Derivatives of tangential stiffness matrices for equilibrium path descriptions
1991 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 32, no 5, 1093-1113 p.Article in journal (Refereed) Published
The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non-linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step-wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post-bifurcation behaviour. For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.
Place, publisher, year, edition, pages
1991. Vol. 32, no 5, 1093-1113 p.
Mathematical Techniques--Finite Element Method, Mathematical Techniques--Matrix Algebra, Stiffness Matrices, Beams And Girders
IdentifiersURN: urn:nbn:se:kth:diva-117953OAI: oai:DiVA.org:kth-117953DiVA: diva2:603961
Correspondence Address: Eriksson, Anders; Royal Inst of Technology, Stockholm, Sweden
NR 201408052013-02-072013-02-072013-02-07Bibliographically approved