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On some path‐related measures for nonlinear structural F. E. problems
Author(s) -
Eriksson Anders
Publication year - 1988
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.1620260808
Subject(s) - tangent , measure (data warehouse) , mathematics , path (computing) , nonlinear system , displacement (psychology) , stiffness , limit (mathematics) , point (geometry) , set (abstract data type) , mathematical analysis , computer science , geometry , structural engineering , engineering , psychology , physics , database , psychotherapist , programming language , quantum mechanics
In the paper, the solution of a non‐linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behaviour, guiding the iteration strategy in coming steps. Two path‐related stiffness measures are derived, giving information concerning the behaviour of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measures.