%0 Journal Article
%T Static and Free Vibration Analysis of Laminated Composite Plates Using Isogeometric Approach Based on the Third Order Shear Deformation Theory
%A Xinkang Li
%A Jifa Zhang
%A Yao Zheng
%J Advances in Mechanical Engineering
%D 2014
%I SAGE Publications
%R 10.1155/2014/232019
%X Isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) is applied for static and free vibration analysis of laminated composite plates by using the third order shear deformation theory (TSDT). TSDT requires C1-continuity of generalized displacements and NURBS basis functions are well-suited for this requirement. Due to the noninterpolatory nature of NURBS basis functions, a penalty method is applied to enforce the essential boundary conditions. The validity and accuracy of the present method are demonstrated through a series of numerical examples of isotropic and laminated composite plates with different shapes, boundary conditions, fiber orientations, lay-up numbers, and so forth. The obtained numerical results are compared with either the analytical solutions or other available numerical methods. 1. Introduction The requirements for higher stiffness and strength-to-weight ratio, better wear resistance, and greater health characteristics over conventional materials have resulted in the wide application of composite laminates in the area of aerospace, automotive, and underwater structures. Therefore, static and dynamic analysis of both thin and thick laminates becomes an important research topic. Based on different assumptions for displacement fields, several theories for analysis of composite laminates have been developed. The classical plate theory (CPT) relying on the Kirchhoff-Love assumptions [1, 2] can only be applied if plates are thin, because transverse shear deformations are not considered. The first order shear deformation theory (FSDT) which accounts for transverse shear effects [3, 4] can be applied for both moderately thick and thin plates. However, in FSDT, the transverse shear strain is assumed to be constant along the thickness direction, and, thus a shear correction factor (SCF) has to be considered. The SCF depends on many factors, such as material coefficients, stacking scheme, plate geometry and boundary conditions; therefore the evaluation of the SCF remains a subject of research [5]. In addition, with constant shear strain assumption, transverse shear stresses obtained may not be zero on the plate surface, which contradicts the traction free boundary conditions. To overcome the limitations of FSDT, a more accurate high order shear deformation theory, termed the third order shear deformation theory (TSDT) [6, 7], has been developed to formulate the mechanical behavior of composite laminates. TSDT introduces the cubic variation of the displacement such that more accurate interlaminar stress distributions can be
%U http://www.hindawi.com/journals/ame/2014/232019/