Analytical Analysis of Distribution of Bending Stresses in Layers of Plywood with Numerical Verification

Abstract

The study presents methods for accurate estimation of bending stresses in the 3-point flexural bending test of plywood, i.e. a wood-based laminate with an alternate crosswise ply configuration. The characteristic bending strength (MOR) and mean modulus of elasticity (MOE) of standard beech plywood was determined using European Standard bending tests EN 310. Correlations were determined between empirically determined bending moduli of the plywood and material moduli of the veneer layer. Calculations were conducted based on the classical plate theory for thin panels comprising the theory of elasticity including the Kirchhoff-Love hypothesis. Rigidity of individual layer was established theoretically in the axial configuration of transformed rigidity matrix values. Numerical laminate models were developed and simulation tests were conducted. Results of experimental and analytical studies were verified using the Finite Element Method (FEM). Analyses were performed in two plywood cross-band arrangement variants. An analysis of the distribution of stresses in individual layers of plywood used an analytical and numerical method assuming the plywood specimen to be a rhombic-anisotropic material. It was found that the bending load capacity of plywood depends on the configuration of individual layers (veneers). Values of stresses originating from bending do not only depend on the distance of the considered plywood layer from the middle layer but also on stiffness in the direction of operating stresses. Bending strength varies in individual directions of the plywood panel. Therefore, the distribution of stresses in individual layers differs from that resulting from the stress distribution for homogeneous isotropic materials. Results are presented in the form of tables, bitmaps, graphs and photographs. The tests were conducted based on the BFU-BU-18 standard beech plywood thickness of 18 mm.