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François-xavier Coudert - One of the best experts on this subject based on the ideXlab platform.
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Necessary and sufficient Elastic Stability conditions in various crystal systems
Physical Review B: Condensed Matter and Materials Physics, 2014Co-Authors: Félix Mouhat, François-xavier CoudertAbstract:While the Born Elastic Stability criteria are well known for cubic crystals, there is some confusion in the literature about the form they should take for lower-symmetry crystal classes. Here we present closed form necessary and sufficient conditions for Elastic Stability in all crystal classes, as a concise and pedagogical reference to Stability criteria in noncubic materials.
Teik-cheng Lim - One of the best experts on this subject based on the ideXlab platform.
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Elastic Stability analysis of auxetic columns using third-order shear deformation theory
physica status solidi (b), 2015Co-Authors: Teik-cheng LimAbstract:The analysis of auxetic structural elements undergoing transverse shear deformation has so far been largely confined to the first-order shear deformation theory (FSDT), which requires a shear correction factor; analysis using the third-order shear deformation theory (TSDT), which does not require a shear correction factor, is currently lacking in regard to auxetic structural elements. This paper adopts the TSDT to evaluate the Elastic Stability of isotropic columns with special emphasis on auxetic ones for pinned–pinned columns with springs of equal rotational stiffness at both ends. Results on columns with pinned–pinned (zero stiffness) and fixed–fixed (infinite stiffness) end conditions with square and circular cross sections reveal that auxeticity (i) reduces the transverse shear deformation, (ii) allows the use of classical theories, and (iii) provides higher Elastic Stability.
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Elastic Stability of Auxetic Solids
Auxetic Materials and Structures, 2014Co-Authors: Teik-cheng LimAbstract:This chapter lays down the foundation for Elastic Stability of columns, circular plates, rectangular plates, cylindrical shells and spherical shells that possess negative Poisson’s ratio . Results show that the plate Poisson’s ratio has no effect on the Elastic Stability of rectangular plates under in-plane biaxial loadings when the critical buckling load is expressed in terms of plate flexural rigidity, but the Poisson’s ratio plays a greater role for circular plate buckling. In the Elastic Stability study of spherical shells, the critical buckling stress is directly proportional to the shell thickness for Poisson’s ratio of 0 and proportional to the square of the shell thickness as the Poisson’s ratio approaches −1. Thereafter a summary of results by Miller et al. (Compos Sci Technol 70:1049–1056, 2010) for flatwise buckling optimization of hexachiral and tetrachiral honeycombs is furnished. Finally examples are given for square plates with array of perforations such that imposition of uniaxial compressive buckling leads to 2D auxeticity.
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Elastic Stability of thick auxetic plates
Smart Materials and Structures, 2014Co-Authors: Teik-cheng LimAbstract:Auxetic materials and structures exhibit a negative Poisson?s ratio while thick plates encounter shear deformation, which is not accounted for in classical plate theory. This paper investigates the effect of a negative Poisson?s ratio on thick plates that are subjected to buckling loads, taking into consideration the shear deformation using Mindlin plate theory. Using a highly accurate shear correction factor that allows for the effect of Poisson?s ratio, the Elastic Stability of circular and square plates are evaluated in terms of dimensionless parameters, namely the Mindlin-to-Kirchhoff critical buckling load ratio and Mindlin critical buckling load factors. Results for thick square plates reveal that both parameters increase as the Poisson?s ratio becomes more negative. In the case of thick circular plates, the Mindlin-to-Kirchhoff critical buckling load ratios and the Mindlin critical buckling load factors increase and decrease, respectively, as the Poisson?s ratio becomes more negative. The results obtained herein show that thick auxetic plates behave as thin conventional plates, and therefore suggest that the classical plate theory can be used to evaluate the Elastic Stability of thick plates if the Poisson?s ratio of the plate material is sufficiently negative. The results also suggest that materials with highly negative Poisson?s ratios are recommended for square plates, but not circular plates, that are subjected to buckling loads.
Félix Mouhat - One of the best experts on this subject based on the ideXlab platform.
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Necessary and sufficient Elastic Stability conditions in various crystal systems
Physical Review B: Condensed Matter and Materials Physics, 2014Co-Authors: Félix Mouhat, François-xavier CoudertAbstract:While the Born Elastic Stability criteria are well known for cubic crystals, there is some confusion in the literature about the form they should take for lower-symmetry crystal classes. Here we present closed form necessary and sufficient conditions for Elastic Stability in all crystal classes, as a concise and pedagogical reference to Stability criteria in noncubic materials.
Amit Rajshekar Kalyani - One of the best experts on this subject based on the ideXlab platform.
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On the Elastic Stability of simply supported anisotropic sandwich panels
Composite Structures, 2007Co-Authors: Bhaskar Nanda Mondal, M. Ganapathi, Amit Rajshekar KalyaniAbstract:Abstract Here, the Elastic Stability behavior of simply supported anisotropic sandwich flat panels subjected to mechanical in-plane loads is investigated using an analytical approach. The formulation is based on first-order shear deformation theory and the shear correction factors employed are based on energy consideration that depends on the lay-up as well as material properties. The governing equations are obtained using the Raleigh–Ritz method assuming a combination of sine and cosine functions in the form of double Fourier series for the displacement fields. The effectiveness of the integrated formulation is tested for global characteristics considering examples related to multi-layered laminates and sandwich panels for which solutions are available.
Caleb D Rucker - One of the best experts on this subject based on the ideXlab platform.
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Elastic Stability of cosserat rods and parallel continuum robots
IEEE Transactions on Robotics, 2017Co-Authors: John Till, Caleb D RuckerAbstract:Classic theories in nonlinear Elasticity have increasingly been used to obtain accurate and efficient models for continuum robots and other Elastic structures. Numerically computed solutions of these models typically satisfy the first-order conditions necessary for equilibrium, but do not provide any information about the Elastic Stability of the solution. The inability to detect or avoid physically unstable model solutions poses a major hindrance to reliable model-based simulation, planning, design, and control. In this paper, we adapt results from optimal control to determine the Stability of Kirchhoff rods and Cosserat rods subject to general end constraints, including coupled multirod models which describe parallel continuum robots. We formulate a sufficient condition for the Stability of a solution, a numerical test for evaluating this condition, and a heuristic Stability metric. We verify that our numerical Stability test agrees with the classical results for the buckling of single columns with various end constraints and for multicolumn frames. We then validate our approach experimentally on a six degree-of-freedom parallel continuum robot.