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Trefftz Finite and Boundary Element Method [Kõva köide]

  • Formaat: Hardback, 272 pages, kõrgus x laius: 230x155 mm, illustrations
  • Sari: Advances in Boundary Elements
  • Ilmumisaeg: 26-May-2000
  • Kirjastus: WIT Press
  • ISBN-10: 1853128554
  • ISBN-13: 9781853128554
  • Formaat: Hardback, 272 pages, kõrgus x laius: 230x155 mm, illustrations
  • Sari: Advances in Boundary Elements
  • Ilmumisaeg: 26-May-2000
  • Kirjastus: WIT Press
  • ISBN-10: 1853128554
  • ISBN-13: 9781853128554
Qin (mechanical and mechatronic engineering, U. of Sydney) details the development of the two techniques and ideas, beginning with basic principles, and illustrates new concepts with examples whenever possible. He explains that the internal fields of Trefftz finite elements fulfill the governing differential equations of the problem a priori , whereas inter-element continuity and boundary conditions are enforced in an integral weighted residual sense or pointwise. He writes for researchers, engineers, and scientists who are adept in the standard calculus and hopefully have some knowledge of matrix presentation. Distributed in North America by Computational Mechanics. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Arvustused

..".a good up-to-date account of some modern methods in numerical analysis...should be of interest to researchers in finite and boundary element methods and...accessible to graduate students interested in these topics as well. Presentation, style and layout...are all very good. This review can warmly recommend Trefftz Finite and Boundary Element Method to anyone looking for a clear introduction to the subject..."

Part 1: finite element technique; shape functions and element stiffness
matrix; brief historical background; basic relationships in engineering
problems; modified variational principles; the concept of T-complete
solution; comparison of T-elements with conventional finite elements;
comparison of T-elements with boundary elements. Part 2: potential problems -
introduction; statement of the problem; T-complete functions; assumed fields;
generation of element matrix equation; rank condition; special purpose
functions; sensitivity to mesh distortion; orthotropic case; the Helmholtz
equation; HT-element with boundary "traction" frame; frameless T-elements.
Part 3: linear elastostatics - introduction; linear theory of elasticity;
assumed fields in plane elasticity; T-complete functions; variational
formulations; element stiffness equation; special-purpose elements;
p-extension approach; three-dimensional elasticity; numerical examples. Part
4: thin plates - introduction; thin plate theory; assumed field; T-complete
functions and particular solutions; variational formulations for plate
bending; generation of element stiffness matrix; p-method elements; special
purpose functions; Extension to thin plates on elastic foundation; Two
alternative plate bending p-elements; Numerical examples and assessment.
Chapter 5 - Thick Plates - Introduction; Basic equations for Reissner-Mindlin
plate theory; Assumed fields and particular solution; Variational formulation
for HT thick plate elements; Implementation of the new family of HT elements;
A 12 DOF quadrilateral element free of shear locking; Extension to thick
plates on elastic foundation; Sensitivity to mesh distortion; Numerical
assessment.
Chapter 6 - Transient Heat Conduction - Introduction; Elements of
heat conduction; Time step formula; Element matrix formulations; T-complete
functions and particular solutions; Numerical examples.
Chapter 7 -
Geometrically Nonlinear Analysis of Plate Bending Problems - Introduction;
Basic equations of nonlinear thin plate bending; Assumed fields and Trefftz
functions; Particular solutions; Modified variational principle; Element
matrix; Iterative scheme; Extension to post-buckling thin plates on elastic
foundation; Geometrically nonlinear analysis of thick plates; Numerical
examples.
Chapter 8 - Elastoplasticity - Introduction; Time discretization;
Basic relations; Assumed fields; Constraints on the approximation functions;
Finite element equilibrium and compatibility equations; Finite element
equations; Finite element governing system.
Chapter 9 - Dynamics of Plate
Bending Problems - Introduction; Basic equations; Time-stepping formulation;
Numerical examples.
Chapter 10 - Trefftz Boundary Element Method -
Introduction; Potential problems; Plane elasticity; Thin plate bending;
Moderately thick plates.