H. Nguyen-Van¹, N.Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.1, pp. 65-96, 2008, DOI:10.3970/cmes.2008.036.065

Abstract A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated with a single node which is termed as node-based elements. The displacement fields of the element are approximated by the linear interpolation functions of the original mesh while the approximations of mechanical strains and electric potential fields are normalized using the stabilized conforming nodal… More >

L. Chen¹ J. H. Lee¹, C.-f. Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.3, pp. 199-224, 2012, DOI:10.3970/cmes.2012.086.199

Abstract This paper presents a numerical procedure to model surface tension using the Generalized Interpolation Material Point (GIMP) method which employs a background mesh in solving the equations of motion. The force due to surface tension is formulated at the mesh grid points by using the continuum surface force (CSF) model and then added to the equations of motion at each grid point. In GIMP, we use the grid mass as the color function in CSF and apply a moving average smoothing scheme to the grid mass to improve the accuracy in calculating the surface interface. The algorithm, named as GIMP-CSF,… More >

Mohsen Sadeghbeigi Olyaie¹, Mohammad Reza Razfar², Semyung Wang³, Edward J. Kansa⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.1, pp. 55-82, 2011, DOI:10.32604/cmes.2011.082.055

Abstract This paper presents the topology optimization design for a linear micromotor, including multitude cantilever piezoelectric bimorphs. Each microbeam in the mechanism can be actuated in both axial and flexural modes simultaneously. For this design, we consider quasi-static and linear conditions, and the smoothed finite element method (S-FEM) is employed in the analysis of piezoelectric effects. Certainty variables such as weight of the structure and equilibrium equations are considered as constraints during the topology optimization design process, then a deterministic topology optimization (DTO) is conducted. To avoid the overly stiff behavior in FEM modeling, a relatively new numerical method known as… More >

C.T.M. Anflor¹, R.J. Marczak²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.3&4, pp. 151-168, 2011, DOI:10.3970/cmes.2011.078.151

Abstract This paper aims to demonstrate the final result of an optimization process when a smooth technique is introduced between intermediary iterations of a topological optimization. In a topological optimization process is usual irregular boundary results as the final shape. This boundary irregularity occurs when the way of the material is removed is not very suitable. Avoiding an optimization post-processing procedure some techniques of smooth are implemented in the original optimization code. In order to attain a regular boundary a smoothness technique is employed, which is, Bezier curves. An algorithm was also developed to detect during the optimization process which curve… More >

H.F.Qiang¹, F.Z.Chen¹, W.R. Gao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 239-262, 2011, DOI:10.3970/cmes.2011.077.239

Abstract Based on smoothed particle hydrodynamics (SPH) method with surface tension proposed by Morris, this paper is intended to modify equations for surface tension by modifying normal and curvature with corrective smoothing particle method (CSPM). Compared with the continuum surface force (CSF) model for surface tension employed in the traditional SPH method, the accuracy in the present paper is much higher in terms of handling the problems with large deformation and surface tension. The reason is that in the traditional SPH method the deficiency of particles is near the boundary and sharp-angled areas, and it causes gross errors of curvature calculation.… More >

N. Vu-Bac¹, H. Nguyen-Xuan², L. Chen³, S. Bordas⁴, P. Kerfriden⁴, R.N. Simpson⁴, G.R. Liu⁵, T. Rabczuk¹

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 331-356, 2011, DOI:10.3970/cmes.2011.073.331

Abstract This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration… More >

K. Wang¹, S.J. Zhou^2,3, Z.F. Nie⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.1, pp. 77-102, 2011, DOI:10.3970/cmes.2011.073.077

Abstract The natural neighbour Galerkin method is tailored to solve boundary value problems of the couple-stress elasticity to model the size dependent behaviour of materials. This method is based on the displacement-based Galerkin approach, and the calculation of the global stiffness matrix is performed using gradient smoothing technique combined with the non-Sibsonian partition of unity approximation scheme. This method possesses the following properties: the complex C1-continuous approximation scheme is avoided without using either Lagrange multipliers or penalty parameters; no domain integrals involved in the assembly of the global stiffness matrix; and the imposition of essential boundary conditions is straightforward. The validity… More >

Sunilkumar N¹, D Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 107-154, 2010, DOI:10.3970/cmes.2010.065.107

Abstract The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries. Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials. There is thus a case for combining these advantages in a so-called hybrid scheme or a 'smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C^p(p ≥ 1) continuity. One such recent attempt, a… More >

A. Colombo¹, U. Galvanetto²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.3, pp. 235-254, 2009, DOI:10.3970/cmes.2009.053.235

Abstract The paper addresses the problem of computing the stable manifolds of equilibria and limit cycles of saddle type in piecewise smooth dynamical systems. All singular points that are generically present along one-dimensional or two-dimensional manifolds are classified and such a classification is then used to define a method for the numerical computation of the stable manifolds. Finally the proposed method is applied to the case of a stick-slip oscillator. More >

H.Nguyen-Van¹, N.Mai-Duy¹ and T.Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.2, pp. 81-112, 2009, DOI:10.3970/cmes.2009.049.081

Abstract This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on… More >