Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS

C. M. Wang, Y. C. Wang, E. Wantanbe, Tomoaki Utsunomiya, Y. Xiang

Research output: Contribution to conferencePaper

3 Citations (Scopus)

Abstract

This paper highlights the problem of obtaining accurate modal stress-resultants, in particular twisting moments and shear forces, for thin vibrating plates that model Very Large Floating Structures (VLFS) when using the Ritz method in conjunction with mathematically complete two-dimensional polynomials as Ritz functions. The twisting moments and shear forces are observed to violate the natural boundary conditions and contain "oscillations". The use of Chebyshev polynomials and trigonometric series as Ritz functions do not solve the problem. Penalty functionals enable the stress-resultants to satisfy the natural boundary conditions but they magnify the oscillations. Based on existing exact solutions of rectangular plates with simply supported and free edges, it was found that the aforementioned problem can be remedied by a post-processing step involving the curve fitting of the "oscillating" results computed from the Ritz method with penalty functionals.

Original languageEnglish
Pages272-278
Number of pages7
Publication statusPublished - Jan 1 2001
Externally publishedYes
Event11th (2001) International Offshore and Polar Engineering Conference - Stavanger, Norway
Duration: Jun 17 2001Jun 22 2001

Other

Other11th (2001) International Offshore and Polar Engineering Conference
CountryNorway
CityStavanger
Period6/17/016/22/01

Fingerprint

Polynomials
Boundary conditions
Curve fitting
Processing

All Science Journal Classification (ASJC) codes

  • Energy Engineering and Power Technology
  • Ocean Engineering
  • Mechanical Engineering

Cite this

Wang, C. M., Wang, Y. C., Wantanbe, E., Utsunomiya, T., & Xiang, Y. (2001). Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS. 272-278. Paper presented at 11th (2001) International Offshore and Polar Engineering Conference, Stavanger, Norway.

Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS. / Wang, C. M.; Wang, Y. C.; Wantanbe, E.; Utsunomiya, Tomoaki; Xiang, Y.

2001. 272-278 Paper presented at 11th (2001) International Offshore and Polar Engineering Conference, Stavanger, Norway.

Research output: Contribution to conferencePaper

Wang, CM, Wang, YC, Wantanbe, E, Utsunomiya, T & Xiang, Y 2001, 'Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS' Paper presented at 11th (2001) International Offshore and Polar Engineering Conference, Stavanger, Norway, 6/17/01 - 6/22/01, pp. 272-278.
Wang CM, Wang YC, Wantanbe E, Utsunomiya T, Xiang Y. Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS. 2001. Paper presented at 11th (2001) International Offshore and Polar Engineering Conference, Stavanger, Norway.
Wang, C. M. ; Wang, Y. C. ; Wantanbe, E. ; Utsunomiya, Tomoaki ; Xiang, Y. / Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS. Paper presented at 11th (2001) International Offshore and Polar Engineering Conference, Stavanger, Norway.7 p.
@conference{eec11be6b9024f0283a3064dbaf65d9f,
title = "Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS",
abstract = "This paper highlights the problem of obtaining accurate modal stress-resultants, in particular twisting moments and shear forces, for thin vibrating plates that model Very Large Floating Structures (VLFS) when using the Ritz method in conjunction with mathematically complete two-dimensional polynomials as Ritz functions. The twisting moments and shear forces are observed to violate the natural boundary conditions and contain {"}oscillations{"}. The use of Chebyshev polynomials and trigonometric series as Ritz functions do not solve the problem. Penalty functionals enable the stress-resultants to satisfy the natural boundary conditions but they magnify the oscillations. Based on existing exact solutions of rectangular plates with simply supported and free edges, it was found that the aforementioned problem can be remedied by a post-processing step involving the curve fitting of the {"}oscillating{"} results computed from the Ritz method with penalty functionals.",
author = "Wang, {C. M.} and Wang, {Y. C.} and E. Wantanbe and Tomoaki Utsunomiya and Y. Xiang",
year = "2001",
month = "1",
day = "1",
language = "English",
pages = "272--278",
note = "11th (2001) International Offshore and Polar Engineering Conference ; Conference date: 17-06-2001 Through 22-06-2001",

}

TY - CONF

T1 - Obtaining accurate modal stress-resultants in freely vibrating plates that model VLFS

AU - Wang, C. M.

AU - Wang, Y. C.

AU - Wantanbe, E.

AU - Utsunomiya, Tomoaki

AU - Xiang, Y.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - This paper highlights the problem of obtaining accurate modal stress-resultants, in particular twisting moments and shear forces, for thin vibrating plates that model Very Large Floating Structures (VLFS) when using the Ritz method in conjunction with mathematically complete two-dimensional polynomials as Ritz functions. The twisting moments and shear forces are observed to violate the natural boundary conditions and contain "oscillations". The use of Chebyshev polynomials and trigonometric series as Ritz functions do not solve the problem. Penalty functionals enable the stress-resultants to satisfy the natural boundary conditions but they magnify the oscillations. Based on existing exact solutions of rectangular plates with simply supported and free edges, it was found that the aforementioned problem can be remedied by a post-processing step involving the curve fitting of the "oscillating" results computed from the Ritz method with penalty functionals.

AB - This paper highlights the problem of obtaining accurate modal stress-resultants, in particular twisting moments and shear forces, for thin vibrating plates that model Very Large Floating Structures (VLFS) when using the Ritz method in conjunction with mathematically complete two-dimensional polynomials as Ritz functions. The twisting moments and shear forces are observed to violate the natural boundary conditions and contain "oscillations". The use of Chebyshev polynomials and trigonometric series as Ritz functions do not solve the problem. Penalty functionals enable the stress-resultants to satisfy the natural boundary conditions but they magnify the oscillations. Based on existing exact solutions of rectangular plates with simply supported and free edges, it was found that the aforementioned problem can be remedied by a post-processing step involving the curve fitting of the "oscillating" results computed from the Ritz method with penalty functionals.

UR - http://www.scopus.com/inward/record.url?scp=0034868158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034868158&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:0034868158

SP - 272

EP - 278

ER -