Abstract
Modifications to linear elastic structures are considered for which the amount of additional stiffening material is increased proportionally. It is proved that, for fixed loading, the strain energy will not be increased and, for fixed displacements, the strain energy will not be decreased by the addition. Furthermore the graphs of strain energy versus the amount of additional material will be monotonic. Also the strain energy absorbed by an incremental amount of additional material must equal the change in the total strain energy for both the cases of fixed loading and fixed displacements. These behavioural properties have been formulated as three theorems. The paper justifies and discusses these and presents some simple illustrations.
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