Modified third order shear-deformation model for anisotropic glulam beams via three-field mixed finite-element formulation

ABSTRACT

Glulam timber structural linear elements often show low span-to-depth ratios. Moreover, timber is intrinsically orthotropic with very low shear moduli. These two circumstances justify the substantial contribution of shear strain to the overall deformation of linear elements. Since design specifications for timber beams commonly adopt 1D models, two such elastic models are proposed in this paper for static plane behavior, where, instead of fully orthotropic, glulam is assumed to be transversely isotropic. These models provide a good compromise between accuracy and simplicity for design proposes. A 3-field mixed formulation is generalized in order to produce two new 1D finite elements suitable for modeling transversely isotropic elastic glulam beams. To assess the accuracy of these new finite elements the results they produce are compared with those determined with a plane stress transversely isotropic 2D finite element. The included examples show that the proposed combination of transverse isotropy with a third order shear deformation model provides a suitable background to the 1D modeling of glulam beams with improved accuracy when compared to the models conventionally used in design. The paper is concluded with a parametric analysis which identifies the cases where the improved models should be used instead of simpler ones.

KEYWORDS:

• glulam beam
• higher-order shear strain
• cross section warping
• 1D finite element
• 3-field mixed formulation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the Portuguese Foundation for Science and Technology under project grants UIDB/00308/2020 (Institute for Systems Engineering and Computers at Coimbra, INESC Coimbra), UIDB/04029/2020 (Institute for Sustainability and Innovation in Engineering Structures, ISISE) and LA/P/0112/2020 (Associate Laboratory Advanced Production and Intelligent Systems ARISE).