Supernatural QUAD4: A template formulation

Abstract

A universal template for a 4-node quadrilateral in plane stress is constructed using a combination of old and new techniques. The use of natural quantities, strongly advocated by J.H. Argyris since his Continua and Discontinua 1965 exposition, is further expanded. The qualifier ‘supernatural’ means that all governing equations: kinematic, constitutive and equilibrium, are expressed in both Cartesian and natural forms. These two sets are used to build different components of the template. With timely help from a computer algebra system, a template that include all possible quadrilateral elements that pass the Individual Element Test of Bergan and Hanssen emerges. It yields an infinite number of hitherto undiscovered instances that may be customized to fit special needs. A striking example is the construction of a two-trapezoid macroelement that is bending exact about one direction, for any amount of distortion. This concludes a five decade search that begins with the formulation of the wing-cover rectangular panel in Argyris’ 1954 seminal serial on Energy Methods and Structural Analysis.

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