Multiresolution finite element method based on a new locking-free rectangular Mindlin plate element

TL;DR

This paper introduces a new locking-free rectangular Mindlin plate element utilizing a multiresolution analysis framework, enabling adjustable analysis clarity based on resolution levels rather than mesh density, improving accuracy and efficiency.

Contribution

It presents a novel multiresolution finite element method for Mindlin plates, extending traditional elements with a mathematically rigorous resolution level concept for better analysis control.

Findings

The proposed element is locking-free and more accurate.

The resolution level effectively controls analysis clarity.

The method generalizes traditional single-resolution elements.

Abstract

A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic node shape function. The basic node shape function is constructed by extending the node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.