New Trends in Thin Structures: Formulation, Optimization and Coupled Problems
October 6, 2008 — October 10, 2008
Coordinators:
- Peter Wriggers (Inst. f. Kontinuumsmechanik, Hannover, Germany)
- Paulo Pimenta de Mattos (University of Sao Paulo, Cidade Univ. São Paulo, Brazil)
The application area of thin structures covers a wide range in all parts of engineering. Hence considerable effort has been devoted over the last years to enhance mathematical models, methods and algorithms for nonlinear structural behaviour. The main focus of this course is to convey modern techniques applied within the range of computational mechanics of beams, plates and shells.
The topics of interest are wide ranging, and include the following computational aspects of (1) Nonlinear theory of shells and beams including dynamics (2) Advanced discretization methods for thin shells and membranes (3) Shear-deformable Shell Finite Elements for SMA composite devices (4) Optimization and design of shells and membranes (5) Fluid-Structure Interaction with thin-walled structures (6) Contact mechanics with application to thin structures and (7) Edge effects in laminated shells. The lectures will cover the background the fully nonlinear formulation of beams and shells and the associated finite element discretization of beams, thin shell and membrane structures undergoing large deformations.The focus will include new robust discretization techniques for shear-rigid shell models. In particular, the use of smooth shape functions for discretizing the curvature dependent thin-shell energy functional will be examined. Basic concepts pertaining to differential geometry of surfaces, spline interpolation, subdivision surfaces, and derivation of shell balance equations in weak form will be introduced as necessary.
Another topic covered is the design of membranes including follower loads as well as ideas regarding manufacturing of membranes including pre-cutting and blanking. Formoptimization of thin shells regarding maximum stiffness and optimization of creases is investigated. In this line of topics also numerical methods are discussed including stabilization methods for inverse problems with modifaction of geometry. Furhermore efficient and fast algorithms for sensitivity analysis are discussed.
Shape memory alloys are nowadays well known and widely adopted as active components for innovative actuators. Related to these developments possible modelling of thin structures made of SMA or SMA-based smart hybrid composites are discussed. This includes also the general discussion of laminated structures and three-dimensional analysis of edge effects.
Contact takes often place when shell or beam structures interact with each other. This can occur on structural level, like in car-crash analysis but also within the investigation of composite materials where fibers interact in laminates with the matrix material or woven fabrics are in contact state. For these problems contact formulations are discussed and formulated up to discretization techniques and algorithms using finite element techniques.
In many advanced application scenarios structures interact with the surrounding or enclosed fluid (liquid or gas). Especially for thin-walled structures such interaction effects are often essential for the overall structural behavior and have to be taken into account. On the other hand thin-walled structures pose a number of challenges to coupled modeling and simulation approaches. Within these lectures those challenges are discussed along with appropriate solution approaches. In details methods for Fluid-structure interaction are discussed like interface tracking and interface capturing schemes; interface treatment and transfer of quantities; this includes important issues coming along with large deformations like the geometric conservation law, computational mesh dynamics and distorting elements.
All lectures will be of theoretical and applied nature, suitable for graduate students of applied mathematics, mechanics, engineering and physics with interest in computer simulation of thin structures and their wide rang of applications.