Changkye Lee¹, Sundararajan Natarajan², Seong-Hoon Kee³, Jurng-Jae Yee^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.3, pp. 1615-1634, 2022, DOI:10.32604/cmes.2022.020377

Abstract The aim of this work is to employ a modified cell-based smoothed finite element method (S-FEM) for topology optimization with the domain discretized with arbitrary polygons. In the present work, the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM. This improves the accuracy and yields an optimal convergence rate. The gradients are smoothed over each smoothing domain, then used to compute the stiffness matrix. Within the proposed scheme, an optimum topology procedure is conducted over the smoothing domains. Structural materials are distributed over each smoothing domain and… More >

Changkye Lee¹, Sundararajan Natarajan², Jack S. Hale³, Zeike A. Taylor⁴, Jurng-Jae Yee^1,*, Stéphane P. A. Bordas^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 411-436, 2021, DOI:10.32604/cmes.2021.014947

Abstract This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severely distorted meshes. The concepts of cell-based, edge-based and node-based S-FEMs are extended in this paper to three-dimensions. Additionally, a cubic bubble function is utilized to improve accuracy and stability. For the bubble function, an additional displacement degree of freedom is added at the centroid of the element. Several numerical studies are performed demonstrating… More >

Nguyễn T. Quyền^1,*, N. Dourado², A. J. P. Gomes^3,4, F. B. N. Ferreira¹

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2765-2795, 2021, DOI:10.32604/cmc.2021.013164

Abstract The combination of a 4-node quadrilateral mixed interpolation of tensorial components element (MITC4) and the cell-based smoothed finite element method (CSFEM) was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures. This formulation was applied to numerous numerical examples of non-woven fabrics. As CSFEM schemes do not require coordinate transformation, spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two, three and four smoothing cells. An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors, which allowed to remove the… More >

S. Kshrisagar¹, A. Francis¹, J. J. Yee², S. Natarajan¹, C. K. Lee^3,*

CMC-Computers, Materials & Continua, Vol.61, No.2, pp. 481-502, 2019, DOI:10.32604/cmc.2019.07967

Abstract In this paper, the node based smoothed-strain Abaqus user element (UEL) in the framework of finite element method is introduced. The basic idea behind of the node based smoothed finite element (NSFEM) is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell [Liu, Dai and Nguyen-Thoi (2007)]. Therefore, the numerical integration is globally performed over smoothing domains. It is demonstrated that the proposed UEL retains all the advantages of the NSFEM, i.e., upper bound solution, overly soft stiffness and free from locking in compressible and nearly-incompressible… More >

Mohsen Sadeghbeigi Olyaie¹, Mohammad Reza Razfar², Edward J. Kansa³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.1, pp. 43-88, 2011, DOI:10.3970/cmes.2011.075.043

Abstract This paper presents integration of reliability analysis with topology optimization design for a linear mircroactuator, including multitude cantilever piezoelectric bimorphs. Each microbimoph in the mechanism can be actuated in both axial and flexural modes simultaneously. We consider quasi-static and linear conditions, and the smoothed finite element method (S-FEM) is employed in the analysis of piezoelectric effects. Since microfabrication methods are used for manufacturing this type of actuator, uncertainty variables become very important. Hence, these variables are considered as constraints during our topology optimization design process and reliability based topology optimization (RBTO) is conducted. To avoid the overly-stiff behavior in FEM… 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 >

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 >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li¹, X. Zhao², T.T. Nguyen², G.Y. Sun¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.2, pp. 109-126, 2008, DOI:10.3970/cmes.2008.028.109

Abstract A smoothed finite element method (SFEM) is presented to analyze linear and geometrically nonlinear problems of plates and shells using bilinear quadrilateral elements. The formulation is based on the first order shear deformation theory. In the present SFEM, the elements are further divided into smoothing cells to perform strain smoothing operation, and the strain energy in each smoothing cell is expressed as an explicit form of the smoothed strain. The effect of the number of divisions of smoothing cells in elements is investigated in detail. It is found that using three smoothing cells for bending strain energy integration and one… More >

H. Nguyen-Van¹, N. Mai-Duy², T. Tran-Cong³

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 209-222, 2008, DOI:10.3970/cmes.2008.023.209

Abstract This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated.… More >