Abstract
Non-linear dynamic behaviour of flexible irregular shell structures was discussed recently by Chroscielewski et al. [3,4], Lubowiecka [7], and Lubowiecka and Chroscielewski [8], where references to other related papers are given. The shell evolution in time was described by two fields: the vector u of the translatory motion of the shell base surface, and the proper orthogonal tensor Q of the mean rotation of the shell cross sections. As a result, the rotation group SO(3)entered the definition of the configuration space. In such problems of structural mechanics finite-dimensional approximations, like the finite element method or the time-stepping algorithm, require non-standard approaches.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cardona C, Geradin C (1988) A beam finite element non-linear theory with finite rotations. Int J Num Meth Engng 26: 2403–2438
Chróścielewski J (1996) The family of C0 finite elements in the non-linear sixparame-ter shell theory (in Polish). Zesz. Nauk. Politechniki Gdańskiej Nr 540, Budownictwo Ladowe LIII: 1–291
Chróścielewski J, Makowski J, Pietraszkiewicz W (2002) Non-linear dynamics of flexible shell structures. Computer Assisted Mechanics and Engineering Sciences 9: 341–357
Chróścielewski J, Makowski J, Pietraszkiewicz W (2000) Large overall motion of flexible branched shell structures. In: Ambrosio J A C, Kleiber M (eds.) Computational aspects of nonlinear structural systems with large rigid body motion. NATO Advanced Research Workshop, Purtusk (Poland), July 2–7 2000. IDMEC, Lisboa, pp 201–218
Chróścielewski J, Makowski J, Stumpf H (1997) Finite element analysis of smooth, folded and multi-shell structures. Comp Meth Appl Mech Engng 141: 1–46
Libai A, Simmonds J G (1998) The nonlinear theory of elastic shells, 2nd ed. Cambridge University Press, Cambridge
Lubowiecka I (2001) Integration of nonlinear dynamic equations of motion in structural mechanics. Dynamics of elastic shell structures (in Polish). PhD Dissertation, Gdansk University of Technology
Lubowiecka I, Chróścielewski J (2002) On dynamics of flexible branched shell structures undergoing large overall motion using finite elements. Comp Struct 80: 891–898
Makowski J, Pietraszkiewicz W, Stumpf H (1999) Jump conditions in the non-linear theory of thin irregular shells. J Elasticity 54: 1–26
Simo JC, Vu-Quoc L (1988) On the dynamics in space of rods undergoing large motions - a geometrically exact approach. Comp Meth Appl Mech Engng 66: 125–161
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Chróścielewski, J., Lubowiecka, I., Pietraszkiewicz, W. (2004). FEM and Time Stepping Procedures in Non-Linear Dynamics of Flexible Branched Shell Structures. In: Kienzler, R., Ott, I., Altenbach, H. (eds) Theories of Plates and Shells. Lecture Notes in Applied and Computational Mechanics, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39905-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-39905-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05904-9
Online ISBN: 978-3-540-39905-6
eBook Packages: Springer Book Archive