Mechanical Interpretations for Invariant Imbedding

by Paul Nelson, Jr., Prof.; Mathematics Dept., Texas Tech. Univ., Lubbock, TX,

Serial Information: Journal of the Engineering Mechanics Division, 1973, Vol. 99, Issue 5, Pg. 957-963

Document Type: Journal Paper

Abstract: The Scott method is examined within the context of solid mechanics, with particular emphasis upon interpretations of the various occurring functions. Two alternative approaches arise, as the basic Riccati variable is taken to be: (1) the stiffness matrix at the right end of the member corresponding to zero load on the body and at the left end; or (2) the flexibility matrix at the right end corresponding to zero body load and zero displacements at the left end. In the stiffness matrix approach the other three quantities appearing are a transmission matrix for displacements, a virtual boundary load, and a displacement that would result from this virtual boundary load. Analogous interpretations hold within the flexibility matrix approach. A clarifying analysis is presented of the distinction between the stiffness matrix in approach 1 and that defined as the inverse of the flexibility matrix in approach 2.

Subject Headings: Matrix (mathematics) | Load factors | Stiffening | Displacement (mechanics) | Domain boundary | Power transmission |

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