On the development of an efficient truly meshless discretization procedure in computational mechanics
Name
48749530-MIT.pdf
Description
Full printable version
Size
8.99 MB
Format
Adobe PDF
Checksum (MD5)
db9199507ef79b07eeaf0bdd6ab63823
Author(s)
De, Suvranu, 1970-
Advisor(s)
Mandayam A. Srinivasan and Klaus-Jürgen Bathe.
Date Issued
2001
Publisher
Massachusetts Institute of Technology
Abstract
The objective of this thesis is to present an efficient and reliable meshless computational technique - the method of finite spheres - for the solution of boundary value problems on complex domains. This method is truly meshless in the sense that the approximation spaces are generated and the numerical integration is performed without a mesh. While the theory behind meshless techniques is rather straightforward, the generation of a computationally efficient scheme is quite difficult. Computational efficiency may be achieved by proper choice of the interpolation functions, effective ways of incorporating the essential boundary conditions and efficient and specialized numerical integration rules. The pure displacement formulation is observed to exhibit volumetric "locking" during incompressible (or nearly incompressible) analysis. A displacement/pressure mixed formulation is developed to overcome this problem. The stability and optimality of the mixed formulation are tested using numerical inf-sup tests for a variety of discretization schemes. Solutions to several example problems are presented showing the application of the method of finite spheres to problems in solid and fluid mechanics. A very specialized application of the technique to physically based real time medical simulations in multimodal virtual environments is also presented. In the current form of implementation, the method of finite spheres is about five times slower than the finite element techniques for problems in two-dimensional elastostatics.
Description
Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2001.
Includes bibliographical references (leaves 157-163).
Subjects
Mechanical Engineering.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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