A kinematically exact finite element formulation of planar elastic - plastic frames

Saje, Miran (author), Planinc, Igor (author), Turk, Goran (author), Vratanar, Blaž (author)

A finite element formulation of finite deformation static analysis of plane elastic-plastic frames subjected to static loads is presented, in which the only function to be interpolated is the rotation of the centroid axis of the beam. One of the advantages of such a formulation is that the problem of the field-consistency does not arise. Exact non-linear kinematic relationships of the finite-strain beam theory are used, which assume the Bernoulli hypothesis of plane cross-sections. Finite displacements and rotations as well as finite extensional and bending strains are accounted for. The effects of shear strains and non-conservative loads are at present neglected, yet they can simply be incorporated in the formulation. Because the potential energy of internal forces does not exist with elastic-plastic material, the principle of virtual work is introduced as the basis of the finite element formulation. A generalized principle of virtual work is proposed in which the displacements, rotation, extensional and bending strains, and the Lagrangian multipliers are independent variables. By exploiting the special structure of the equations of the problem, the displacements, the strains and the multipliers are eliminated from the generalized principle of virtual work. A novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation. It is shown that (N-1)-point numerical integration must be employed in conjunction with N-node interpolation polynomials for the rotation, and the Lobatto rule is recommended. Regarding the integration over the cross-section, it is demonstrated by numerical examples that, due to discontinuous integrands, no integration order defined as `computationally efficient yet accurate enough' could be suggested. The theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples.

• Language: English
• Keywords: plane frame, exact kinematics, plasticity, generalized principle of virtual work, finite elements
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publisher: Elsevier
• Year: 1997
• Number of pages: Str. 125-151
• Numbering: Vol. 144, no. 1/2
• PID: 20.500.12556/RUL-32127
• UDC: 519.61/.64:531.1:539.374
• ISSN on article: 0045-7825
• DOI: 10.1016/S0045-7825(96)01172-3
• COBISS.SI-ID: 163169
• Publication date in RUL: 10.07.2015

SAJE, Miran, PLANINC, Igor, TURK, Goran and VRATANAR, Blaž, 1997, A kinematically exact finite element formulation of planar elastic - plastic frames. Computer methods in applied mechanics and engineering [online]. 1997. Vol. 144, no. 1/2, p. 125–151. [Accessed 17 May 2025]. DOI 10.1016/S0045-7825(96)01172-3. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=32127

Record is a part of a journal

• Title: Computer methods in applied mechanics and engineering
• Shortened title: Comput. methods appl. mech. eng.
• Publisher: Elsevier
• ISSN: 0045-7825
• COBISS.SI-ID: 6695685

Secondary language

• Language: English
• Keywords: ravninski okvir, točna kinematika, posplošeni princip virtualnega dela, plastičnost, končni elementi