Non-linear analysis of two-layer timber beams considering interlayer slip and uplift

A new mathematical model and its finite element formulation for the non-linear analysis of mechanical behaviour of a two-layer timber planar beam is presented. A modified principle of virtual work is employed in formulating the finite element method. The basic unknowns are strains. The following assumptions are adopted in the mathematical model: materials are taken to be non-linear and can differ from layer to layer; interacting shear and normal contact tractions between layers are derived from the non-linear shear contact traction-slip and the non-linear normal contact traction-uplift characteristics of the connectors; the geometrically linear and materially non-linear Bernoulli's beam theory is assumed for each layer. The formulation is found to be accurate, reliable and computationally effective. The suitability of the theory is validated by the comparison of the numerical solution and the experimental results of full-scale laboratory tests on a simply supported beam. An excellent agreement between measured and calculated results is observed for all load levels. The further objective of the paper is the analysis of the effect of different normal contact traction-uplift constitutive relationships on the kinematic and static quantities in a statically determined and undetermined structure. While the shear contact traction-slip constitutive relationship dictates the deformability of the composite beam and has a substantial influence on most of the static and kinematic quantities of the composite beam, a variable normal contact traction-uplift constitutive relationship is in most cases negligible

Locking-free two-layer Timoshenko beam element with interlayer slip

A new locking-free strain-based finite element formulation for the numerical treatment of linear static analysis of two-layer planar composite beams with interlayer slip is proposed. In this formulation, the modified principle of virtual work is introduced as a basis for the finite element discretization. The linear kinematic equations are included into the principle by the procedure, similar to that of Lagrangian multipliers. A strain field vector remains the only unknown function to be interpolated in the finite element implementation of the principle. In contrast with some of the displacement-based and mixed finite element formulations of the composite beams with interlayer slip, the present formulation is completely locking-free. Hence, there are no shear and slip locking, poor convergence and stress oscillations in these finite elements. The generalization of the composite beam theory with the consideration of the Timoshenko beam theory for the individual component of a composite beam represents a substantial contribution in the field of analysis of non-slender composite beams with an interlayer slip. An extension of the present formulation to the non-linear material problems is straightforward. As only a few finite elements are needed to describe a composite beam with great precision, the new finite element formulations is perfectly suited for practical calculations. (c) 2007 Elsevier B.V. All rights reserved

Genetic Differentiation of the Western Capercaillie Highlights the Importance of South-Eastern Europe for Understanding the Species Phylogeography

The Western Capercaillie (Tetrao urogallus L.) is a grouse species of open boreal or high altitude forests of Eurasia. It is endangered throughout most mountain range habitat areas in Europe. Two major genetically identifiable lineages of Western Capercaillie have been described to date: the southern lineage at the species' southernmost range of distribution in Europe, and the boreal lineage. We address the question of genetic differentiation of capercaillie populations from the Rhodope and Rila Mountains in Bulgaria, across the Dinaric Mountains to the Slovenian Alps. The two lineages' contact zone and resulting conservation strategies in this so-far understudied area of distribution have not been previously determined. The results of analysis of mitochondrial DNA control region sequences of 319 samples from the studied populations show that Alpine populations were composed exclusively of boreal lineage; Dinaric populations of both, but predominantly (96%) of boreal lineage; and Rhodope-Rila populations predominantly (>90%) of southern lineage individuals. The Bulgarian mountains were identified as the core area of the southern lineage, and the Dinaric Mountains as the western contact zone between both lineages in the Balkans. Bulgarian populations appeared genetically distinct from Alpine and Dinaric populations and exhibited characteristics of a long-term stationary population, suggesting that they should be considered as a glacial relict and probably a distinct subspecies. Although all of the studied populations suffered a decline in the past, the significantly lower level of genetic diversity when compared with the neighbouring Alpine and Bulgarian populations suggests that the isolated Dinaric capercaillie is particularly vulnerable to continuing population decline. The results are discussed in the context of conservation of the species in the Balkans, its principal threats and legal protection status. Potential conservation strategies should consider the existence of the two lineages and their vulnerable Dinaric contact zone and support the specificities of the populations