This paper on "Improved Mindlin Plate and Shell Elements" was presented at the NAFEMS World Congress on Effective Engineering Analysis - 25-28 April 1999, Newport, Rhode Island, USA.

Summary

This paper presents a treatment of out-of-plane shear strain energy in Mindi in plate and shell elements, suitable for analysis of laminated composite and sandwich structures. It has been successfully applied to 3, 4, and 6-node elements. These elements use the conventional 3 (plate) or 5 (shell) nodal degrees of freedom, have no communicable mechanisms, have no spurious shear energy (shear locking) and do not require arbitrary reduction of out-of-plane shear moduli or under-integration.
The Martin-Breiner 6-node curved shell element (MB6) uses additional concepts which avoid spurious membrane energy (membrane locking). All elements use artificial out-of-plane rotational stiffness, added at the element level to avoid convergence problems or singularity due to flat spots in shells.
Element performance has been tested on a large set of problems which includes the NAFEMS LE2, LE3, LE5, and T1, the Scordelis-Lo roof, the pinched cylinder with a diaphragm, Plunkett's vibrating wedge, and the Morley skew plate.
In regular rectangular meshes, the Martin-Breiner 6-node triangular curved shell (MB6) is about equivalent to the conventional 8-node quadrilateral with 2x2 integration (which is very good). In distorted meshes, this 6-node triangular element is distinctly better. It is the only quadratic element (of which we are aware) which is nearly exact in both the NAFEMS LE2 bending and membrane patch test. It should be universally adopted.
Results for 6 of the test cases are included in this paper.