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C W Lim - One of the best experts on this subject based on the ideXlab platform.
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Combined load buckling for cylindrical shells based on a symplectic Elasticity Approach
Journal of Theoretical and Applied Mechanics, 2015Co-Authors: Jiabin Sun, C W LimAbstract:Buckling behavior of cylindrical shells subjected to combined pressure, torsion and axial compression is presented by employing a symplectic method. Both symmetric and non-symmetric boundary conditions are considered. Hamiltonian canonical equations are established by introducing four pairs of dual variables. Then, solution of fundamental equations is converted into a symplectic eigenvalue problem. It is concluded that the influence of pressure on buckling solutions is more significant than that due to compressive load, in particular for a longer external pressured cylindrical shell. Besides, buckling loads and circumferential wavenumbers can be reduced greatly by relaxed in-plane axial constraints.
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Symplectic Elasticity: Theory and Applications
Applied Mechanics Reviews, 2011Co-Authors: C W LimAbstract:Symplectic Elasticity: Theory and Applications Many of the early works on symplectic Elasticity were published in Chinese and as a result, the early works have been unavailable and unknown to researchers worldwide. It is the main objective of this paper to highlight the contributions of researchers from this part of the world and to disseminate the technical knowledge and innovation of the symplectic Approach in analytic Elasticity and applied engineering mechanics. This paper begins with the history and background of the symplectic Approach in theoretical physics and classical mechanics and subsequently discusses the many numerical and analytical works and papers in symplectic Elasticity. This paper ends with a brief introduction of the symplectic methodology. A total of more than 150 technical papers since the middle of 1980s have been collected and discussed according to various criteria. In general, the symplectic Elasticity Approach is a new concept and solution methodology in Elasticity and applied mechanics based on the Hamiltonian principle with Legendre's transformation. The superiority of this symplectic Approach with respect to the classical Approach is at least threefold: (i) it alters the classical practice and solution technique using the semi-inverse Approach with trial functions such as those of Navier, Lévy, and Timosh-enko; (ii) it consolidates the many seemingly scattered and unrelated solutions of rigid body movement and elastic deformation by mapping with a series of zero and nonzero eigenvalues and their associated eigenvectors; and (iii) the Saint–Venant problems for plane Elasticity and elastic cylinders can be described in a new system of equations and solved. A unique feature of this method is that bending of plate becomes an eigenvalue problem and vibration becomes a multiple eigenvalue problem.
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dynamic behaviour of axially moving nanobeams based on nonlocal Elasticity Approach
Acta Mechanica Sinica, 2010Co-Authors: C W LimAbstract:In this article, transverse free vibrations of axially moving nanobeams subjected to axial tension are studied based on nonlocal stress Elasticity theory. A new higher-order differential equation of motion is derived from the variational principle with corresponding higher-order, non-classical boundary conditions. Two supporting conditions are investigated, i.e. simple supports and clamped supports. Effects of nonlocal nanoscale, dimensionless axial velocity, density and axial tension on natural frequencies are presented and discussed through numerical examples. It is found that these factors have great influence on the dynamic behaviour of an axially moving nanobeam. In particular, the nonlocal effect tends to induce higher vibration frequencies as compared to the results obtained from classical vibration theory. Analytical solutions for critical velocity of these nanobeams when the frequency vanishes are also derived and the influences of nonlocal nanoscale and axial tension on the critical velocity are discussed.
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a new analytic symplectic Elasticity Approach for beams resting on pasternak elastic foundations
Journal of Mechanics of Materials and Structures, 2010Co-Authors: C W Lim, W A YaoAbstract:Analytic solutions describing the stresses and displacements of beams on a Pasternak elastic foundation are presented using a symplectic method based on classical two-dimensional Elasticity theory. Hamilton’s principle with a Legendre transformation is employed to derive the Hamiltonian dual equation, and separation of variables reduces the dual equation to an eigenequation that differs from the conventional eigenvalue problems involved in vibration and buckling analysis. Using adjoint symplectic orthonormality, a group of eigensolutions of zero eigenvalue, corresponding to the Saint-Venant problem, are derived. This Approach differs from the traditional semi-inverse analysis, which requires stress or deformation trial functions in the Lagrangian system. The final solutions, which account for the effects of an elastic foundation and applied lateral loads, are approximated by an eigenfunction expansion. Comparisons with existing numerical solutions are conducted to validate the efficiency of this new Approach.
