The Experts below are selected from a list of 96 Experts worldwide ranked by ideXlab platform
C B Kandilas - One of the best experts on this subject based on the ideXlab platform.
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solving the plane Elastostatic Problem by the analog equation method
Computers & Structures, 1997Co-Authors: J T Katsikadelis, C B KandilasAbstract:Abstract A novel BEM-based method, the analog equation method (AEM), is employed to solve the plane Elastostatic Problem described by the Navier equations. The actual Problem is converted to an equivalent one described by two uncoupled Poisson's equations with fictitious source terms, under the same boundary conditions. The fictitious sources are established using the indirect BEM method for the potential Problem. The method incorporates features and advantages of FDM, FEM and BEM. Numerical examples are presented which illustrate the merits of the method, as well as its accuracy.
J T Katsikadelis - One of the best experts on this subject based on the ideXlab platform.
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the 2d Elastostatic Problem in inhomogeneous anisotropic bodies by the meshless analog equation method maem
Engineering Analysis With Boundary Elements, 2008Co-Authors: J T KatsikadelisAbstract:The meshless analog equation method (MAEM) is employed to solve the 2D Elastostatic Problem for inhomogeneous anisotropic bodies. In this case, the response of the body is governed by two coupled PDEs of second order with variable (position-dependent) coefficients, which are solved using the new meshless method developed by Katsikadelis for solving PDEs. The method is based on the concept of the analog equation of Katsikadelis, hence its name (MAEM), which converts the original coupled PDEs into two uncoupled Poisson's equations, the analog equations, under fictitious sources. The fictitious sources are represented by MQ-RBFs. Integration of the analog equations allows the approximation of the sought solution by new RBFs. Then inserting the solution into the PDEs and BCs and collocating at the mesh-free nodal points yields a system of linear equations, which permit the evaluation of the expansion coefficients. The method exhibits key advantages over other RBF collocation methods as it is highly accurate and the matrix of the resulting linear equations is always invertible. The accuracy is increased using optimal values of the shape parameters of the multiquadrics and of the integration constants of the analog equation by minimizing the total potential of the elastic body. Several examples are studied, which demonstrate the efficiency and high accuracy of the solution method.
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the bem for the Elastostatic Problem in inhomogeneous plane bodies
2004Co-Authors: M S Nerantzaki, J T Katsikadelis, J G PlatanidiAbstract:1. SUMMARY A new BEM approach is presented for the plane Elastostatic Problem for inhomogeneous plane bodies with variable thickness. The incapability of establishing the fundamental solution for equations with variable coefficients is overcome by using the known fundamental solution of the Navier equations for the homogeneous isotropic plane stress Problem to derive the necessary boundary integral equations. This formulation introduces two additional unknown field functions, which physically represent the two components of a fictitious body force. They are determined from two supplementary domain integral equations. The latter are converted to boundary ones by employing a meshless technique based on global approximation by radial basis functions series. Thus, the presented method maintains the pure boundary character of the BEM. The obtained numerical results demonstrate the effectiveness and accuracy of the method. The inhomogeneity in plate elastic bodies results from the position dependent material constants as well as from its variable thickness. The response of such bodies leads to boundary value Problems for partial differential equations with variable coefficients. The conventional BEM can be employed only if the respective fundamental solution is known or can be established. This, however, is out of question for differential equations with variable coefficients. Though the Problem is of great interest, very few solutions can be found in the literature. Most of them deal with specific variation laws of the material constants. A more general solution has been reported by Chen et al. [1], where we refer for additional literature. The herein presented method uses the known fundamental solution of the Navier equations for the homogeneous isotropic plane body to establish the necessary boundary integral equations. This new formulation, based on the concept of the analog equation [2], introduces two additional unknown field functions, which physically represent the two components of a fictitious body force. They are determined from two supplementary domain integral equations. The latter are converted to pure boundary integral equations by employing a meshless technique based on global approximation by radial basis functions series. Then the displacements and the stresses are evaluated from their integral representations based on the known fundamental solution. Thus, the presented method maintains the pure boundary character of the BEM, since the discretization into elements and the integrations are limited only to the boundary. Example Problems are studied. The obtained numerical results demonstrate the effectiveness and accuracy of the method. A significant advantage of the proposed method is that the same computer program is utilized to obtain numerical results regardless the specific form of the governing differential operator. Hence the solution for the anisotropic body may result as a special case.
