Development of high-order manifold method

Guangqi Chen, Yuzo Ohnishi, Takahiro Ito

Research output: Contribution to journalArticle

123 Citations (Scopus)

Abstract

The Manifold Method of Material Analysis (MM) with high-order displacement functions has been derived based on triangular meshes for the requirement of high accurate calculations from practical applications. The matrices of equilibrium equations for the second-order MM have been given in detail for program coding. The derivation of the method is made by means of approximation theory and very few new mathematical concepts are used in this paper. So, it may be understood by most engineering researchers. By close comparison with widely used Finite Element Method, the advantages of MM can be seen very clearly in the following aspects: (1) the capability of processing large deformation and handing discontinuities like block oriented Discontinuous Deformation Analysis method; (2) making element meshes easily and (3) using high-order displacement functions easily. The C program codes for the second-order MM has been developed, and it has been applied to the example of a beam bending under a central point loading. The calculated results are quite good in agreement with theoretical solutions. By contrast, the results calculated for the same model by use of the original first-order MM are far from the theoretical solutions. Therefore, it is important and necessary to develop high-order Manifold Method for the complicated deformation problems.

Original languageEnglish
Pages (from-to)685-712
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Volume43
Issue number4
DOIs
Publication statusPublished - Oct 30 1998
Externally publishedYes

Fingerprint

Higher Order
Approximation theory
Triangular Mesh
Approximation Theory
Large Deformation
Finite element method
Discontinuity
Processing
Coding
Finite Element Method
Mesh
First-order
Engineering
Necessary
Requirements

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

Cite this

Development of high-order manifold method. / Chen, Guangqi; Ohnishi, Yuzo; Ito, Takahiro.

In: International Journal for Numerical Methods in Engineering, Vol. 43, No. 4, 30.10.1998, p. 685-712.

Research output: Contribution to journalArticle

Chen, Guangqi ; Ohnishi, Yuzo ; Ito, Takahiro. / Development of high-order manifold method. In: International Journal for Numerical Methods in Engineering. 1998 ; Vol. 43, No. 4. pp. 685-712.
@article{52ce68c055914802b17f07b9cff57f3e,
title = "Development of high-order manifold method",
abstract = "The Manifold Method of Material Analysis (MM) with high-order displacement functions has been derived based on triangular meshes for the requirement of high accurate calculations from practical applications. The matrices of equilibrium equations for the second-order MM have been given in detail for program coding. The derivation of the method is made by means of approximation theory and very few new mathematical concepts are used in this paper. So, it may be understood by most engineering researchers. By close comparison with widely used Finite Element Method, the advantages of MM can be seen very clearly in the following aspects: (1) the capability of processing large deformation and handing discontinuities like block oriented Discontinuous Deformation Analysis method; (2) making element meshes easily and (3) using high-order displacement functions easily. The C program codes for the second-order MM has been developed, and it has been applied to the example of a beam bending under a central point loading. The calculated results are quite good in agreement with theoretical solutions. By contrast, the results calculated for the same model by use of the original first-order MM are far from the theoretical solutions. Therefore, it is important and necessary to develop high-order Manifold Method for the complicated deformation problems.",
author = "Guangqi Chen and Yuzo Ohnishi and Takahiro Ito",
year = "1998",
month = "10",
day = "30",
doi = "10.1002/(SICI)1097-0207(19981030)43:4<685::AID-NME442>3.0.CO;2-7",
language = "English",
volume = "43",
pages = "685--712",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "4",

}

TY - JOUR

T1 - Development of high-order manifold method

AU - Chen, Guangqi

AU - Ohnishi, Yuzo

AU - Ito, Takahiro

PY - 1998/10/30

Y1 - 1998/10/30

N2 - The Manifold Method of Material Analysis (MM) with high-order displacement functions has been derived based on triangular meshes for the requirement of high accurate calculations from practical applications. The matrices of equilibrium equations for the second-order MM have been given in detail for program coding. The derivation of the method is made by means of approximation theory and very few new mathematical concepts are used in this paper. So, it may be understood by most engineering researchers. By close comparison with widely used Finite Element Method, the advantages of MM can be seen very clearly in the following aspects: (1) the capability of processing large deformation and handing discontinuities like block oriented Discontinuous Deformation Analysis method; (2) making element meshes easily and (3) using high-order displacement functions easily. The C program codes for the second-order MM has been developed, and it has been applied to the example of a beam bending under a central point loading. The calculated results are quite good in agreement with theoretical solutions. By contrast, the results calculated for the same model by use of the original first-order MM are far from the theoretical solutions. Therefore, it is important and necessary to develop high-order Manifold Method for the complicated deformation problems.

AB - The Manifold Method of Material Analysis (MM) with high-order displacement functions has been derived based on triangular meshes for the requirement of high accurate calculations from practical applications. The matrices of equilibrium equations for the second-order MM have been given in detail for program coding. The derivation of the method is made by means of approximation theory and very few new mathematical concepts are used in this paper. So, it may be understood by most engineering researchers. By close comparison with widely used Finite Element Method, the advantages of MM can be seen very clearly in the following aspects: (1) the capability of processing large deformation and handing discontinuities like block oriented Discontinuous Deformation Analysis method; (2) making element meshes easily and (3) using high-order displacement functions easily. The C program codes for the second-order MM has been developed, and it has been applied to the example of a beam bending under a central point loading. The calculated results are quite good in agreement with theoretical solutions. By contrast, the results calculated for the same model by use of the original first-order MM are far from the theoretical solutions. Therefore, it is important and necessary to develop high-order Manifold Method for the complicated deformation problems.

UR - http://www.scopus.com/inward/record.url?scp=0032183165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032183165&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1097-0207(19981030)43:4<685::AID-NME442>3.0.CO;2-7

DO - 10.1002/(SICI)1097-0207(19981030)43:4<685::AID-NME442>3.0.CO;2-7

M3 - Article

AN - SCOPUS:0032183165

VL - 43

SP - 685

EP - 712

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 4

ER -