Structural matrix computations with units

Despite the well-known benefits of physical units, matrices, and matrix alg ebra in engineering computations, most engineering analysis packages are es sentially dimensionless. They simply hold the engineer responsible for sele cting a set of engineering units and making sure their use is consistent. A lthough this practice may be satisfactory for the solution of established p roblem-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 pap er begins with a description of the data structures and algorithms needed t o represent and manipulate physical quantity variables and matrices of phys ical quantities. The result is a high-level scripting language that offers enhanced type checking for expressions and assignments, automatic conversio n of systems of units, and program control structures for the solution of e ngineering problems. These ideas have been implemented in Aladdin, a new co mputational environment for matrix and finite-element calculations. The cap abilities of Aladdin are demonstrated through the deflection analysis of a cantilever beam.