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on new symplectic Elasticity Approach for exact free vibration solutions of rectangular kirchhoff plates
International Journal of Engineering Science, 2009Co-Authors: C W Lim, Yang Xiang, Weian YaoAbstract:Abstract In the classical Approach, it has been common to treat free vibration of rectangular Kirchhoff or thin plates in the Euclidian space using the Lagrange system such as the Timoshenko’s method or Levy’s method and such methods are the semi-inverse methods. Because of various shortcomings of the classical Approach leading to unavailability of analytical solutions in certain basic plate vibration problems, it is now proposed here a new symplectic Elasticity Approach based on the conservative energy principle and constructed within a new symplectic space. Employing the Hamiltonian variational principle with Legendre’s transformation, exact analytical solutions within the framework of the classical Kirchhoff plate theory are established here by eigenvalue analysis and expansion of eigenfunctions in both perpendicular in-plane directions. Unlike the classical semi-inverse methods where a trial shape function required to satisfy the geometric boundary conditions is pre-determined at the outset, this symplectic Approach proceeds without any shape functions and it is rigorously rational to facilitate analytical solutions which are not completely covered by the semi-inverse counterparts. Exact frequency equations for Levy-type thin plates are presented as a special case. Numerical results are calculated and excellent agreement with the classical solutions is presented. As derivation of the formulation is independent on the assumption of displacement field, the present method is applicable not only for other types of boundary conditions, but also for thick plates based on various higher-order plate theories, as well as buckling, wave propagation, and forced vibration, etc.
Weian Yao - One of the best experts on this subject based on the ideXlab platform.
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on new symplectic Elasticity Approach for exact free vibration solutions of rectangular kirchhoff plates
International Journal of Engineering Science, 2009Co-Authors: C W Lim, Yang Xiang, Weian YaoAbstract:Abstract In the classical Approach, it has been common to treat free vibration of rectangular Kirchhoff or thin plates in the Euclidian space using the Lagrange system such as the Timoshenko’s method or Levy’s method and such methods are the semi-inverse methods. Because of various shortcomings of the classical Approach leading to unavailability of analytical solutions in certain basic plate vibration problems, it is now proposed here a new symplectic Elasticity Approach based on the conservative energy principle and constructed within a new symplectic space. Employing the Hamiltonian variational principle with Legendre’s transformation, exact analytical solutions within the framework of the classical Kirchhoff plate theory are established here by eigenvalue analysis and expansion of eigenfunctions in both perpendicular in-plane directions. Unlike the classical semi-inverse methods where a trial shape function required to satisfy the geometric boundary conditions is pre-determined at the outset, this symplectic Approach proceeds without any shape functions and it is rigorously rational to facilitate analytical solutions which are not completely covered by the semi-inverse counterparts. Exact frequency equations for Levy-type thin plates are presented as a special case. Numerical results are calculated and excellent agreement with the classical solutions is presented. As derivation of the formulation is independent on the assumption of displacement field, the present method is applicable not only for other types of boundary conditions, but also for thick plates based on various higher-order plate theories, as well as buckling, wave propagation, and forced vibration, etc.
