Scholarly
Volume:9, Issue: 5, 2015 Page No: 692 - 698
International Journal of Mechanical, Industrial and Aerospace Sciences
ISSN: 2517-9950
FEM Models of Glued Laminated Timber Beams Enhanced by Bayesian Updating of Elastic Moduli
Two finite element (FEM) models are presented in
this paper to address the random nature of the response of glued
timber structures made of wood segments with variable elastic
moduli evaluated from 3600 indentation measurements. This total
database served to create the same number of ensembles as was the
number of segments in the tested beam. Statistics of these ensembles
were then assigned to given segments of beams and the Latin
Hypercube Sampling (LHS) method was called to perform 100
simulations resulting into the ensemble of 100 deflections subjected
to statistical evaluation. Here, a detailed geometrical arrangement of
individual segments in the laminated beam was considered in the
construction of two-dimensional FEM model subjected to in fourpoint
bending to comply with the laboratory tests. Since laboratory
measurements of local elastic moduli may in general suffer from a
significant experimental error, it appears advantageous to exploit the
full scale measurements of timber beams, i.e. deflections, to improve
their prior distributions with the help of the Bayesian statistical
method. This, however, requires an efficient computational model
when simulating the laboratory tests numerically. To this end, a
simplified model based on Mindlin’s beam theory was established.
The improved posterior distributions show that the most significant
change of the Young’s modulus distribution takes place in laminae in
the most strained zones, i.e. in the top and bottom layers within the
beam center region. Posterior distributions of moduli of elasticity
were subsequently utilized in the 2D FEM model and compared with
the original simulations.