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 |  موضوع: بحث بعنوان A Four-node Facet Shell Element for Laminated Shells Based on the Third Order Zigzag Theory الإثنين 12 أبريل 2021, 5:44 pm | |
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A Four-node Facet Shell Element for Laminated Shells Based on the Third Order Zigzag Theory
Adnan Ahmed a, Santosh Kapuria a,b,⇑
a Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
b CSIR-Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India
و المحتوى كما يلي :
a b s t r a c t
In this work, we develop a facet shell element for deep laminated shells, by extending a successful fournode quadrilateral element for laminated plates based on the efficient third order zigzag theory. The
obstacle course test comprising of three standard problems is undertaken to examine its performance
for various modes of shell behavior. The absence of shear and membrane locking problems is established
through the analysis of ultra thin shells. The accuracy of the element is assessed for the static and free
vibration responses of composite and sandwich shells in comparison with the three dimensional
elasticity solutions. In terms of accuracy, computational efficiency and robustness, the present element
is shown to give better performance than various classical and recent finite elements considered in this
study. In the case of sandwich shells, for which the equivalent single layer theories showed a high level of
error, the present element is shown to yield more accurate results than even the higher-order sandwich
shell theories that have been developed specifically for the three-layer sandwich shells.
a r t i c l e i n f o
Article history:
Received 3 July 2016
Revised 31 August 2016
Accepted 2 September 2016
Available online 7 September 2016
Keywords:
Finite element
Shell
Laminate
Composite
Sandwich
Zigzag theory
Conclusion
A four-node facet shell element has been developed for the
analysis of general laminated shell structures using the computationally efficient and accurate third order zigzag theory. The FE
for the smeared third order theory having the same number of
DOFs is also developed as a special case. The element has been
tested against the three-problem standard obstacle course that
was compiled by Belytschko et al. [56] to examine the performance
of shell elements in various modes of shell behavior for isotropic
shells. The comparison with the similar test results of other classical and recent shell elements shows that the present element is
among the best performers of all major available shell elements
for isotropic shells. Further, the results obtained for ultra-thin
cases of the obstacle course problems show that the present element is free from shear and membrane locking problems.
The accuracy of the present element has been examined for
singly- and doubly-curved composite and sandwich deep shells
in comparison with the 3D elasticity solutions, and other available
2D theory based analytical and FE solutions. The comparison
shows that the present ZIGT FE results are in excellent agreement
with the 3D elasticity solutions as well as the analytical solutions
of the ZIGT. For sandwich shells, the ZIGT FE results are even more
accurate than the HSAST’s which were specially developed for
three-layer sandwich shells [79,80]. On the other hand, the ESL
theories yield unacceptably high level of error (38–294%) even
for the fundamental natural frequency of moderately thick sandwich shells. The detailed numerical study reveals that the present
ZIGT based element is superior to all other available elements for
deep laminated shells in terms of accuracy, computational efficiency and robustness and has been shown to perform well for
all boundary conditions, shell geometries and laminate configurations considered here for both stress and free vibration analysis.
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