Tuesday, June 14th, 2016. Time: 12 p.m.

Place: O.C. Zienkiewicz Conference Room, C1 Building, UPC Campus Nord, Barcelona.

ABSTRACT

In the history of finite element methods the year 1960 stands out. The term "finite element" appears for the first time in the open literature in an article by Clough. And Turner, Dill, Martin and Melosh (most of whom were employees of The Boeing Company) publish the first journal paper on nonlinear structural analysis. The then-five-year-old direct stiffness method (what we now call displacement-assumed finite element method) was applied to: 

Nonlinear FEM evolved rapidly over the next 25 years. The three Lagrangian kinematic descriptions (LKD) in common used today: Total Lagrangian (TL), Updated Lagrangian (UL) and Corotational (CR) appeared and eventually found their way into production FEM codes. Yet none of the three can be considered universally applicable because they display strengths and weaknesses that limit their application range. For example, TL is unable to cope with very large rotations as may happen, for example, in aircraft maneuvers or robotics, whereas CR is hampered by truly large, flow-like deformations as in metal forming. To increase the problem range, some commercial FEM codes (e.g., ABAQUS) are trying to implement two LKD. But this can be an expensive undertaking since it involves recoding the entire FEM library, which may involve millions of code lines.

Can be a unified kinematic description be implemented in a single library? The idea is that the user would pick the one that best fits the target problem, like flicking a three-way switch: flip-flap-flop.

The presentation describes research in progress that attacks that problem. The basic tool is use of a finite strain measure originally proposed by Seth in 1964 for 1D and extended to 3D tensorial form by Hill in 1981. The Seth-Hill (SH) family has a parameter m called the SH index that varies from 2 to-2. It embodies several well known Lagrangian measures: Green-Lagrange for m=2, Biot for m=1, Hencky for m=0, and Almansi-Hamel for m=-2., as well as their Eulerian counterparts. While offering a nonlinear FEM course, the author discovered that the nonlinear bar element in 3D could be universally formulated within the SH framework. Some interesting results emerged: the TL, CR and UL forms of the residual and stiffness equations emerged for m=2, 1 and -2, respectively. Which means that a bar element module, equipped with the SH index as argument, could produce the three standard descriptions, as well as an infinity of other ones, without need of recoding. For example, settting m=0 would give the Hencky or logarithmic measure, which is preferred by many workers for modeling finite strain elastoplasticity.

Can this unification technique be extended to more complicated FEM models? The next one in line to try is the 3-node membrane triangle moving in 3D. The extension is based in the concept of "natural stretch gages". This is an extension of the "strain node" concept developed by the author in his 1966 Berkeley thesis, which 20 years later evolved into the assumed natural strain (ANS) formulation. Preliminary results appear encouraging, but at this stage it is too early to draw general conclusions. 

SPEAKER CV

Carlos A. Felippa. Professor of Aerospace Engineering. Department of Aerospace Engineering Sciences and Center for Aerospace Structures University of Colorado at Boulder, Boulder, USA.

Ph.D. in Civil Engineering and M.S. in Civil Engineering by the University of California (USA). Civil Engineer by the Universidad Nacional de Córdoba (Argentina).