The Trefftz Finite and Boundary Element Method
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Book 1
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Book 1
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The Trefftz Finite and Boundary Element Method: (Advances in Boundary Elements)

The Trefftz Finite and Boundary Element Method: (Advances in Boundary Elements)


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About the Book

This text provides an accessible and up-to-date introduction to the Trefftz finite element method. The author's main emphasis is on fundamental concepts and the development of different Trefftz element formulations for stress analysis of various elastic problems. The book is a reference for postgraduate students, researchers, scientists and professional engineers in computational mechanics, structural design, and applied mathematics.

Table of Contents:
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.

Review :
..".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..."


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Product Details
  • ISBN-13: 9781853128554
  • Publisher: WIT Press
  • Publisher Imprint: WIT Press
  • Height: 230 mm
  • Returnable: N
  • Width: 155 mm
  • ISBN-10: 1853128554
  • Publisher Date: 26 May 2000
  • Binding: Hardback
  • Language: English
  • Series Title: Advances in Boundary Elements


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