Finite deformation of 2-D laminated curved beams with variable curvatures

Lin, Kao-Chin; Lin, Chi-Kung

doi:10.1016/j.ijnonlinmec.2011.06.002

Cited by 20 publications

(14 citation statements)

References 16 publications

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“…The curved beam is such that the dimension of the cross section is much less than the dimension of the radius of curvature [8]. In this study, deformation operation was performed easily, because the thickness of curved wood was thin.…”

Section: Loading Diagram and Failure Position Of Chair Types Are Showmentioning

confidence: 99%

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Investigation of the maximum front to back load in the chairs made from curved and modified poplar wood

et al. 2017

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The aim of this research was to build a chair resistant to force from front to back. To achieve this goal, poplar wood was treated with heat and steam, and then curved at an angle of 90°. Curved frame was used for manufacturing chairs. In this study, three different designs of chairs were used. Control sample is a chair of custom type. The first design was a chair with a curved frame forming the structure back down to bottom (one-piece type) and the second design with two curved parts (twopiece type). Front to back load tests were conducted by mechanical universal testing machine in accordance with DIN EN 1729-2 standard. For each design, the test was repeated three times. The results of the experiment showed that differences between the designs were significant. The full type chairs were broken at the load about 1725 N, but the partial type chairs at about 1421 N. For the top to bottom load test, the full type chairs were broken at about 1052 N, other chairs were more resistant. In general, by introducing a design using the curved frame made of treated poplar, the resistance of chairs is improved. Keywords Wooden chairs Á The maximum front to back load Á The maximum top to down load Á Curved poplar wood & Ali Bayatkashkoli

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Section: Loading Diagram and Failure Position Of Chair Types Are Showmentioning

confidence: 99%

“…All the quantities of axial force, shear force, radial, and tangential displacements of laminated curved beam are expressed as functions of angle of tangent slope. The analytical solutions of laminated curved beams of circular and spiral were presented [8].…”

Section: Introductionmentioning

confidence: 99%

Investigation of the maximum front to back load in the chairs made from curved and modified poplar wood

et al. 2017

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“…A model for small strain but finite rotation, which accounts for both bending and membrane deformation, is introduced in the following to analyze the deformation and maximum strain in the microstructure. It degenerates into the well-known Elastica theory (Fertis, 1999; Lin and Lin, 2011; Timoshenko and Gere, 1961) if the effect of membrane deformation is neglected.…”

Section: An Analytic Model For the Horseshoe Microstructuresmentioning

confidence: 99%

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

Cheng

Jang

et al. 2016

Journal of the Mechanics and Physics of Solids

250

108

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Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

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“…In the study of Kim et al [19], an improved formulation for free vibration and spatial stability of nonsymmetric thin-walled curved beams was presented based on the displacement field considering variable curvature effects and the second-order terms of finite-semitangential rotations. Lin and Lin [20] used Lagrangian description together with Eulerian description to derive analytical solutions of laminated curved beams with variable curvature under pure bending and axial forces. Luu and Lee [21] considered geometrically nonlinearity in their buckling and postbuckling analyses of elliptic curved beams subjected to a central concentrate vertical load under clamped-clamped, hinged-hinged, and clamped-hinged boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures

Wan

Liu

2019

Advances in Materials Science and Engineering

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In this paper, geometrically nonlinear analysis of functionally graded curved beams with variable curvatures based on Timoshenko beam theory is presented. Considering the axial extension and the transversal shear deformation, geometrically nonlinear governing equations for the FGM curved beams with variable curvatures subjected to thermal and mechanical loads are formulated. Material properties of the curved beams are assumed to vary arbitrarily in the thickness direction and be independent on the temperature change. By using the numerical shooting method to solve the coupled ordinary differential equations, the nonlinear response of static thermal bending of a FGM semielliptic beams subjected to transversely nonuniform temperature rise is obtained numerically. e effects of material gradient, shear deformation, and temperature rise on the response of the curved beam are discussed in detail. Nonlinear bending of a closed FGM elliptic structure subjected to two pinching concentrated loads is also analyzed. is paper presents some equilibrium paths and configurations of the elliptic curved beam for different pinching concentrated loads.

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Finite deformation of 2-D laminated curved beams with variable curvatures

Cited by 20 publications

References 16 publications

Investigation of the maximum front to back load in the chairs made from curved and modified poplar wood

Investigation of the maximum front to back load in the chairs made from curved and modified poplar wood

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures

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