Introduction Of STEM For Stress Analysis In
Statically Determined Bodies
Author(s)
A. N. Galybin
Abstract
This article presents a novel approach to the identification of stress states in
statically determined bodies. The approach is based on the stress trajectory
concept and therefore it is referred to as the stress trajectories element method,
(STEM). Three different variants of STEM are presented and some problems
associated with these are posed.
Keywords: boundary value problems, stress trajectories, numerical methods.
1 Introduction
This article is an introduction to a novel numerical method that is currently under
development in Wessex Institute of Technology. The method is aimed at the
identification of stresses in statically determined bodies by employing stress
trajectories.
The concept of stress trajectories comes from photoelasticity, therefore one
can adopt the following definition due to Frocht [1]: Stress trajectories are curves
the tangents to which represent the directions of one of the principal stresses at
the points of tangency. A single stress trajectory is also called an isostatic or a
line of principal stresses.
Stresses at each point inside a continuous body represent a second-rank tensor
which components satisfy differential equations of equilibrium, DEE, and certain
constitutive equations. The latter is of theoretical and/or experimental nature, it is
often called \“rheology”, however only statically determined bodies are
considered in this paper. These constitute a broad class and some examples are
found in engineering:
− in elasticity, the laplacian applied to the first invariant of the stress tensor
should vanish (if body forces are neglected);
Keywords
boundary value problems, stress trajectories, numerical methods.
Related Book
Other papers in this volume
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