Structural Matrix Computations with Units

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 of engineering units and making sure their use is consistent. Although this practice may be satisfactory for the solution of established problem-solving procedures, identifying and correcting unintentional errors in computations developed by teams of engineers remains a difficult problem unless units are an integral part of the computational procedure. This paper begins with a description of the data structures and algorithms needed to represent and manipulate physical quantity variables and matrices of physical quantities. The result is a high-level scripting language that offers enhanced type checking for expressions and assignments, automatic conversion of systems of units, and program control structures for the solution of engineering problems. These ideas have been implemented in Aladdin, a new computational environment for matrix and finite-element calculations. The capabilities of Aladdin are demonstrated through the deflection analysis of a cantilever beam.