TY - JOUR
T1 - Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solids, with application to plates and shells-I. Theory
AU - Atluri, Satya N.
N1 - Funding Information:
Acknowledgements-This work was supported by AFOSR, under grant 8lXKl57 to Georgia Institute of Technology, with Dr. Anthony Amos as the AFOSR program official. The author gratefully acknowledges this support. The author thanks Ms. Margarete Eiteman for her care in the preparation of this manuscript. Finally the author thanks HG who taught him how to be peaceful and inspired him to seek beauty in his work as well.
PY - 1984
Y1 - 1984
N2 - Attention is focused in this paper on: (i) definitions of alternate measures of "stress-resultants" and "stress-couples" in a finitely deformed shell (finite mid-plane stretches as well as finite rotations); (ii) mixed variational principles for shells, undergoing large mid-plane stretches and large rotations, in terms of a stress function vector and the rotation tensor. In doing so, both types of polar decomposition, namely rotation followed by stretch, as well as stretch followed by rotation, of the shell midsurface, are considered; (iii) two alternate bending strain measures which depend on rotation alone for a finitely deformed shell; (iv) objectivity of constitutive relations, in terms of these alternate strain/"stress-resultants", and "stress-couple" measures, for finitely deformed shells. To motivate these topics, and for added clarity, a discussion of relevant alternate stress measures, work-conjugate strain measures, and mixed variational principles with rotations as variables, is presented first in the context of three-dimensional continuum mechanics. Comments are also made on the use of the presently developed theories in conjunction with mixed-hydrid finite element methods. Discussion of numerical schemes and results is deferred to the Part II of the paper, however.
AB - Attention is focused in this paper on: (i) definitions of alternate measures of "stress-resultants" and "stress-couples" in a finitely deformed shell (finite mid-plane stretches as well as finite rotations); (ii) mixed variational principles for shells, undergoing large mid-plane stretches and large rotations, in terms of a stress function vector and the rotation tensor. In doing so, both types of polar decomposition, namely rotation followed by stretch, as well as stretch followed by rotation, of the shell midsurface, are considered; (iii) two alternate bending strain measures which depend on rotation alone for a finitely deformed shell; (iv) objectivity of constitutive relations, in terms of these alternate strain/"stress-resultants", and "stress-couple" measures, for finitely deformed shells. To motivate these topics, and for added clarity, a discussion of relevant alternate stress measures, work-conjugate strain measures, and mixed variational principles with rotations as variables, is presented first in the context of three-dimensional continuum mechanics. Comments are also made on the use of the presently developed theories in conjunction with mixed-hydrid finite element methods. Discussion of numerical schemes and results is deferred to the Part II of the paper, however.
UR - http://www.scopus.com/inward/record.url?scp=33846448253&partnerID=8YFLogxK
U2 - 10.1016/0045-7949(84)90085-3
DO - 10.1016/0045-7949(84)90085-3
M3 - Article
AN - SCOPUS:33846448253
SN - 0045-7949
VL - 18
SP - 93
EP - 116
JO - Computers and Structures
JF - Computers and Structures
IS - 1
ER -