Journal article

A Note on the Co-linearity of forces and Displacements in an Elastic Structure

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Author list: Gradin, Per;Gulliksson, Mårten;Isaksson, Per

Publication year: 2011

Start page: Art. no. 4003912

ISSN: 1735-3572

DOI: http://dx.doi.org/10.1115/1.4003912

View additional information: View in Web of Science


Abstract

Theconditions under which force vectors and corresponding displacement vectors becomeco-linear are investigated under the assumption of a linear elasticstructure and for an arbitrary number of loading points. Itis shown that there exist an infinite number of directionsalong which the load and displacement vectors in each loadingpoint coincide. Moreover, the problem of co-linearity is analogous tothe problem of finding the extreme values of the workperformed on an elastic structure under the constraint that eachforce has a given magnitude. The result for a finitenumber of loading points is extended to a continuous loaddistribution on the boundary of an elastic structure, i.e., itis possible to find an infinite number of load distributionssuch that the displacement in a point on the boundaryis co-linear with the boundary stress vector in that samepoint.


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