Dismiss
InnovationQ will be updated on Sunday, Oct. 22, from 10am ET - noon. You may experience brief service interruptions during that time.
Browse Prior Art Database

Towards optimal mixed finite elements for general shell structures

IP.com Disclosure Number: IPCOM000128101D
Original Publication Date: 1999-Dec-31
Included in the Prior Art Database: 2005-Sep-14
Document File: 8 page(s) / 26K

Publishing Venue

Software Patent Institute

Related People

Iosilevich, Alexander G: AUTHOR [+3]

Related Documents

http://theses.mit.edu:80/Dienst/UI/2.0/Describe/0018.mit.theses/1999-116: URL

Abstract

Optimal finite elements are available for many engineering applications, such as incompressible media, beam and plate bending problems. However, no existing general shell elements have been shown to satisfy the mathematical conditions of optimality in the analysis of shell structures. The objective in this thesis is to work towards optimal shell elements that possess properties of uniform convergence independent of the problem solved. We develop a thorough numerical convergence study methodology for bending dominated and membrane-dominated shells and apply it to the family of quadrilateral MITC (Mixed-Interpolated Tensorial Components) shell elements proposed by Bathe, Dvorkin and Bucalem. The study demonstrates the superior performance of these elements. We also develop a new simple and effective triangular mixedinterpolated shell element and demonstrate the element reliability. Deriving the relation between the MITC approach and the classical constrained minimization problem leads to the conclusion that the optimal shell elements must satisfy the relevant inf-sup condition in the analysis of bending-dominated shells. In practice, this condition is virtually impossible to check analytically, especially when general geometries and/or distorted meshes are considered. Using appropriate bounds, we develop a new numerical inf-sup test aimed to indicate if a particular finite element discretization satisfies this fundamental condition. While the displacement-based elements, of course, fail the test, the quadrilateral and the new triangular MITC elements pass the test. Thesis Supervisor: Klaus-Jurgen Bathe Title: Professor of Mechanical Engineering [2]

This text was extracted from a PDF file.
This is the abbreviated version, containing approximately 14% of the total text.

Page 1 of 8

 This record is the front matter from a document that appears on a server at MIT and is used through permission from MIT. See http://theses.mit.edu:80/Dienst/UI/2.0/Describe/0018.mit.theses/1999-116 for copyright details and for the full document in image form.

Towards Optimal Mixed Finite Elements for General Shell Structures

by

Alexander C. Iosilevich
Submitted in partial fulfillment of the requirements for the degree of Doctor of Science in Mechanical Engineering

at the Massachusetts Institute of Technology

February 1999
SIGNATURE OF author: [[signature omitted]]

Department of Mechanical Engineering

October 16, 1998

CERTIFIED BY: [[SIGNATURE OMITTED]]

Klaus-Rirgen Bathe

Professor of Mechanical Engineering Thesis Supervisor ACCEPTED BY: [[SIGNATURE OMITTED]]

Ain Ants Sonin

Chairman, Graduate Committee

ARCHIVES MASSACHUSETTS INSTITUTE OF TECHNOLOGY LIBRARIES JUL 12 1999

Massachusetts Institute of Technology Page 1 Dec 31, 1999

Page 2 of 8

Towards optimal mixed finite elements for general shell structures

Towards Optimal Mixed Finite Elements for General Shell Structures

by

Alexander G. Iosilevich

Submitted to the Department of Mechanical Engineering on October 16, 1998, in partial fulfillment of the requirements for the degree of Doctor of Science in Mechanical Engineering

Abstract

Optimal finite elements are available for many engineering applications, such as incompressible media, beam and plate bending problems. However, no existing general shell elements have been shown to satisfy the mathematical conditions of optimality in the analysis of shell structures. The objective in this thesis is to work towards optimal shell elements that possess properties of uniform convergence independent of the problem solved.

We develop a thorough numerical convergence study methodology for bending dominated and membrane-dominated shells and apply it to the family of quadrilateral MITC (Mixed-Interpolated Tensorial Components) shell elements proposed by Bathe, Dvorkin and Bucalem. The study demonstrates the superior performance of these elements. We also develop a new simple and effective triangular mixedinterpolated shell element and demonstrate the element reliability.

Deriving the relation between the MITC approach and the classical constrained minimization problem leads to the conclusion that the optimal shell elements must satisfy the relevant inf-sup condition in the analysis of bending-dominated shells. In practice, this condition is virtually impossible to check analytically, especially when general geometries and/or distorted meshes are considered. Using appropriate bounds, we develop a new numerical inf-sup test aimed to indicate if a particular finite element discretization satisfies this fundamental condition. While the displacement-based elements, of course, fail the test, the quadrilateral and the new triangular MITC elements pass the test.

Thesis Supervisor: Klaus-Jurgen Bathe Title: Professor of Mechanical Engineering

[2]

Acknow...