Institute for Systems Research

This report begins with a description of thedata structures and algorithms needed torepresent and manipulate physical quantity variables,and matrices of physical quantities.

The second half of this report focuses on the implementation of Aladdin,a new computational environment for matrix and finite element calculations.Aladdin employs a novel combination of system programming languages,scripting language concepts, and stack machine technology.The result is a high-level scripting language that offers enhancedtype checking for expressions and assignments,problem-oriented scaling of variables, automatic conversion of systems of units, and program control structures for the solution of engineering problems.

Functionality of the Aladdin stack machine is illustratedby working step by step through the parsing and execution ofa simple statement involving units.The capabilities of Aladdin are demonstrated through thedeflection analysis of a cantilever beam.

One four-node-thick shell finite element and one eight-node-thick shell finite element is formulated and implemented in ALADDIN [1]. The finite elements are based on a three-dimensional continuum formulation, and are simplified by assuming a flat element geometry. Numerical experiments are presented for in- plane displacements of a flat plate, and out-of-plane bending of a cantilever structure. In each case, material nonlinearities are modeled with bi-linear and Ramberg-Osgood stress-strain curves. The report concludes with recommendations for further work in the areas of nonlinear finite element solution procedures and enhancements to ALADDIN's problem-solving infrastructure.