Deterministic design and a priori parameters are used in traditional optimization approaches. The material characteristics of solid wood are not deterministic in reality. Hence, realistic approaches include the uncertainties of parameters. Uncertainty characteristics of wood are mainly originated in natural variation. In addition to this, incertitudes from lack of knowledge are inherent.
Accordingly, the aleatoric approach of randomness can be expanded to a polymorphic uncertainty model. Fuzzy probability based randomness is used in this work. The distribution functions of random variables are parametrized by fuzzy variables. So coupling of both, aleatoric and epistemic uncertainties is involved.
Interactions of fuzzy variables and crosscorrelations of random variables are considered between uncertain variables. Crosscorrelated random fields are used to represent spatial variation of material parameters. The autocovariance structures are modeled structurally dependent.
In this contribution, FEM is applied as a basic solution of a loaded timber structure. A local orthotropic formulation with respect to specifically located tree trunk axes is used. The optimal positions of the tree trunk axes for each wooden log are examined as design parameters. Polymorphic uncertainties are incorporated for a priori parameters. The tools for uncertainty analysis and the basic FEM solution are embedded in an automated and parallelized optimization processing. An analysis of a two-tier glulam beam, according to a purlin of a timber roof construction, is shown as example for the framework.