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A C1 bending element for composite plates based on a high-order shear deformation theory

In this paper, the proposed element is developed where Reddy’s plate theory is successfully implemented. It has nine nodes and each node contains 7 degrees of freedom. The performance of the element is tested with different numerical examples, which show its precision and range of applicability | Vietnam Journal of Mechanics, VAST, Vol. 30, No. 4 (2008), pp. 337 – 346 Special Issue of the 30th Anniversary A C1 BENDING ELEMENT FOR COMPOSITE PLATES BASED ON A HIGH-ORDER SHEAR DEFORMATION THEORY Tran Ich Thinh1 , Ngo Nhu Khoa2 , Do Tien Dung3 1 Hanoi University of Technology, Vietnam 2 Thai Nguyen University, Vietnam 3 Viet Hung Technology College, Hanoi, Vietnam Abstract. A new C1 rectangular element is proposed and the finite element formulation based on Reddy’s higher-order shear deformation plate theory is developed. Although the plate theory is quite attractive but it could not be exploited as expected in finite-element analysis. This is due to the dificulties associated with satisfaction of inter-elemental continuity requirement and satisfy zero shear stress boundary conditions of the plate theory. In this paper, the proposed element is developed where Reddy’s plate theory is successfully implemented. It has nine nodes and each node contains 7 degrees of freedom. The performance of the element is tested with different numerical examples, which show its precision and range of applicability. 1. INTRODUCTION Laminated composite plates are finding extensive usage in the aeronautical, ship building and aerospace industries as well as in other fields of modern technology. The problem of shear deformation has got a good amount of attention after the popularity of fibre reinforced laminated composites, which is now one of the major areas of research in recent times. Actually, the role of transverse shear is very important in composites, as the material is weak in shear due to its low shear modulus compared to extensional rigidity. In this context, a number of plate theories have been developed where the major emphasis is to model the shear deformation in a refined manner. Amongst these plate theories (higher-order shear deformation theories-HSDT) only a representative selection is made in reference [1–17]. In single layer displacement-based theories, the .