The paper examines a static bending of porous functional plates (FGP) and rectangular plate solutions, based on an underlying high-order shear deformation theory. The proposed high-order shear ...deformation theory, as opposed to other theories, includes four unknowns. For this reason, a new shear strain function is considered. The technique of Navier is used in closed-form FGP solutions. Results of deflections and stresses are presented for simply supported border conditions. Current figures are contrasted with the non-poreous plate deflecting solutions and the literature's stresses. Effects of different parameters, including thickness, gradient index and porosity of FGM plates, are discussed.
•Flexural properties of CLT panels made with low-value sugar maple has been studied.•Melamine provided better bonding than Resorcinol but not much on flexural properties.•Stronger outer layers ...strengthen the overall major direction flexural performance of CLT.•Studied layups provided better bending and shear performance than standard layup E1.•The finite element model provided satisfactory estimation based on lamination data.
The objective of this study is to examine the mechanical performance of cross laminated timber (CLT) panels made of low-value sugar maple under out of plane loads through mechanical tests and numerical simulation. The laminations were sorted into High and Low classes based on the measured modulus of elasticity (MOE). Two 3-layer sugar maple CLT layups as High-Low-High and Low-High-Low glued with resorcinol-based adhesive and one CLT layup of High-Low-High glued with melamine-based adhesive were prepared. Block shear, long-span bending (span-to-depth ratio of 33:1) and short-span bending (5.5:1) tests were conducted to evaluate the bonding, flexural and shear behavior of these low-value sugar maple CLTs. With a limited sample size, the lab-manufactured low-value sugar maple CLT provided a 50% to 80% higher MOE and at least two times higher MOR than CLT type E1 from APA/PRG 320. Similar MOE and MOR improvements were found by comparing CLT made with other species from literatures. The finite element simulation of bending tests was conducted with the orthogonal constitutive law and the progressive damage model based on the calibrated material properties parameters from lumber rating and references. The simulation results on each CLT panel type have a reasonable comparison with experimental test data. Therefore, these integrated experiment and simulation methods can provide detailed mechanical behaviors of the low-value sugar maple CLT, which can also be applied to other CLT species and layup.
In recent years, there are numerous papers that deal with two-phase strain-driven model, including softening effect, and two-phase stress-driven model, with stiffening effect, and also the nonlocal ...strain gradient model, with both the softening and stiffening effects, to seek the impacts of length scales on the mechanics of structures in small scales. The current paper is a novel well-posed mixture model to cover all previous theories through employing various proposed small scales. Concurrent accounting of stiffening and softening effects is performed through employing a combination of the two-phase strain-driven elasticity with the two-phase stress-driven elasticity, with two additional local phase fraction factors and two various type of nonlocal parameters. Accordingly, in this model the total strain or stress at a certain point is regarded as a function of the stress or strain of all neighboring points in addition to the point of interest. Compatibility between integral and differential relations without any conflict of restrictions is doable through considering constitutive boundary conditions as key point of this match. To demonstrate its application values, the proposed mixture model as an efficient theoretical tool is hired for static bending, vibration and wave propagation in a mixed two-phase stress/strain driven elasticity system and the new essential relations are developed through examples for static bending, free vibration and wave propagating in Euler-Bernoulli nanobeams. The results are obtained by proposing an efficient exact solution, and the integrity as well as reliability of the present constitutive differential relations are evaluated through some validation studies. The output results in the framework of new suggested mixture model address some points about static bending, free vibration and wave propagation that is more comprehensive than the previous results of the contemporary continuum theories. Thus, based on the observations, this mixed two-phase stress/strain driven elasticity could be cover a widespread range of dynamic response in the nano-systems that the contemporary continuum theories can be only investigated some aspects of those problems.
•A novel well-posed mixture model of elasticity is proposed.•Integral and differential constitutive laws are attained.•Concurrent stiffening and softening effects could be observe in this model.•Static bending, free vibration and wave propagation are investigated.•Other contemporary continuum theories are particular states of this model.
