. Siddiqui, Sayyad Z. Qamar, and Farooq Al-Jahwari Mechanical and Industrial Engineering Department, Box 33, Sultan Qaboos University, Al Khoudh 123, Sultanate of Oman; tasneem@squ.edu.om ABSTRACT An elastic-plastic analysis of anisotropic laminated composite plate with a circular hole is carried out using a 2-dimensional finite element model based on higher order shear deformation theory. The variation in material properties through thickness is defined using discrete layer approach. The generalized Huber-Mises yield criterion for anisotropic material is used to determine the onset of plastic flow. The inclusion of anisotropic parameters of plasticity generalizes the plastic yield function. These anisotropic parameters of plasticity are updated during the hardening history of anisotropic laminated composite plate. The plastic potential, which is an anisotropic yield function, is used to determine an associated flow rule. Finally, an elastic-plastic incremental constitutive relation is obtained using finite element method. By means of an incremental and iterative procedure, the numerical solution of deformation problems in nonlinear anisotropic laminated plate is achieved using higher order shear deformation theory. The spread of plastic zones around the circular holes are discussed. The method yield accurate values of transverse shear stresses as compared to other shear deformation theories and hence the growth of plastic zones. Keywords: Laminated plates, anisotropic plasticity, elastic-plastic analysis 1. INTRODUCTION It is common to assume isotropic material behavior while studying the deformation of metallic solids due to applied external loads. Typically, this assumption is extended to both elastic and elastic-plastic responses. However, there are two categories of problems which involve anisotropic behavior. First is the introduction of anisotropy due to a deformation mechanism into an initially isotropic material, most commonly observed in metal forming operations. This phenomenon is usually termed as induced anisotropy. Second is the class of materials which are initially anisotropic or orthrotropic in nature usually termed as composites. In later category, there is a lack of well defined generalized plasticity theory to explain the nonlinear behavior due to material or geometric nonlinearities. Several investigators have developed theories to describe induced anisotropy while fewer attempts have been made to describe anisotropic plasticity in composites. Hill [1] proposed an anisotropic yield criterion based on generalization of Von-Mises criterion. Subsequently, there have been several modifications have been suggested by researchers. Yet, these theories do not properly account for all the effects associated with orientation dependent deformation mechanism. Extension of these theories to describe inelastic behavior of laminated orthotropic composite plates is also limited. Whang [2] was the first one to consider the elastic-plastic analysis of orthotropic laminated plates based on classical lamination theory. Owen [3] had extended the analysis of plates and shells based on first-order shear deformation theory (FSDT). The analysis for laminated plates was further developed to account for higher-order shear deformation theory (HSDT) by Pervez [4]. Several research had been carried out for elastic-plastic analysis of a laminated composite plate with regular and irregular shaped hole [5-7] using only classical lamination theory and FSDT. The work in this paper is based on HSDT to study the orientation dependent deformation behavior in the vicinity and around a circular hole. The study will help the designer to avoid failure in the areas of geometric 991