A MODIFIED TRIANGULATION ALGORITHM TAILORED FOR THE SMOOTHED FINITE ELEMENT METHOD (S-FEM)

2013 ◽  
Vol 11 (01) ◽  
pp. 1350069 ◽  
Author(s):  
Y. LI ◽  
M. LI ◽  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Advancing Front ◽  
Stiffness Matrices ◽  
Smoothed Finite Element Method ◽  
Complicated Geometry ◽  
Discrete Domains ◽  
Volume Method ◽  
Element Method

Meshing is one of the key tasks in using the finite element method (FEM), the smoothed finite element method (S-FEM), finite volume method (FVM), and many other discrete numerical methods. Linear triangular (T3) mesh is one of the most widely used mesh, because it can be generated and refined automatically for discrete domains of complicated geometry, and hence save significantly the time for model creation. This paper presents a modified triangulation algorithm based on the advancing front technique to provide a comprehensive linear triangular mesh generator with six connectivity lists, including element–node (Ele–N) connectivity, element–edge (Ele–Eg) connectivity, edge–node (Eg–N) connectivity, edge–element (Eg–Ele) connectivity, node–edge (N–Eg) connectivity and node–element (N–Ele) connectivity. These six connectivity lists are generated along the way when the T3 elements are created, and hence it is done in a most efficient fashion. The connectivity is recorded in the usual counter-clockwise convention for convenient utilization in various S-FEM models for effective analyses. In addition, an algorithm is developed for renumbering the nodes in the T3 mesh to obtain a minimized bandwidth of stiffness matrices for both FEM and S-FEM models.

On the Use of the Finite Element Method on Some Acoustical Problems

1982 ◽  
Vol 104 (1) ◽  
pp. 108-112 ◽  
Author(s):  
L. Cederfeldt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Methods ◽  
The Finite Element Method ◽  
Expansion Chamber ◽  
Low Frequencies ◽  
Angle Bend ◽  
Complicated Geometry ◽  
Sound Reduction ◽  
Element Method

In a project carried out in 1974-1975, financially supported by the National Swedish Council for Building Research, the finite element method was applied on some acoustical problems to illustrate the possibilities of the method. Calculations have been made for the following examples; sound attenuation of a lined right angle bend, a lined straight duct, and expansion chamber and the sound reduction of a resilient skin. The FEM has its power for small geometries particularly at low frequencies, that is, when analytical methods usually are weak. The more complicated geometry and boundary conditions of the studied problem may be the more powerful the FEM is compared to analytical methods.

Rayleigh-Ritz Based Substructure Synthesis for Multiply Supported Structures

1998 ◽  
Vol 122 (1) ◽  
pp. 2-6 ◽  
Author(s):  
C. Morales
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Synthesis Method ◽  
The Finite Element Method ◽  
Compatibility Conditions ◽  
Substructure Synthesis ◽  
Stiffness Matrices ◽  
Element Method

This paper is concerned with the convergence characteristics and application of the Rayleigh-Ritz based substructure synthesis method to structures for which the use of a kinematical procedure taking into account all the compatibility conditions, is not possible. It is demonstrated that the synthesis in this case is characterized by the fact that the mass and stiffness matrices have the embedding property. Consequently, the estimated eigenvalues comply with the inclusion principle, which in turn can be utilized to prove convergence of the approximate solution. The method is applied to a frame and is compared with the finite element method. [S0739-3717(00)00201-4]

The Finite-Element Method—Part II

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Gaussian Quadrature ◽  
The Finite Element Method ◽  
Gaussian Quadrature Formula ◽  
Stiffness Matrices ◽  
Minimum Number ◽  
Element Technique ◽  
Element Method

Numerical integration is an important part of the finite-element technique. As seen in Section 6.5 of Chap. 6, volume integrations as well as surface integrations should be carried out in order to represent the elemental stiffness equations in a simple matrix form. In deriving the variational principle, it is implicitly assumed that these integrations are exact. However, exact integrations of the terms included in the element matrices are not always possible. In the finite-element method, further approximations are made in the procedure for integration, which is summarized in this section. Numerical integration requires, in general, that the integrand be evaluated at a finite number of points, called Integration points, within the integration limits. The number of integration points can be reduced, while achieving the same degree of accuracy, by determining the locations of integration points selectively. In evaluating integration in the stiffness matrices, it is necessary to use an integration formula that requires the least number of integrand evaluations. Since the Gaussian quadrature is known to require the minimum number of integration points, we use the Gaussian quadrature formula almost exclusively to carry out the numerical integrations.

Error analysis of finite element and finite volume methods for some viscoelastic fluids

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Mária Lukáčová-Medvid’ová ◽  
Hana Mizerová ◽  
Bangwei She ◽  
Jan Stebel
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Analysis ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
Weissenberg Number ◽  
Type Model ◽  
The Finite Element Method ◽  
Volume Method ◽  
Element Method

AbstractWe present the error analysis of a particular Oldroyd-B type model with the limiting Weissenberg number going to infinity. Assuming a suitable regularity of the exact solution we study the error estimates of a standard finite element method and of a combined finite element/finite volume method. Our theoretical result shows first order convergence of the finite element method and the error of the order 𝓞(

An Efficient Finite Element Algorithm in Elastography

2016 ◽  
Vol 08 (03) ◽  
pp. 1650037 ◽  
Author(s):  
Eric Li ◽  
W. H. Liao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Soft Tissues ◽  
Tetrahedral Mesh ◽  
Tetrahedral Elements ◽  
Time Harmonic ◽  
Smoothed Finite Element Method ◽  
Complicated Geometry ◽  
First Time ◽  
Element Method

