New Elements For Thin/Thick And Laminated Composite Plates And The Method Of Quadrilateral Area Co-ordinates

In the past 40 years, the construction of plate bending elements based on the Mindlin-Reissner theory (the first-order shear deformation theory) for isotropic and laminated composite plates has attracted many researchers. In this dissertation, several rational, simple methods are presented to overcome the difficulties in the construction and application of above elements. Good results can be obtained by the proposed approaches. The main contributions of this dissertation are as follows:â… .The area co-ordinate method, which has been successfully applied to construct triangular elements, is generalized to construct quadrilateral elements. An area co-ordinate theory for quadrilateral elements is systematically established. By using the quadrilateral area co-ordinate and the generalized conforming method, two eight-node quadrilateral membrane elements, MQ8-I and MQ8-II, are developed. They exhibit good performance for both regular and distorted meshes. It is also demonstrated that the area co-ordinate method is an efficient tool for developing quadrilateral elements.â…¡.The shear locking phenomenon in thick plate bending elements is discussed. A rational, simple interpolation method for shear strain field is presented. Two new approaches for constructing thin-thick plate bending elements are also suggested: (i) Assume shear strain field and deflection field; and (ii) Assume shear strain field and rotation field. According to (i), triangular and quadrilateral thin-thick plate bending elements, TCGC-T9 and TACQ, are successfully constructed by using area the co-ordinate and the generalized conforming method. According to (ii), triangular and quadrilateral thin-thick plate bending elements, TMT and TMQ, are also successfully constructed. These four elements and are robust and free of shear locking. They can be employed to analyze very thin to moderately thick plates.â…¢.Two new displacement-based laminated composite plate elements, CTACQ and CTMQ, based on the first-order shear deformation theory, are successfully constructed. They are generalized from elements TACQ and TMQ by adding bilinear in-plane displacement field of the mid-plane, respectively. A new simple hybrid procedure is also proposed to improve stress solutions. Thus, excellent results for both displacements and stresses, especially the transverse shear stresses, can be obtained. The proposed elements are excellent for moderately thick and thin composite plates.