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solving the plane Elastostatic Problem by the analog equation method
Computers & Structures, 1997Co-Authors: J T Katsikadelis, C B KandilasAbstract:Abstract A novel BEM-based method, the analog equation method (AEM), is employed to solve the plane Elastostatic Problem described by the Navier equations. The actual Problem is converted to an equivalent one described by two uncoupled Poisson's equations with fictitious source terms, under the same boundary conditions. The fictitious sources are established using the indirect BEM method for the potential Problem. The method incorporates features and advantages of FDM, FEM and BEM. Numerical examples are presented which illustrate the merits of the method, as well as its accuracy.
Stephen C Cowin - One of the best experts on this subject based on the ideXlab platform.
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inhomogeneous Elastostatic Problem solutions constructed from stress associated homogeneous solutions
Journal of The Mechanics and Physics of Solids, 2004Co-Authors: M Fraldi, Stephen C CowinAbstract:Abstract In this paper, we present a theorem that provides solutions for anisotropic and inhomogeneous Elastostatic Problems by using the known solution of an associated anisotropic and homogeneous Problem if the associated Problem has a stress state with a zero eigenvalue everywhere in the domain of the Problem. The fundamental property on which this stress - associated solution (SAS) theorem is built is the coaxiality of the eigenvector associated with the zero stress eigenvalue in the homogeneous Problem and the gradient of the scalar function ϕ characterizing the inhomogeneous character of the inhomogeneous Problem. It is shown that most of the solutions of anisotropic elastic Problems presented in the literature have this property and, therefore, it is possible to use the SAS theorem to construct new exact solutions for inhomogeneous Problems, as well as to find—using the SAS theorem—solutions for the shape intrinsic and angularly inhomogeneous Problems.
M Fraldi - One of the best experts on this subject based on the ideXlab platform.
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inhomogeneous Elastostatic Problem solutions constructed from stress associated homogeneous solutions
Journal of The Mechanics and Physics of Solids, 2004Co-Authors: M Fraldi, Stephen C CowinAbstract:Abstract In this paper, we present a theorem that provides solutions for anisotropic and inhomogeneous Elastostatic Problems by using the known solution of an associated anisotropic and homogeneous Problem if the associated Problem has a stress state with a zero eigenvalue everywhere in the domain of the Problem. The fundamental property on which this stress - associated solution (SAS) theorem is built is the coaxiality of the eigenvector associated with the zero stress eigenvalue in the homogeneous Problem and the gradient of the scalar function ϕ characterizing the inhomogeneous character of the inhomogeneous Problem. It is shown that most of the solutions of anisotropic elastic Problems presented in the literature have this property and, therefore, it is possible to use the SAS theorem to construct new exact solutions for inhomogeneous Problems, as well as to find—using the SAS theorem—solutions for the shape intrinsic and angularly inhomogeneous Problems.
M. Rahman - One of the best experts on this subject based on the ideXlab platform.
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A Rigid Elliptical Disc-Inclusion, in an Elastic Solid, Subjected to a Polynomial Normal Shift
Journal of elasticity and the physical science of solids, 2002Co-Authors: M. RahmanAbstract:The article investigates the Elastostatic Problem of axial translation of a rigid elliptical disc-inclusion embedded into an elastic solid. The case of constant translation was previously studied by Kassir and Sih. The present study focuses on the more general case in which the translation is characterized by an arbitrary-order polynomial in the Cartesian coordinates of the points of the disc. By means of Fourier transforms, the Problem is reduced to a two-dimensional integral equation. Ferrers–Dyson's and Galin's theorems and some of their refinements by the present author are then employed to derive a closed-form solution of the integral equation, permitting the displacements and the stresses in the entire solid to be expressed in explicit analytical form. In particular, the behavior of the stress field in the immediate vicinity of the edge of the disc is analyzed in great detail and closed-form expressions for the stress intensity factors are deduced for an arbitrary-order polynomial normal shift. Furthermore, these results are generalized, based on an idea by Tada and Paris, to flat rigid inclusions of an arbitrary shape having an axis of symmetry.
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Elastostatic surface displacements of a half-space reinforced by a thin film due to an axial ring load
International Journal of Engineering Science, 1997Co-Authors: M. Rahman, G. NewazAbstract:Abstract The Elastostatic Problem of a semi-infinite solid whose surface is reinforced by a thin film and acted upon by an axial ring load is investigated in this paper. Explicit expressions are derived for the surface displacements of the solid.