Research Papers

Finite Element Analysis Using Nonconforming Mesh

[+] Author and Article Information
Ashok V. Kumar, Ravi Burla

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611

Sanjeev Padmanabhan

 Spatial Corp., 10955 Westmoor Drive, Suite 425, Westminster, CO 80021

Linxia Gu

 South Dakota School of Mines and Technology, 501 East Saint Joseph Street, Rapid City, SD 57701

J. Comput. Inf. Sci. Eng 8(3), 031005 (Aug 19, 2008) (11 pages) doi:10.1115/1.2956990 History: Received July 29, 2007; Revised March 14, 2008; Published August 19, 2008

A method for finite element analysis using a regular or structured grid is described that eliminates the need for generating conforming mesh for the geometry. The geometry of the domain is represented using implicit equations, which can be generated from traditional solid models. Solution structures are constructed using implicit equations such that the essential boundary conditions are satisfied exactly. This approach is used to solve boundary value problems arising in thermal and structural analysis. Convergence analysis is performed for several numerical examples and the results are compared with analytical and finite element analysis solutions to show that the method gives solutions that are similar to the finite element method in quality but is often less computationally expensive. Furthermore, by eliminating the need for mesh generation, better integration can be achieved between solid modeling and analysis stages of the design process.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Analysis domain and boundary representations. (a) Conforming mesh in FEM (b) Scattered nodes in meshless methods. (c) Nonconforming structured grid methods.

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Figure 2

Boundary element with multiple curves and associated Boolean tree

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Figure 3

A general steady state heat transfer problem

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Figure 4

A general elastostatic problem

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Figure 5

Essential boundary function

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Figure 6

Boundary value function

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Figure 7

Representation of band in boundary elements having essential boundary

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Figure 8

Rectangular plate with a constant heat flux

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Figure 9

Effect of range parameter on the solution

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Figure 10

Quarter cylinder used for modeling

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Figure 11

Grids used for convergence analysis

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Figure 12

Plot of temperature variation along the radial direction

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Figure 13

Error in computed temperature in the radial direction for different grids

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Figure 14

Cantilever beam with end loading and the analysis grid

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Figure 15

Plot of L2 error norm with respect to the number of nodes

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Figure 16

Plot of energy error norm with respect to the number of nodes

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Figure 17

Comparison of analysis time

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Figure 18

A 3D rib structure

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Figure 19

Strain energy convergence comparison with FEM

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Figure 20

Plot of bending stresses using implicit boundary finite element method

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Figure 21

Plot of bending stresses using traditional FEM



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