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Three‐dimensional solid‐to‐beam transition elements for structural dynamics analysis
Author(s) -
Gmür Thomas C.,
Kauten Randy H.
Publication year - 1993
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.1620360902
Subject(s) - finite element method , discretization , beam (structure) , convergence (economics) , projection (relational algebra) , degrees of freedom (physics and chemistry) , mathematics , mathematical analysis , structural engineering , algorithm , engineering , physics , quantum mechanics , economics , economic growth
Complex structural components such as those encountered in many industrial applications may generally be considered as being composed of shell‐ or beam‐like portions linked to three‐dimensional solid continua. When discretized into finite elements, these structures present geometrical and mathematical difficulties at the connections between the different element types since the nodal degrees of freedom allocated to the solid, shell and beam elements are incompatible with each other. The development of specific and reliable transition finite elements is, thus, of outstanding practical importance. This paper presents efficient C 0 compatible transition elements with a variable number of nodes for modelling solid to beam junctions. Based upon the standard isoparametric solid and beam formulations, the current approach includes the properties of both solids and beams, verifies the basic continuity, smoothness and completeness criteria inherent in the finite element convergence requirements, and avoids the shear locking phenomenon typical of C 0 elements by using a strain‐projection method. Several numerical examples which compare this formulation to analytical and experimental solutions are provided in order to show the applicability and efficiency of this approach.