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How to recognize the order of infinitesimal mechanisms: A numerical approach
Author(s) -
Salerno Ginevra
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350702
Subject(s) - infinitesimal , finite element method , stiffness , displacement (psychology) , displacement field , mathematics , field (mathematics) , order (exchange) , mathematical analysis , structural engineering , engineering , pure mathematics , psychology , finance , economics , psychotherapist
Structures presenting kinematical inderterminacy are usually called mechanisms . This paper is entirely concerned with assemblies which reveal themselves to be mechanisms at a null value of the load. Among them a first distinction is made between infinitesimal and finite ones, the former being characterized by one or several directions of lower (but not zero) stiffness, whereas the latter show at least one finite admissible displacement for which none of the bars undergoes any elongation. Moreover, there exists the possibility to make a further distinction among the infinitesimal mechanisms, according to which is the order of the stiffness along the direction considered above. The way of evaluating this order is to perform a local analysis of the strain energy of the assembly, once the displacement field is parametrized in terms of a suitable parameter. By means of a finite element technique, this analysis can be easily performed through the numerical approach presented in this report.