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Smoothed Finite Element Method (smoothed + finite_element_method)

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Engineering100%

Selected Abstracts

A stabilized smoothed finite element method for free vibration analysis of Mindlin,Reissner plates

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2009
H. Nguyen-Xuan
Abstract A free vibration analysis of Mindlin,Reissner plates using the stabilized smoothed finite element method is studied. The bending strains of the MITC4 and STAB elements are incorporated with a cell-wise smoothing operation to give new proposed elements, the mixed interpolation and smoothed curvatures (MISCk) and SMISCk elements. The corresponding bending stiffness matrix is computed along the boundaries of the smoothing elements (smoothing cells). Note that shearing strains and the shearing stiffness matrix of the proposed elements are unchanged from the original elements, the MITC4 and STAB elements. It is confirmed by numerical tests that the present method is free of shear locking and has the marginal improvements compared with the original elements. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Addressing volumetric locking and instabilities by selective integration in smoothed finite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2009
Nguyen-Xuan Hung
Abstract This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Upper and lower bounds for natural frequencies: A property of the smoothed finite element methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2010
Zhi-Qian Zhang
Abstract Node-based smoothed finite element method (NS-FEM) using triangular type of elements has been found capable to produce upper bound solutions (to the exact solutions) for force driving static solid mechanics problems due to its monotonic ,soft' behavior. This paper aims to formulate an NS-FEM for lower bounds of the natural frequencies for free vibration problems. To make the NS-FEM temporally stable, an ,-FEM is devised by combining the compatible and smoothed strain fields in a partition of unity fashion controlled by ,,[0, 1], so that both the properties of stiff FEM and the monotonically soft NS-FEM models can be properly combined for a desired purpose. For temporally stabilizing NS-FEM, , is chosen small so that it acts like a ,regularization parameter' making the NS-FEM stable, but still with sufficient softness ensuring lower bounds for natural frequency solution. Our numerical studies demonstrate that (1) using a proper ,, the spurious non-zero energy modes can be removed and the NS-FEM becomes temporally stable; (2) the stabilized NS-FEM becomes a general approach for solids to obtain lower bounds to the exact natural frequencies over the whole spectrum; (3) ,-FEM can even be tuned for obtaining nearly exact natural frequencies. Copyright © 2010 John Wiley & Sons, Ltd. [source]

A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010
G. R. Liu
Abstract It is well known that the lower bound to exact solutions in linear fracture problems can be easily obtained by the displacement compatible finite element method (FEM) together with the singular crack tip elements. It is, however, much more difficult to obtain the upper bound solutions for these problems. This paper aims to formulate a novel singular node-based smoothed finite element method (NS-FEM) to obtain the upper bound solutions for fracture problems. In the present singular NS-FEM, the calculation of the system stiffness matrix is performed using the strain smoothing technique over the smoothing domains (SDs) associated with nodes, which leads to the line integrations using only the shape function values along the boundaries of the SDs. A five-node singular crack tip element is used within the framework of NS-FEM to construct singular shape functions via direct point interpolation with proper order of fractional basis. The mix-mode stress intensity factors are evaluated using the domain forms of the interaction integrals. The upper bound solutions of the present singular NS-FEM are demonstrated via benchmark examples for a wide range of material combinations and boundary conditions. Copyright © 2010 John Wiley & Sons, Ltd. [source]