Intrinsic Sensitivity Matrices for Structural Optimization of Trusses

This paper introduces an intrinsic symmetric, positive or positive semi‐definite matrix that contains the essential data for characterizing the change of a measure of stress as a function of self‐equilibrating load states. The concept is important in the theory of structures because it isolates intrinsic characteristics of a structure's sensitivity to design changes irrespective of externally applied load cases. It is computationally important because it provides alternative and sometimes more efficient procedures for calculating design sensitivities than the conventional approach. The intrinsic sensitivity matrix leads to a necessary and sufficient basis for determining force redundancy and identifying elements whose removal will reduce an indeterminate structure to a determinate one. It leads to theorems relating changes in sizing variables to changes in element stresses. Its use offers to reduce calculations when there are many more loadings than elements and when a sequence of changes to the design requires a sequence of sensitivity matrices.