The paper is concerned with the structural mechanics elementary number theory bolker pdf assemblies of bars and pinjoints, particularly where they are simultaneously statically and kinematically indeterminate. The physical significance of the four linear-algebraic vector subspaces of the equilibrium matrix is examined, and an algorithm is set up which determines the rank of the matrix and the bases for the four subspaces.
In particular, this algorithm gives full details of any states of self-stress and modes of inextensional deformation which an assembly may possess. In some circumstances a state of self-stress may impart first-order stiffness to an inextensional mode. A matrix method for detecting this effect is devised, and it is shown that if there is no state of self-stress which imparts first-order stiffness to a given mode, then that mode can undergo rather large distortion which involves either zero change in length of the bars or, possibly, changes in length of third or higher order in the displacements. The paper contains simple examples which illustrate all of the main points of the work.
Check if you have access through your login credentials or your institution. 1986 Published by Elsevier Ltd. We connect Luce’s and Savage’s ways of modeling uncertainty. Luce’s modeling of uncertainty can be applied to modern decision theories. Most models of uncertainty can be embedded in Savage’s model. Using mosaics, we can connect Luce’s modeling of uncertainty with Savage’s.