Transition Plate‐Bending Elements for Compatible Mesh Gradation

In this paper, a new approach to the development of the transition plate-bending elements with variable midside nodes is presented. These elements will facilitate abrupt changes in mesh refinement between domains consisting of quadrilateral elements. For compatible mesh gradation, special shape functions with slope discontinuity at midside nodes are used. The transition elements are formulated based on the Mindlin-Reissner plate theory to take shear deformation into account. To evaluate the proper element stiffness pertinent to shear, the substitute shear strain polynomials in Cartesian coordinates are constructed. A modified Gaussian integration is adopted to eliminate the slope discontinuity problem in the element domain. Some numerical examples are presented that illustrate the validity and effectiveness of these transition elements for the efficient analysis of plate-bending problems.