NL14

The main objective of this course is to provide engineers who use computer codes, graduate students, and researchers with a review of numerical techniques and solution algorithms for nonlinear mechanics. It presents the current state-of-the-art in finite element modeling of nonlinear problems in solid and structural mechanics and illustrates difficulties (and possible solutions) which appear in a number of applications.

Different sources of nonlinear behavior are presented in a systematic manner. Special attention is paid to nonlinear constitutive behavior of materials, large deformations and rotations of structures, contact and instability problems with either material (localization) or geometric (buckling) nonlinearities, which are needed to fully grasp weaknesses of structural design.

The course will also provide insight both on advanced mathematical aspects as well as into the practical aspects of several computational techniques, such as the finite element method, isogeometric analysis, meshless techniques, mimetic differences.
The objective is thus to provide the participants with a solid basis for using computational tools and software in trying to achieve the optimal design, and/or to carry out a refined analysis of nonlinear behavior of structures.

The course finally provides a basis to account for multi-physics and multi-scale effects, which are likely to achieve a significant break-through in a number of industrial applications

Tutorials are organized as a final section each day and they are meant not as a standard lecture but as an interactive part of the course. In fact, tutorials are based on addressing simple problems to be solved during the class on the fly and they are meant as a basis for an interactive discussion between the teaching body and the course attendees. We strongly encourage students to bring their own laptops and we plan to distribute files, so that students can run examples, interact, and participate lively to the tutorials. Depending on the specific topic, the tutorials will be managed by one or more of the teachers and they will be based on using different software. Special emphasis will be given to FEAP personal version (http://www.ce.berkeley.edu/projects/feap/feappv/) or programs written in Matlab, or Maple.

The course material will consist of electronic copies of lecture materials and survey papers. Copies of Finite Element Analysis Program (FEAP) computer codes, written by Prof. Robert L. Taylor at UC Berkeley, and the complete volume of notes will be made available to all attendees.