Elastography is an imaging approach to measure the stiffness of tissues to provide diagnostic information. Currently, finite element method (FEM) has been widely used in elastography. However, FEM tends to an overly stiff model that sometimes gives unsatisfactory accuracy, particularly using triangular elements in 2D or tetrahedral elements in 3D. In general, it is difficult or even impossible to generate quadrilateral or brick elements to precisely capture the anatomic details for mechanobiologic modeling as the biologic system can be rather sophisticated. In addition, biologic soft tissues are often considered as “incompressible” materials, where conventional FEM could suffer from volumetric locking in numerical solution. On the other hand, linear triangular and tetrahedral mesh can be automatically generated for complicated geometry, which significantly saves the time for the creation of model. With these reasons, for the first time, smoothed finite element method (SFEM) is developed to analyze elastography problems. A range of numerical examples, including static, dynamic, viscoelastic and time harmonic cases have exemplified herein to validate that SFEM is able to provide more accurate and stable solutions using the same set of mesh compared with the standard FEM. Furthermore, SFEM is also effective to inversely compute the mechanical properties of abnormal tissue.

scholarly journals Modal analysis of damaged structures by the modified finite element method

1998 ◽  
Vol 20 (1) ◽  
pp. 29-46 ◽  
Author(s):  
Nguyen Cao Menh ◽  
Nguyen Tien Khiem ◽  
Dao Nhu Mai ◽  
Nguyen Viet Khoa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Standard Procedure ◽  
Frame Structures ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Stiffness Matrices ◽  
Flexible Supports ◽  
Cubic Polynomial ◽  
Element Method

The classical 3D beam element has been modified and developed as a new finite element for vibration analysis of frame structures with flexible connections and cracked members. The mass and stiffness matrices of the modified elements are established basing on a new form of shape functions, which are obtained in investigating a beam with flexible supports and crack modeled through equivalent springs. These shape functions remain the cubic polynomial form and contain flexible connection (or crack) parameters. They do not change standard procedure of the finite element method (FEM). Therefore, the presented method is easy for engineers in application and allows to analyze Eigen-parameters of structures as functions of the connection (or crack) parameters. The proposed approach has been applied to calculate natural frequencies and mode shape of typical frame structures in presented examples.

scholarly journals About the edge-based smoothed finite element method for the Reissner-Mindlin plate-bending problem

2009 ◽  
Vol 31 (2) ◽  
pp. 75-86
Author(s):  
Nguyen Xuan Hung ◽  
Nguyen Thoi Trung
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mindlin Plate ◽  
Stiffness Matrices ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Discrete Shear Gap ◽  
Transverse Shear Locking ◽  
Element Method

The paper further develops the edge-based smoothed finite element method (ES-FEM) for analysis of Reissner-Mindlin plates using triangular meshes. The bending and shearing stiffness matrices are obtained using strain smoothing technique over the smoothing domains associated with edges of elements. Transverse shear locking can be avoided with help of the discrete shear gap (DSG) method. The numerical examples show that the present ES-FEM-DSG method obtains very accurate results compared to the exact solution and other existing elements.

scholarly journals An Inhomogeneous Cell-Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Yan Cai ◽  
Guangwei Meng ◽  
Liming Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Continuous System ◽  
Functionally Graded ◽  
Gaussian Integration ◽  
Stiffness Matrices ◽  
Inherent Frequency ◽  
Smoothed Finite Element Method ◽  
Element Method

To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

SMOOTHED FINITE ELEMENTS LARGE DEFORMATION ANALYSIS

2010 ◽  
Vol 07 (03) ◽  
pp. 513-524 ◽  
Author(s):  
S. J. LIU ◽  
H. WANG ◽  
H. ZHANG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Large Deformations ◽  
Meshfree Methods ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Smoothed Finite Element Method ◽  
First Time ◽  
Element Method

The smoothed finite element method (SFEM) was developed in order to eliminate certain shortcomings of the finite element method (FEM). SFEM enjoys some of the flexibilities of meshfree methods. One advantage of SFEM is its applicability to modeling large deformations. Due to the absence of volume integration and parametric mapping, issues such as negative volumes and singular Jacobi matrix do not occur. However, despite these advantages, SFEM has never been applied to problems with extreme large deformation. For the first time, we apply SFEM to extreme large deformations. For two numerical problems, we demonstrate the advantages of SFEM over FEM. We also show that SFEM can compete with the flexibility of meshfree methods.

An Efficient Cell-Based Smoothed Finite Element Method for Free Vibrations of Magneto-Electro-Elastic Beams

2019 ◽  
Vol 17 (04) ◽  
pp. 1950001 ◽  
Author(s):  
Liming Zhou ◽  
Shuhui Ren ◽  
Yan Cai ◽  
Feng Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Coupling Effect ◽  
Magnetic Coupling ◽  
Free Vibrations ◽  
Fe Model ◽  
The Finite Element Method ◽  
Smoothed Finite Element Method ◽  
Gradient Smoothing ◽  
Element Method

Magneto-electro-elastic (MEE) materials are widely used in intelligent structure systems owing to their electronic, mechanical and magnetic coupling effects. To overcome the over-stiffness of the finite element method (FEM) stiffness matrix and simulate the free vibration of MEE structures more accurately, we introduced the gradient smoothing technique into MEE multi-physical-field FE model and thereby deduced the cell-based smoothed finite element method (CS-FEM) equations of MEE materials. The MEE beams and layered beam affected by the coupling effect of multiple physical fields under different boundary conditions were computed by CS-FEM, after comparing results with those of FEM and reference solutions, the accuracy and efficiency of CS-FEM were validated.

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