Field-consistency - toward a science of constrained multi-strain-field finite element formulations

Abstract

The finite element method has progressed rapidly from simple engineering principles through rigorous mathematical formalisations to become a body of engineering knowledge incorporating well-defined conceptual schemes and operational procedures. The current practice however leads to a series of difficulties which are actually inter-related. In this paper, we describe an additional conceptual scheme called 'field-consistency', and demonstrate new methodology and terminology that helps to clear up this area of the finite element method that had remained difficult to understand for some time. The new procedure also enhances the predictive capabilities of error analyses of the method, giving it some of the self-criticality needed for a 'falsifiable' scientific basis. This paper is also in a limited sense, an essay on how the processes of the method of science are seen to work in this area of engineering know-how.