The present paper considers the analytical static bending response of a finite uniform free-free Euler-Bernoulli elastic beam resting on a Winkler elastic foundation with a spatially inhomogeneous ...stiffness coefficient. Specifically, a linear variation of the foundation coefficient is assumed. The beam-foundation system is loaded by a force and a moment applied at one beam's (top) end, a configuration which may resemble that of a foundation pile. The analytical solution of the governing Ordinary Differential Equation is derived and represented in explicit closed-form in terms of generalized hypergeometric functions. Through the derived solution, parametric analyses are carried out, by interpreting the parametric variation of the mechanical response of the beam-foundation system due to changes in its mechanical properties.
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•Free-free Euler-Bernoulli beam on Winkler foundation with linear in space stiffness coefficient under point loads.•Rigorous derivation of closed-form exact parametric analytical solution.•Capability of linear support coefficient to include rigid beam on soft support and classical Winkler model.•Dependence of beam-foundation response only on two non-dimensional characteristic parameters.•Characteristic response features by parametric analysis on normalized deflection, bending moment and shear.•Discussion on max deflection, bending moment and shear curves, for design guidance.
It is important to comprehend the physical and mechanical properties of Scots pine wood from various geographical origins in order to use it effectively and rationally in production. The purpose of ...the study is to determine the physical and mechanical properties of Scots pine wood from 17 climatic ecotypes and to conduct a comparative analysis of the received indicators for the studied climatypes separately and for subspecies, which were grouped according to the classification of L.F. Pravdin. The physical properties that were chosen for the investigation were wood density in an absolutely dry state and at 12 % moisture content. The mechanical characteristics were the tensile strength of the wood along the fibers and the tensile strength in static bending. The range of geographic origins of the seed harvesting locations was from 47 to 62 °N and 22 to 85 °E. The investigation was conducted using contemporary universal testing equipment, MTS Insight 100. It was found that the density of the wood varied from 370 kg/m3 (Kursk climatype) to 524 kg/m3 (Volgograd climatype) under absolutely dry conditions and from 397 kg/m3 (Kursk climatype) to 550 kg/m3 (Volgograd climatype) at 12 % moisture content. The tensile strength of wood along the fibers ranged from 32 MPa (Kursk climatype) to 54 MPa (Volgograd climatype), while the tensile strength in static bending was from 55 to 92 MPa for the Vologda and Ulyanovsk climatypes, respectively. The maximum wood density at 12 % moisture content was 497±8 kg/m3, which is typical for European subspecies. The minimum value of this indicator was 423±30 kg/m3. The medium values had Lapland subspecies and Steppe subspecies 483±16 kg/m3 and 464±12 kg/m3, respectively. The tensile strength of wood along the fibers in the studied subspecies ranged from 47±1 MPa (European subspecies) to 33±4 MPa (Siberian subspecies). For Lapland subspecies, it was 44±2 MPa and slightly lower for Steppe subspecies, which was 42±2 MPa. The maximum value of the tensile strength in static bending for European subspecies was 78±4 MPa. The minimum value for the Siberian subspecies was 61±14 MPa. This indicator was equal for Steppe subspecies and Lapland subspecies, which was 72±4 MPa. For citation: Rabko S.U., Melnik P.G., Kozel A.V., Paplauskaya L.F., Tupik P.V., Nosnikau V.V. Comparison of Physical and Mechanical Properties of Scots Pine Wood Grown in Different Climatypes. Lesnoy Zhurnal = Russian Forestry Journal, 2023, no. 4, pp. 26–40. (In Russ.). https://doi.org/10.37482/0536-1036-2023-4-26-40
This paper initiates the theoretical analysis of nonlinear microbeams and investigates the static bending, postbuckling and free vibration. The nonlinear model is conducted within the context of ...non-classical continuum mechanics, by introducing a material length scale parameter. The nonlinear equation of motion, in which the nonlinear term is associated with the mean axial extension of the beam, is derived by using a combination of the modified couple stress theory and Hamilton’s principle. Based on this newly developed model, calculations have been performed for microbeams simply supported between two immobile supports. The static deflections of a bending beam subjected to transverse force, the critical buckling loads and buckled configurations of an axially loaded beam, and the nonlinear frequencies of a beam with initial lateral displacement are discussed. It is shown that the size effect is significant when the ratio of characteristic thickness to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio. Our results also indicate that the nonlinearity has a great effect on the static and dynamic behaviors of microscale beams. To attain accurate and reliable characterization of the static and dynamic properties of microscale beams, therefore, both the microstructure-dependent parameters and the nonlinearities have to be incorporated in the design of microscale beam devices and systems.
