Francesco Tornabene^*, Matteo Viscoti, Rossana Dimitri

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 719-798, 2022, DOI:10.32604/cmes.2022.022210

Abstract The article proposes an Equivalent Single Layer (ESL) formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions. A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates. The generalized blending methodology accounts for a distortion of the structure so that disparate geometries can be considered. Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum. In addition, re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model. The unknown variables are described employing a… More > Graphic Abstract

Heng Cheng¹, Zebin Xing¹, Miaojuan Peng^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 945-964, 2022, DOI:10.32604/cmes.2022.020755

Abstract In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steady-state heat conduction problems. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty method is applied to enforce the boundary conditions, thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form. The influences of node distribution, weight functions, scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively, and these numerical solutions show that less computational… More >

S. N. Atluri¹, Shengping Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 241-268, 2005, DOI:10.3970/cmes.2005.007.241

Abstract Various MLPG methods, with the MLS approximation for the trial function, in the solution of a 4$^{th}$ order ordinary differential equation are illustrated. Both the primal MLPG methods and the mixed MLPG methods are used. All the possible local weak forms for a 4$^{th}$ order ordinary differential equation are presented. In the first kind of mixed MLPG methods, both the displacement and its second derivative are interpolated independently through the MLS interpolation scheme. In the second kind of mixed MLPG methods, the displacement, its first derivative, second derivative and third derivative are interpolated independently through the MLS interpolation scheme. The… More >

J. Sladek¹, V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 477-490, 2004, DOI:10.3970/cmes.2004.006.477

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the LBIEs are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-d problems. The final form of local integral equations has a pure contour character only in… More >

Mohammad Ilati¹, Mehdi Dehghan²

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.4, pp. 325-360, 2015, DOI:10.3970/cmes.2015.109.325

Abstract In this paper, at first, a new combined shape function is proposed. Then, based on this shape function, the meshless local weak form method is applied to find the numerical solution of time-dependent non-linear Brusselator and Gierer- Meinhardt systems. The combined shape function inherits the properties of radial point interpolation (RPI), moving least squares (MLS) and moving Kriging (MK) shape functions and is controlled by control parameters, which take different values in the domain [0;1]. The combined shape function provides synchronic use of different shape functions and this leads to more flexibility in the used method. The main aim of… More >

P.H. Wen¹, X.J. Huang¹, M.H. Aliabadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.3, pp. 199-225, 2013, DOI:10.3970/cmes.2013.096.199

Abstract In this paper, a Local Integral Equation Method (LIEM) is presented for solving two-dimensional nonlocal elasticity problems . The approach is based on the Eringen’s model with LIEM and the interpolation using the radial basis functions to obtain the numerical solutions for 2D problems. A weak form for the set of governing equations with a unit test function is transformed into the local integral equations. The meshless approximation technique with radial basis functions is employed for the implementation of displacements. A set of the local domain integrals is obtained in analytical form for the local elasticity and by using a… More >

J. Sladek¹, P. Stanak¹, Z-D. Han², V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.5, pp. 423-475, 2013, DOI:10.3970/cmes.2013.092.423

Abstract A review is presented for analysis of problems in engineering & the sciences, with the use of the meshless local Petrov-Galerkin (MLPG) method. The success of the meshless methods lie in the local nature, as well as higher order continuity, of the trial function approximations, high adaptivity and a low cost to prepare input data for numerical analyses, since the creation of a finite element mesh is not required. There is a broad variety of meshless methods available today; however the focus is placed on the MLPG method, in this paper. The MLPG method is a fundamental base for the… More >

Y.C. Cai¹ and H.H. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 179-204, 2008, DOI:10.3970/cmes.2008.034.179

Abstract The popular Shepard PU approximations are easy to construct and have many advantages, but they have several limitations, such as the difficulties in handling essential boundary conditions and the known problem of linear dependence regarding PU-based methods, and they are not the good choice for MLPG method. With the objective of alleviating the drawbacks of Shepared PU approximations, a new meshless PU-based Shepard and Least Square (SLS) interpolation is employed here to develop a new type of MLPG method, which is named as Local Meshless Shepard and Least Square (LMSLS) method. The SLS interpolation possesses the much desired Kronecker-delta property,… More >

V. Sladek¹, J. Sladek¹, Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.3, pp. 243-264, 2010, DOI:10.3970/cmes.2010.063.243

Abstract The paper deals with diminishing the prolongation of the computational time due to procedural evaluation of the shape functions and their derivatives in weak formulations implemented with meshless approximations. The proposed numerical techniques are applied to problems of stationary heat conduction in functionally graded media. Besides the investigation of the computational efficiency also the accuracy and convergence study are performed in numerical tests. 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 >