Dynamic Analysis of MLS Difference Method using First Order Differential Approximation

Kyeong-Hwan Kim; Young-Cheol Yoon; Sang-Ho Lee

doi:10.7734/COSEIK.2018.31.6.331

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2018 Vol.31, Issue 6 Preview Page Next Page

Dynamic Analysis of MLS Difference Method using First Order Differential Approximation 1차 미분 근사를 이용한 MLS차분법의 동적해석

2018. pp. 331-337

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Abstract

This paper presents dynamic algorithm of the MLS(moving least squares) difference method using first order differential Approximation. The governing equations are only discretized by the first order MLS derivative approximation. The system equation consists of an assembly of the approximate function, so the shape of system equation is similar to FEM(finite element method). The CDM(central difference method) is used for time integration of dynamic equilibrium equation. The natural frequency analyses of the MLS difference method and FEM are performed, and two analysis results are compared. Also, the accuracy of the proposed numerical method is verified by displaying the dynamic analysis results together with the results by the existing second order differential approximation. In the process of assembling the first order MLS derivative approximation, the oscillation error was suppressed and the stress distribution was interpreted as relatively uniform.

Keywords

MLS difference method

first order differential approximation

dynamic analysis

central difference method

natural frequency

본 논문은 MLS(moving least squares) 차분법의 1차 미분 근사함수를 바탕으로 시간에 따른 수치해석이 가능한 해석기 법을 제시한다. 오직 1차 미분 근사함수로만 지배방정식을 이산화했으며, 근사함수를 조립하는 형태로 전체 시스템 방정식 을 구성하여 차분법으로 이산화된 운동방정식이 유한요소법(finite element method)과 유사한 모습을 갖게 되었다. 운동방정 식을 시간적분하기 위해서 중앙차분법(central difference method)을 사용하였다. 유한요소 알고리즘을 통해서 MLS 차분법 과 유한요소법의 고유진동 해석을 수행하였으며, 두 해석결과를 비교하였다. 또한, 동적해석 결과를 기존의 2차 미분 근사함 수를 활용한 해석결과와 함께 도시함으로써 제안된 수치기법의 정확성을 검증하였다. 1차 미분 근사함수를 조립하는 과정에 서 해석결과의 떨림현상이 억제되었으며 상대적으로 균일한 응력분포를 구할 수 있었다.

키워드

MLS 차분법

1차 미분 근사

동적해석

중앙차분법

고유진동

References

Aluru, N.R. (2000) A point collocation method based on reproducing kernel approximations, Int. J. Numer. Methods Eng., 47, pp.1083~1121. 10.1002/(SICI)1097-0207(20000228)47:6<1083::AID-NME816>3.0.CO;2-N0029-5981

10.1002/(SICI)1097-0207(20000228)47:6<1083::AID-NME816>3.0.CO;2-N

Belytschko, T., Lu, Y.Y., Gu, L. (1994) Element- Free Galerkin Methods, Int. J. Numer. Methods Eng., 37, pp.229~256. 10.1002/nme.16203702050029-5981

10.1002/nme.1620370205

Clough, R.W., Penzien, J. (1975) Dynamics of Structures, McGraw-Hill.

Dominguez, J. (1993) Boundary Elements in Dynamics, Computational Mechanics Publications.

Kim, D.W., Kim, Y.S. (2003) Point Collocation Methods Using the Fast Moving Least-Square Reproducing Kernel Approximation, Int. J. Numer. Methods Eng., 56, pp.1445~1464. 10.1002/nme.6180029-5981

10.1002/nme.618

Kim, K.H., Lee, S.H., Yoon, Y.C. (2016) A Study of Rayleigh Damping Effect on Dynamic Crack Propagation Analysis using MLS Difference Method, J. Comput. Struct. Eng. Inst. Korea, 29(6), pp.583~590. 10.7734/COSEIK.2016.29.6.583

10.7734/COSEIK.2016.29.6.583

Lee, S.H., Kim K.H., Yoon, Y.C. (2016) Particle Difference Method for Dynamic Crack Propagation, Int. J. Impact Eng., 87, pp.132~145. 10.1016/j.ijimpeng.2015.06.0010734-743X

10.1016/j.ijimpeng.2015.06.001

Lee, S.H., Yoon, Y.C. (2004) Meshfree Point Collocation Method for Elasticity and Crack Problems, Int. J. Numer. Methods Eng., 61, pp.22~48. 10.1002/nme.10530029-5981

10.1002/nme.1053

Liu, W.K., Jun, S., Zhang, Y. (1995) Reproducing Kernel Particle Methods, Comput. Methods in Appl. Mech. and Eng., 191, pp.1421~1438.0045-7825

Salehi, R. (2017) A Meshless Point Collocation Method for 2-D Multi-Term Time Fractional Diffusion-Wave Equation, Numer. Algorithms, 74, pp.1145~1168. 10.1007/s11075-016-0190-z1017-1398

10.1007/s11075-016-0190-z

Wen, P.H., Aliabadi, M.H. (2007) An Improved Meshless Collocation Method for Elastostatic and Elastodynamic Problems, Commun. Num. Methods Eng., 24, pp.635~651. 10.1002/cnm.9771069-8299

10.1002/cnm.977

Yoon, Y.C. (2016) Development of MLS Difference Method for Material Nonlinear Problem, J. Comput. Struct. Eng. Inst. Korea, 29, pp.237~244. 10.7734/COSEIK.2016.29.3.237

10.7734/COSEIK.2016.29.3.237

Yoon, Y.C., Kim, K.H., Lee, S.H. (2014) Analysis of Dynamic Crack Propagation Using MLS Difference Method, J. Comput. Struct. Eng. Inst. Korea, 27, pp.17~26. 10.7734/COSEIK.2014.27.1.17

10.7734/COSEIK.2014.27.1.17

Yoon, Y.C., Lee, S.H., Belytschko, T. (2006) Enriched Meshfree Collocation Method with Diffuse Derivatives for Elastic Fracture, Comput. & Math. Appl., 51(8), pp.1349~1366. 10.1016/j.camwa.2006.04.0100898-1221

10.1016/j.camwa.2006.04.010

Yoon, Y.C., Song, J.-H. (2014) Extended Particle Difference Method for Weak and Strong Discontinuity Problems: Part I. Derivation of the Extended Particle Derivative Approximation for the Representation of Weak and Strong Discontinuities, Comput. Mech., 53(6), pp.1087~1103. 10.1007/s00466-013-0950-80178-7675

10.1007/s00466-013-0950-8

Zhang, X., Liu, X.H., Song, K.Z., Lu, M.W. (2001) Least-squares Collocation Meshless Method, Int. J.Numer. Methods Eng., 51, pp.1089~1100. 10.1002/nme.2000029-5981

10.1002/nme.200

Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 31
No :6
Pages :331-337
Received Date : 2018-10-05
Revised Date : 2018-10-09
Accepted Date : 2018-10-10
DOI :https://doi.org/10.7734/COSEIK.2018.31.6.331

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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