This paper presents a new, simple, containing only four unknown functions, individual-layer, static model for rectangular sandwich plate unsymmetrical with respect to its middle plane. The shear ...strains in the outer layers of the plate are neglected while the shear strains in the middle layer are variable and equivalent to zero on its outer surfaces. Local constitutive models of the layers consistent with the assumed kinematics are derived. A detailed analysis of all partial problems is presented. In order to determine the unknown functions, appearing in the kinematic model assumed, one needs to solve a set of three coupled partial differential equations and separately the fourth governing equation that contains only one unknown function. In the case of the plate symmetrical about its middle plane only two uncoupled partial differential equations for the bending problem must be solved. Deflections predicted by the present model for a symmetrical sandwich plate are compared with counterparts, existing in the literature, predicted by two theories that include flexibility of the middle layer of the plate. Good agreement of these results has been obtained.
Beam, plate, and shell structures manufactured from functionally graded materials (FGMs) are becoming increasingly prevalent in practice. The manufacture of these structures is not free from flaws, ...one of which is that the thickness distribution of the material does not change continuously. This is the first study to apply two distinct analytical solutions to examine the static and free vibration responses of imperfect FG nanobeams in terms of material distribution and temperature influence. The calculation formulas are based on the novel shear strain theory, which, despite being simple, accounts for both bending and shear strain, rendering the calculation procedure highly convenient. Either of the two precise solutions is computed using direct integrals and can be computed for various boundary conditions, which is not possible with Navier's solutions. The results of the verification indicate that the approaches given in the article guarantee the needed precision. This study also analyzes the effect of several geometrical, material, nonlocal, and imperfection characteristics on the static bending and free oscillation response of imperfect FG nanobeams.
A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing ...the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of different theories are carried out to show the efficiency and accuracy of the new theory. In addition, some discussions on the influence of various parameters such as the power-law index, the slenderness ratio, and the aspect ratio are carried out, which are useful for the design and testing of advanced composite structures.
The current study provides a discussion on two aspects of size-effects which is known to be a characteristic behavior of micro-scaled structures. First it provides the experimentalists with a novel ...micro-bend technique wherein the micro-cantilever is loaded at different points along its length. This eases the experimental process by reducing the efforts of the experimentalists in sample preparation (as the same sample can be used for obtaining results corresponding to different L/H ratio). Also, precision cutting and mounting of the samples to obtain the micro-cantilever of desirous overhang length is not required. Further, the above described technique is used to test nickle micro-cantilevers of three thicknesses (15, 25, 50 μm) and different L/H (=200, 300, 400) ratios. They are elastically bent to undergo small deflections. Apart from reporting the obvious size-effects for smaller thicknesses and fitting the experiments with a model for determining the length scale parameter, size-effects for beams with different thicknesses and varying L/H ratios are presented. Secondly, a discussion on the widely fluctuating nature of numerical values that the length scale parameter assumes is presented. And it is postulated that the numerical value of length scale parameter is a function of material, model and geometry of beam cross-section.
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