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on new symplectic Elasticity Approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported
International Journal of Solids and Structures, 2007Co-Authors: C W Lim, S Cui, Weian YaoAbstract:Abstract This paper presents a bridging research between a modeling methodology in quantum mechanics/relativity and Elasticity. Using the symplectic method commonly applied in quantum mechanics and relativity, a new symplectic Elasticity Approach is developed for deriving exact analytical solutions to some basic problems in solid mechanics and Elasticity which have long been bottlenecks in the history of Elasticity. In specific, it is applied to bending of rectangular thin plates where exact solutions are hitherto unavailable. It employs the Hamiltonian principle with Legendre’s transformation. Analytical bending solutions could be obtained by eigenvalue analysis and expansion of eigenfunctions. Here, bending analysis requires the solving of an eigenvalue equation unlike in classical mechanics where eigenvalue analysis is only required in vibration and buckling problems. Furthermore, unlike the semi-inverse Approaches in classical plate analysis employed by Timoshenko and others such as Navier’s solution, Levy’s solution, Rayleigh–Ritz method, etc. where a trial deflection function is pre-determined, this new symplectic plate analysis is completely rational without any guess functions and yet it renders exact solutions beyond the scope of applicability of the semi-inverse Approaches. In short, the symplectic plate analysis developed in this paper presents a breakthrough in analytical mechanics in which an area previously unaccountable by Timoshenko’s plate theory and the likes has been trespassed. Here, examples for plates with selected boundary conditions are solved and the exact solutions discussed. Comparison with the classical solutions shows excellent agreement. As the derivation of this new Approach is fundamental, further research can be conducted not only on other types of boundary conditions, but also for thick plates as well as vibration, buckling, wave propagation, etc.
Emad Hasan - One of the best experts on this subject based on the ideXlab platform.
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runoff sensitivity to climate change in the nile river basin
Journal of Hydrology, 2018Co-Authors: Emad Hasan, Aondover Tarhule, Pierreemmanuel Kirstetter, Race Clark, Yang HongAbstract:Abstract In data scarce basins, such as the Nile River Basin (NRB) in Africa, constraints related to data availability, quality, and access often complicate attempts to estimate runoff sensitivity using conventional methods. In this paper, we show that by integrating the concept of the aridity index (AI) (derived from the Budyko curve) and climate Elasticity, we can obtain the first order response of the runoff sensitivity using minimal data input and modeling expertise or experience. The concept of runoff Elasticity relies on the fact that the energy available for evapotranspiration plays a major role in determining whether the precipitation received within a drainage basin generates runoff. The Approach does not account for human impacts on runoff modification and or diversions. By making use of freely available gauge-corrected satellite data for precipitation, temperature, runoff, and potential evapotranspiration, we derived the sensitivity indicator ( β ) to determine the runoff response to changes in precipitation and temperature for four climatic zones in the NRB, namely, tropical, subtropical, semiarid and arid zones. The proposed sensitivity indicator can be partitioned into different Elasticity components i.e: precipitation ( e p ), potential evapotranspiration ( e ET p ), temperature ( e T ) and the total Elasticity ( e tot ) . These elasticities allow robust quantification of the runoff response to the potential changes in precipitation and temperature with a high degree of accuracy. Results indicate that the tropical zone is energy-constrained with low sensitivity, ( β 1.0 ) , implying that input precipitation exceeds the amounts that can be evaporated given the available energy. The subtropical zone is subdivided into two distinct regions, the lowland (Machar and Sudd marshes), and the highland area (Blue Nile Basin), where each area has a unique sensitivity. The lowland area has high sensitivity, ( β > 1.0 ) . The subtropical-highland zone moves between energy-limited to water-limited conditions during periods of wet and dry spells with varying sensitivity. The semiarid and arid zones are water limited, with high sensitivity, ( β > 1.0 ) . The calculated runoff elasticities show that a 10% decrease in precipitation leads to a decrease in runoff of between 19% in the tropical zone and 30% in the arid zones. On the other hand, a 10% precipitation increase leads to a runoff increase of 14% in the tropical zone and 22% in the arid zone. The estimated runoff changes are consistent with the result obtained using other methods. Thus, the Elasticity Approach combines data parsimony and analytical simplicity to produce results that are practically useful for most purposes while facilitating communication with stakeholders with different levels of scientific knowledge. More research is needed to extend the application of the method to incorporate the effects of human activities, and land use change.
Anirudh Sharma - One of the best experts on this subject based on the ideXlab platform.
