Differential Geometric Aspects of Stress Theory

Reuven Segev (Ben-Gurion University of the Negev)

Thursday 6th March 14:00-15:00 Maths 116

Abstract

Stress tensors are used in the strength analysis of structures, fluid dynamics, electromagnetism, and general relativity. However, from the theoretical point of view, the stress tensor object is not a primitive one. It is derived on the basis of some physically motivated mathematical assumptions. Following a short introduction to the fundamentals of classical theory, we will present a formulation of stress theory on general differentiable manifolds devoid of any particular Riemannian metric. The basic mathematical object is the configuration space – the Banach manifold of k-times continuously differentiable sections of a fiber bundle over a compact base manifold – the material body. The choice of topology is natural so that the set of embeddings of the body manifold in a space manifold is open in the manifold of all mappings. Forces are defined as elements of the cotangent bundle of the configuration space, and their action on virtual velocities – elements of the tangent bundle – is interpreted physically as virtual power. Stresses and hyper-stresses emerge naturally from a representation theorem for forces as measures valued in the dual bundles of some jet bundles.

Add to your calendar

Download event information as iCalendar file (only this event)