NL12

The main objective of this course is to provide engineers who use computer codes, graduate students, and researchers with an extensive review of advanced 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.

Each lecture day is concluded and completed by tutorial interactive sessions, where the lecturers will present simple problems, or introduce the attendees to numerical codes (mainly FEAP) to solve advanced problems, with the possibility also to discuss the solution of specific problems, or to interact with the lecturers on the material presented during other lectures.

The course material will consist of copies of transparencies from the lectures 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.