A survey of recent shell finite elements

Abstract

Since the mid-1960s when the forms of curved shell "nite elements were originated, including those pioneered by Professor Gallagher, the published literature on the subject has grown extensively. The "rst two present authors and Liaw presented a survey of such literature in 1990 in this journal. Professor Gallagher maintained an active interest in this subject during his entire academic career, publishing milestone research works and providing periodic reviews of the literature. In this paper, we endeavor to summarize the important literature on shell "nite elements over the past 15 years. It is hoped that this will be a be"tting tribute to the pioneering achievements and sustained legacy of our beloved Professor Gallagher in the area of shell "nite elements. This survey includes: the degenerated shell approach; stress-resultant-based formulations and Cosserat surface approach; reduced integration with stabilization; incompatible modes approach; enhanced strain formulations; 3-D elasticity elements; drilling d.o.f. elements; co-rotational approach; and higher-order theories for composites.

Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element

“…Great progress has been made over past decades towards better understanding of the vibration characteristics of laminated composite plates/shells [1,2,3]. Due to limited availability of analytic solutions for practical applications, numerical approximate methods have become the most effective tools.…”

“…Bert [1] and Mohamad [2] have conducted surveys and provided details on the development of the finite element methods for modeling and modal analysis of laminated plates/shells. Further extensive references on shells can be found in the excellent review of Yang et al [3].…”

A cell-based smoothed discrete shear gap method (CS-DSG3) using triangular elements for static and free vibration analyses of shell structures

“…In the past three decades, the finite element method (FEM) has been used as a powerful numerical tool to simulate behaviors of shell structures [4]. Compared with four-node quadrilateral shell element [5][6][7][8], three-node triangular shell element [9,10] is particularly attractive due to its simplicity, automatic meshing and re-meshing in adaptive analysis.…”

Discrete viscous sheets

“…Considering the analogous case of thin elastic shells, we note that while shells can be represented with volumetric tetrahedra, in practice this is avoided, as the thin geometry necessitates excessive refinement to avoid locking and associated numerical problems [Yang et al 2000]. The same geometric challenges arise in thin liquid sheets, motivating the development of reduced-dimensional models of thin viscous sheets.…”