Matrix and finite element stack machines for structural engineering computations with units

Despite the well known benefits of physical units, matrices, and matrix algebra in engineering computations, most engineering analysis packages are essentially dimensionless. This paper describes the design and implementation of matrix and finite element stack machines for Aladdin, a new computational environment that embeds units inside matrix and finite element calculations. Functionality of the Aladdin stack machine is illustrated by working step by step through the setup and execution of three examples: (1) Parsing and stack machine execution for x = 2 in; (2) Deflection analysis of a cantilever beam, and (3) Rollup maneuver for a long cantilever beam.