Improving the Bergan Wang Quadrilateral plate element by using the UI approach for analysis of isotropic and FGM sandwich plates

This work presents the improvement of Bergan Wang Quadrilateral (BWQ) element using the UI (unified and integrated) approach. In this approach, a new formulation of quadrilateral plate element is developed with a single independent variable just like what Bergan and Wang applied to develop a non-conforming BWQ element. The difference between the two approaches lies in the formulation of transverse displacement w, wherein the UI approach transverse displacement w is expressed as the sum of transverse bending, and shear displacements (w_b and w_s) and the transverse bending displacement w_b becomes the single independent variable. The transverse shear displacement w_s is defined as the second derivative of the transverse bending displacement w_b. The rotations, curvatures, and shear strains are the first, second, and third derivatives of the bending displacement w_b. The resulting non-conforming element, called UI-Q4 element, has proper rank, no shear locking problem, and passes the patch test. To examine the element convergence and accuracy, standard benchmark problems of isotropic plates, i.e. square plates, Razzaque and Morley skew plates, and circular plates, are used. The UI-Q4 element shows very good performance, which is observed by comparing it with MITC4, DSQK and BWQ elements. Moreover, the application of UI-Q4 element for analysing functionally graded material (FGM) sandwich plate analysis also performs well and delivers results which are quickly converged to the reference values.