Research Article
Oct 1973
Mechanical Interpretations for Invariant Imbedding
Publication: Journal of the Engineering Mechanics Division
Volume 99, Issue 5
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.
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Published In
Journal of the Engineering Mechanics Division
Volume 99 • Issue 5 • October 1973
Pages: 957 - 963
Copyright
© 1973 American Society of Civil Engineers.
History
Published in print: Oct 1973
Published online: Feb 3, 2021
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Authors
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Paul Nelson Jr.
Prof., Mathematics Dept., Texas Tech. Univ., Lubbock, Tex.
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