The fundamental solution for shallow circular cylindrical shells - Part I: Derivations

Goong Chen, Matthew P. Coleman, Daowei Ma, Philip John Morris, Puhong You

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The equations which model the elastostatic shallow circular cylindrical shell (see, e.g., [6,15,23,29]) constitute an important elliptic partial differential equation (PDE) system in the study of shell structures. When the system is subjected to a concentrated point load, the response is described by a fundamental solution of the PDE system. We have found some mathematical inconsistencies in the existing literature. Therefore, in this paper, we discuss these errors, then we use partial fractions and Fourier transform techniques to determine the fundamental solution. Explicit expressions in terms of special functions and convolution integrals are derived and simplified so that the formulas are suitable for algorithmic evaluation and for application elsewhere.

Original languageEnglish (US)
Pages (from-to)1235-1257
Number of pages23
JournalInternational Journal of Engineering Science
Volume38
Issue number11
StatePublished - Dec 1 2000

Fingerprint

Partial differential equations
Convolution
Elasticity
Fourier transforms

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Engineering(all)
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Chen, Goong ; Coleman, Matthew P. ; Ma, Daowei ; Morris, Philip John ; You, Puhong. / The fundamental solution for shallow circular cylindrical shells - Part I : Derivations. In: International Journal of Engineering Science. 2000 ; Vol. 38, No. 11. pp. 1235-1257.
@article{a737e09b502840118d4c8ae38293e6ea,
title = "The fundamental solution for shallow circular cylindrical shells - Part I: Derivations",
abstract = "The equations which model the elastostatic shallow circular cylindrical shell (see, e.g., [6,15,23,29]) constitute an important elliptic partial differential equation (PDE) system in the study of shell structures. When the system is subjected to a concentrated point load, the response is described by a fundamental solution of the PDE system. We have found some mathematical inconsistencies in the existing literature. Therefore, in this paper, we discuss these errors, then we use partial fractions and Fourier transform techniques to determine the fundamental solution. Explicit expressions in terms of special functions and convolution integrals are derived and simplified so that the formulas are suitable for algorithmic evaluation and for application elsewhere.",
author = "Goong Chen and Coleman, {Matthew P.} and Daowei Ma and Morris, {Philip John} and Puhong You",
year = "2000",
month = "12",
day = "1",
language = "English (US)",
volume = "38",
pages = "1235--1257",
journal = "International Journal of Engineering Science",
issn = "0020-7225",
publisher = "Elsevier Limited",
number = "11",

}

The fundamental solution for shallow circular cylindrical shells - Part I : Derivations. / Chen, Goong; Coleman, Matthew P.; Ma, Daowei; Morris, Philip John; You, Puhong.

In: International Journal of Engineering Science, Vol. 38, No. 11, 01.12.2000, p. 1235-1257.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The fundamental solution for shallow circular cylindrical shells - Part I

T2 - Derivations

AU - Chen, Goong

AU - Coleman, Matthew P.

AU - Ma, Daowei

AU - Morris, Philip John

AU - You, Puhong

PY - 2000/12/1

Y1 - 2000/12/1

N2 - The equations which model the elastostatic shallow circular cylindrical shell (see, e.g., [6,15,23,29]) constitute an important elliptic partial differential equation (PDE) system in the study of shell structures. When the system is subjected to a concentrated point load, the response is described by a fundamental solution of the PDE system. We have found some mathematical inconsistencies in the existing literature. Therefore, in this paper, we discuss these errors, then we use partial fractions and Fourier transform techniques to determine the fundamental solution. Explicit expressions in terms of special functions and convolution integrals are derived and simplified so that the formulas are suitable for algorithmic evaluation and for application elsewhere.

AB - The equations which model the elastostatic shallow circular cylindrical shell (see, e.g., [6,15,23,29]) constitute an important elliptic partial differential equation (PDE) system in the study of shell structures. When the system is subjected to a concentrated point load, the response is described by a fundamental solution of the PDE system. We have found some mathematical inconsistencies in the existing literature. Therefore, in this paper, we discuss these errors, then we use partial fractions and Fourier transform techniques to determine the fundamental solution. Explicit expressions in terms of special functions and convolution integrals are derived and simplified so that the formulas are suitable for algorithmic evaluation and for application elsewhere.

UR - http://www.scopus.com/inward/record.url?scp=0033742457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033742457&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033742457

VL - 38

SP - 1235

EP - 1257

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

IS - 11

ER -