Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept

International Journal for Numerical Methods in Engineering - Tập 37 Số 15 - Trang 2551-2568 - 1994
N. Büchter1, Ekkehard Ramm1, Deane Roehl1
1Institut für Baustatik, Universität Stuttgart, Pfaffenwaldring 7, D70550, Stuttgart, Germany

Tóm tắt

AbstractConventional shell formulations, such as 3‐ or 5‐parameter theories or even 6‐parameter theories including the thickness change as extra parameter, require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness. This means that the normal stress in thickness direction has to either vanish or be constant. In general, these extra constraints cannot be satisfied explicitly or they Sead to elaborate strain expressions.The main objective of the present study is to introduce directly a complete 3‐D constitutive law without modification. Therefore, a 7‐parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects. In order to preserve the basic features of a displacement formulation the extra strain term is incorporated via the enhanced assumed strain concept recently proposed by Simo and Rifai to improve the performance of finite elements. Since the extra strain parameter can be eliminated on the element level after discretization, the formulation preserves the formal structure of a 6‐parameter shell theory. The resulting hybrid‐mixed shell formulation is applied to large deformation problems with hyperelasticity, small and large strain plasticity.

Từ khóa


Tài liệu tham khảo

10.1002/cnm.1630070105

10.1108/eb023748

10.1016/0141-0296(91)90050-M

10.1016/0045-7825(90)90143-A

Naghdi P., 1972, Encyclopedia of Physics, 425

10.1007/BF00804602

10.1007/BF00533829

10.1007/BF00537191

10.1002/nme.1620290802

Green A. E., 1968, Theoretical Elasticity

N.Buchter ‘Zusammenführung von Degenerationskonzept und Schalentheorie bei endlichen Rotationen’ Ph. D.‐Dissertation Bericht Nr. 14 Institut für Baustatik Universitat Stuttgart 1992.

10.1007/978-3-322-93983-8

U.Andelfinger ‘Untersuchungen zur Zuverlässigkeit hybrid gemischter finiter Elemente für Flächentragwerke’ Ph. D.‐Dissertation Bericht Nr. 13 Institut fur Baustatik Universität Stuttgart 1991.

10.1002/nme.1620360805

10.1002/nme.1620340105

10.1002/nme.1620330705

D.Roehl ‘Zur Berechnung von großen elasto‐plastichen Deformationen bei Flächentragwerken und Kontinua’ Ph. D.‐Dissertation Bericht Nr. 16 Institut für Baustatik Universität Stuttgart 1994.

Andelfinger U., 1992, Proc. Complas III, Barcelona, 1992

Simo J. C., Improved versions of assumed enhanced strain tri‐linear elements for 3D finite deformation problems

10.1002/nme.1620030213

Stein E., 1989, Computational Mechanics'. bei Festkörpern und Ingenieurstrukturen unter Verwendung von Finile‐Element‐Methoden, Mitteilungen der Gesellschaft für angewandte Mathematik und Mechanik, 1, 3

10.1016/0045-7825(92)90129-8

10.1016/0045-7825(88)90076-X

10.1016/0045-7825(88)90104-1

Thông tin
Thông tin xuất bản

International Journal for Numerical Methods in Engineering

Tập 37 Số 15

2551-2568

Thông tin tác giả