Optimal development of doubly curved surfaces

Surfaces of many engineering structures are commonly fabricated as doubly curved shapes to fulfill functional requirements such as hydrodynamic, aesthetic, or structural. Given a three-dimensional design surface, the first step of the fabrication process is flattening or planar development of this surface into a planar shape so that the manufacturer can not only determine the initial shape of the flat plate but also estimate the strain distribution required to form the shape. In this thesis, we develop an algorithm for optimal development of a general doubly curved surface in the sense that the strain from the surface to its planar development is minimized. A planar development corresponding to minimum stretching or shrinkage is highly desirable for the following reasons: (1) it saves material; (2) it reduces the work needed to form the planar shape to the doubly curved design surface. The development process is modeled by tensile strains isoparametric directions, or along principal curvature directions from the curved surface to its planar development. The distribution of the appropriate minimum strain field is obtained by solving a constrained nonlinear programming problem. Based on the strain distribution and the coefficients of the first fundamental form of the curved surface, another unconstrained nonlinear programming problem is solved to obtain the optimal developed planar shape. Convergence, complexity, and accuracy of the algorithm are studied. Examples show the effectiveness of this algorithm.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Ocean Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

1999

Author dc:creator

• Yu, Guoxin, 1968-

Advisor dc:contributor.advisor

• Nicholas M. Patrikalakis and Takashi Maekawa.

• Ocean Engineering.
• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/9553

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/9553