S. Ullah¹, B. Pichler¹, S. Scheiner^1,2, C. Hellmich^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.3, pp. 279-316, 2010, DOI:10.3970/cmes.2010.057.279

Abstract Point-wise optical measurements of 3D displacement vectors over time are a key input for monitoring shotcrete tunnel shells during construction according to the New Austrian Tunnelling Method (NATM). Aiming at estimation of the stresses prevailing in the highly loaded, hydrating material, we here deal with two different interpolation strategies for reconstructing, from measured displacement vectors, the 3D displacement field histories of the inner surface of the tunnel shell. The first approach considers spatial interpolation of displacement components in a fixed Cartesian base frame, while the second (new) approach refers to displacement components in a moving base frame consisting of vectors… More >

David Stevens¹, Henry Power^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 111-146, 2010, DOI:10.3970/cmes.2010.055.111

Abstract Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs). Unlike traditional RBF collocation methods, the local Hermitian interpolation (LHI) method examined here can be scaled to arbitrarily large problems without numerical ill-conditioning or computational cost issues, due to the presence of small overlapping interpolation systems which grow in number but not in size as the global dataset grows. The flexibility of the full-domain multiquadric collocation method to directly interpolate arbitrary boundary conditions is maintained, via the local interpolations. The Kirchhoff transformation… More >

D. Soares Jr.¹, J. Sladek², V. Sladek²

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 115-140, 2009, DOI:10.3970/cmes.2009.050.115

Abstract In recent years the idea of using mesh-free or mesh-less methods for numerical solution of partial differential equations has received much attention, due to their potential advantage in eliminating the costly effort of mesh generation and re-meshing. A variety of meshless methods has been proposed so far. Many of them are derived from a weak-form formulation on global domain or a set of local subdomains. In the global formulation background cells are required for the integration of the weak form. In methods based on local weak-form formulation no cells are required and therefore they are often referred to as truly… More >

Delfim Soares Jr. ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 97-114, 2009, DOI:10.3970/cmes.2009.050.097

Abstract In this work, meshless methods based on the local Petrov-Galerkin (MLPG) approach are presented to analyse electromagnetic wave propagation problems. Formulations adopting the Heaviside step function and the Gaussian weight function as the test functions in the local weak form are considered. The moving least square (MLS) method is used to approximate the physical quantities in the local integral equations. After spatial discretization is carried out, a system of ordinary differential equations of second order is obtained. This system is solved in the time-domain by the Houbolt's method, allowing the computation of the so-called primary fields (either the electric or… More >

J. Sladek¹, V. Sladek¹, P. Solek², C.L. Tan³, Ch. Zhang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 61-96, 2009, DOI:10.3970/cmes.2009.047.061

Abstract The meshless local Petrov-Galerkin (MLPG) method for transient linear thermoelastic analysis is presented. Orthotropic material properties are considered here. In uncoupled thermoelasticity, the temperature field is not influenced by displacements. Therefore, in the first step, the heat conduction equation is solved for the temperature distribution in the domain. The equations of motion are then solved with the inertial term considered. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations for solving two- and three-dimensional problems. Local integral equations are written on small sub-domains with circular or spherical shapes. They surround nodal… More >

A. Djeukou¹, O. von Estorff²

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 23-42, 2009, DOI:10.3970/cmes.2009.047.023

Abstract The paper deals with the response of rectangular composite plates to low-velocity impact. A third-order shear deformation theory as well as the Newmark integration are used to determine the contact force history analytically. The interaction between the impactor and the plate is modeled with the help of a two degrees-of-freedom system, consisting of springs and masses. The Choi's linearized Hertzian contact model is used to determine the contact force. The maximum impact force is employed for a static damage analysis of the composite plate by means of the radial point interpolation method, while the Tsai-Wu failure criterion is applied for… More >

L.M.J.S. Dinis¹, R.M. Natal Jorge², J. Belinha³

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 1-34, 2009, DOI:10.3970/cmes.2009.044.001

Abstract The Natural Neighbour Radial Point Interpolation Method (NNRPIM) is extended to the large deformation analysis of non-linear elastic structures. The nodal connectivity in the NNRPIM is enforced using the Natural Neighbour concept. After the Voronoï diagram construction of the unstructured nodal mesh, which discretize the problem domain, small cells are created, the "influence-cells". These cells are in fact influence-domains entirely nodal dependent. The Delaunay triangles are used to create a node-depending background mesh used in the numerical integration of the NNRPIM interpolation functions. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed with the Radial Point Interpolators.… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 253-276, 2009, DOI:10.3970/cmes.2009.043.253

Abstract Since the works of Newton and Lagrange, interpolation had been a mature technique in the numerical mathematics. Among the many interpolation methods, global or piecewise, the polynomial interpolation p(x) = a₀ + a₁x + ... + a_nxⁿ expanded by the monomials is the simplest one, which is easy to handle mathematically. For higher accuracy, one always attempts to use a higher-order polynomial as an interpolant. But, Runge gave a counterexample, demonstrating that the polynomial interpolation problem may be ill-posed. Very high-order polynomial interpolation is very hard to realize by numerical computations. In this paper we propose a new polynomial interpolation… More >

J. Sladek¹, V. Sladek¹, P. Solek²

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 223-252, 2009, DOI:10.3970/cmes.2009.043.223

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in 3-D continuously non-homogeneous anisotropic bodies. Functionally graded materials (FGM) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. The Heaviside step function is used as the test functions in the local weak form resulting into the derived local integral equations (LIEs). For transient elastodynamic problems either the Laplace transform or the time difference techniques are applied. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical… More >

J. Sladek¹, V. Sladek¹, C.L. Tan², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.3, pp. 161-174, 2008, DOI:10.3970/cmes.2008.032.161

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non-homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdomain to which… More >