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Interference effect of two nearby strip footings on layered soil: theory of Elasticity Approach
Acta Geotechnica, 2010Co-Authors: Priyanka Ghosh, Anirudh SharmaAbstract:In recent times, rapid urbanisation coupled with scarcity of land forces several structures to come up ever closer to each other, which may sometime cause severe damage to the structures from both strength and serviceability point of view, and therefore, a need is felt to devise simplified methods to capture the effect of footing interference. In the present study, an attempt has been made to model the settlement behaviour of two strip footings placed in close spacing on layered soil deposit consisting of a strong top layer underlying a weak bottom layer. Theory of Elasticity is employed to derive the governing differential equations and subsequently solved by the finite difference method. The perfectly rough strip footings are considered to be resting on the surface of two-layer soil system, and the soil is assumed to behave as linear elastic material under a range of static foundation load. The effect of various parameters such as the elastic moduli and thickness of two layers, clear spacing between the footings and footing load on the settlement behaviour of closely spaced footings has been determined. The variation of vertical normal stress at the interface of two different soil layers as well as at the base of the failure domain also forms an important part of this study. The results are presented in terms of settlement ratio (ξ_δ), and their variation is obtained with the change in clear spacing between two footings. The present theoretical investigation indicates that the settlement of closely spaced footings is found to be higher than that of single isolated footing, which further reduces with increase in the spacing between the footings.
Yu M Gutkin - One of the best experts on this subject based on the ideXlab platform.
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surface interface effects on elastic behavior of an edge dislocation in the shell of a core shell nanowire
European Journal of Mechanics A-solids, 2013Co-Authors: Rezazadeh S Kalehbasti, Yu M Gutkin, H M ShodjaAbstract:Abstract The elastic behavior of an edge dislocation placed in the shell of a free-standing core–shell nanowire is considered within the theory of surface/interface Elasticity. Using the method of complex potential functions the expressions for the stress field of the dislocation, image forces on the dislocation, and the dislocation strain energy are derived and studied in detail. A special attention is paid to non-classical effects revealed within the surface/interface Elasticity Approach where a characteristic length parameter referred to as surface/interface modulus is introduced. These effects are (i) the stress oscillations along the shell surface and core–shell interface for negative values of the surface/interface elastic moduli; (ii) a strong dependence of image forces on the core size; (iii) extra repelling (attraction) of the dislocation from (to) the shell surface and core–shell interface characterized by positive (negative) interface modulus; and (iv) a decrease of the dislocation strain energy in the central region of the shell and its local increase with an extra maximum in the vicinity of the shell surface for negative values of the surface/interface elastic moduli. These non-classical effects increase with diminishing core radius and shell thickness and are very strong in the layers of 1 nm thickness adjacent to the core–shell interface and shell surface. The effects of the residual surface stress are also addressed.
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size dependent interaction of an edge dislocation with an elliptical nano inhomogeneity incorporating interface effects
International Journal of Solids and Structures, 2012Co-Authors: H M Shodja, H Ahmadzadehbakhshayesh, Yu M GutkinAbstract:The elastic behavior of an edge dislocation, which is positioned outside of a nanoscale elliptical inhomogeneity, is studied within the interface Elasticity Approach incorporating the elastic moduli and surface tension of the interface. The complex potential function method is used. The dislocation stress field and the image force acting on the dislocation are found and analyzed in detail. The difference between the solutions obtained within the classical-Elasticity and interface-Elasticity Approaches is discussed. It is shown that for the stress field, this difference can be significant in those points of the inhomogeneity-matrix interface, where the radius of curvature is smaller and which are closer to the dislocation. For the image force, this difference can be considerable or dispensable in dependence on the dislocation position, its Burgers vector orientation, and relations between the elastic moduli of the matrix, inhomogeneity and their interface. Under some special conditions, the dislocation can occupy a stable equilibrium position in atomically close vicinity of the interface. The size effect is demonstrated that the normalized image force strongly depends on the inhomogeneity size when it is in the range of several tens of nanometers, in contrast with the classical solution where this force is always constant. The general issue is that the interface Elasticity effects become more evident when the characteristic sizes of the problem (inhomogeneity size, interface curvature radius and dislocation-interface spacing) reduce to the nanoscale.