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This paper describes a scheme which enables an electronic digital computer to deal directly with matrices and matrix instructions. It enables the transformation between the specification of matrix calculations on paper and the actual operations within the computer to be carried out in easy and concise terms. Using this scheme the paper develops the appropriate programmes of instructions to be given to the computer for the calculations involved when applying the Argyris matrix method for the analysis of stresses and displacements in arbitrary clastic structures. In order to introduce the reader to the technique a programme for a simple structure is given in Part I. General purpose programmes applicable to more complex structures are given in Parts II and III.

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