Adaptive mesh h-refinement method using transition elements in plate bending problems

Abstract

In this study, an adaptive mesh h-refinement procedure was presented in plate bending problems. By introducing the transition elements with variable midisde nodes, some drawbacks due to the displacement constraints in common adaptive h-refinement performed by quadrilateral elements are eliminated, which are imposed on the irregular nodes to preserve interelement compatibility. For the above objective, two types of 5-node to 7-node transition plate bending elements, nonconforming and compatible elements, were developed in this study. The first nonconforming elements have curved sides where midside node exists, while the second compatible ones have singular snap sides for compatible 4-node to 4-node elements transition. To avoid excessive shear stiffness of Mindlin plate element, nonconforming displacement modes were added to noncomforming elements, and substitute shear strain fields were constructed in the case of compatible elements. All the transition elements have the requisite numbers of zero eigenvalues associated with rigid body motions and do not produce any spurious mechanism. It was verified from numerical fests that these elements can be used for efficient analysis of plate structures, enabling to refine mesh locally and use these for adaptive mesh refinement. Using the simple error estimator derived from postprocessing of finite element stresses, some numerical examples for the adaptive h-refinement using the transition elements together with existing 4-node elements were presented. In most cases of analysis, the optimal rates of h-convergence were reached and nearly optimal meshes were produced for both nonconforming and compatible model.