Structural Matrix Computations with Units: Data Structures, Algorithms, and Scripting Language Design

Abstract

Despite the well-known benefits of physical units, matrices,and matrix algebra in engineering computations,most engineering analysis packages are essentially dimensionless.They simply hold the engineer responsible for selecting a set ofengineering units and making sure their use is consistent.While this practice may be satisfactory for the solution ofself-contained and well-established problem-solving procedures,where the structure of the output is well known and understood,identifying and correcting unintentional errors in the solution ofnew and innovative computations can be significantly easierwhen units are an integral part of the computation procedure.<p>This report begins with a description of thedata structures and algorithms needed torepresent and manipulate physical quantity variables,and matrices of physical quantities.<p>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.<p>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.