Application of plate theory to laminated wood composites with non-rigid adhesive

Abstract

A closed-form solution for laminated wood and sandwich biocomposite panels assembled with non-rigid adhesives and subjected to edgewise loading is presented. The solution satisfies the equilibrium equations of the layers, the compatibility equations of stresses and strains at the interfaces and the boundary conditions. To investigate the effects of the finite values of bonding stiffness on the mechanical responses of the panels, numerical evaluations are conducted. The results obtained have shown that the adhesive stiffness has a strong effect on the panel mechanical response. Beyond a certain level of stiffness, the usual assumption of perfect bonding used in classical theories is acceptable. This could provide an answer to what constitutes perfect bonding in terms of the ratio of the inner layer stiffness to the bonding stiffness.

Numerical Analysis for U‐Shaped Thin‐Walled Structure Reinforced Timber Beam Based on Thin‐Layer Beam Theory

“…In thinlayer beam theory approaches, mainly known as sandwich construction in the form of thin face panels, the analytical model and solution to estimate the effective mechanical properties of adhesives are unavoidable. eoretical studies about the bending capacity subjected to various working loads have been given, and the research on nonrigid adhesive applied the plate theory developed by Hussein [1,2,9,39,40]. In fact, the approaches were initiated by the Kirchhoff-Love plate theory.…”

“…where k is the load position. Based on the graphs [2,9], and by taking α into numerical evaluation for the parametric study, ω max always increase inducing values of αL/2 decrease when EI ∞ /EI 0 remains increasing proportionally.…”

“…As timber structures are brittle materials, different reinforcement techniques can be adopted for avoiding easily damageable parts of the building, such as concrete, steel, and FRP used for timber beams and sandwich beams [1][2][3][4][5][6][7]. However, the reinforcements often make beam confront stiffness degradation and bonded layers separation due to interlay slip associated with flexibility and deformation of connectors [8][9][10]. Shear stress plays a significant role in bending strength of composite beam as discussed in many research studies, and some numerical methods to estimate it have been established [5,9,[11][12][13][14][15][16].…”

“…However, the reinforcements often make beam confront stiffness degradation and bonded layers separation due to interlay slip associated with flexibility and deformation of connectors [8][9][10]. Shear stress plays a significant role in bending strength of composite beam as discussed in many research studies, and some numerical methods to estimate it have been established [5,9,[11][12][13][14][15][16]. Malek et al proposed that shear stress in the interface of concrete and plate beams leads to flexural cracks compared to other items including tensile stress, analytically given by unique definition from high-order ordinary differential equations applied to the concrete beam [17].…”

“…Alternatively, Edward and omas [2] developed a plate theory to reflect the mechanical behavior of thin-layer composite structures shown by the model without externally imposed shear force in the cross section of thin layer [2]. Based on the plate theory, Hussein has completed analytical and experimental studies that give a calculated simulation focussed on the influence of the adhesive [9]. Recently, the plate theory was used in the thin-walled steel to strengthen timber composite structures [33].…”