Editor: Qing-Hua Qin

Trefftz and Fundamental Solution-Based Finite Element Methods

eBook: US $99 Special Offer (PDF + Printed Copy): US $168
Printed Copy: US $119
Library License: US $396
ISBN: 978-981-4998-55-0 (Print)
ISBN: 978-981-4998-54-3 (Online)
Year of Publication: 2021
DOI: 10.2174/97898149985431210101


This reference explains hybrid-Trefftz finite element method (FEM). Readers are introduced to the basic concepts and general element formulations of the method. This is followed by topics on non-homogeneous parabolic problems, thermal analysis of composites, and heat conduction in nonlinear functionally graded materials. A brief summary of the fundamental solution based-FEM is also presented followed by a discussion on axisymmetric potential problems and the rotordynamic response of tapered composites. The book is rounded by chapters that cover the n-sided polygonal hybrid finite elements and analysis of piezoelectric materials.

Key Features

  • - Systematic presentation of 9 topics
  • - Covers FEMs in two sections: 1) hybrid-Trefftz method and 2) fundamental FEM solutions
  • - Bibliographic references
  • - Includes solutions to problems in the numerical analysis of different material types
  • - Includes solutions to some problems encountered in civil engineering (seepage, heat transfer, etc).

This reference is suitable for scholars involved in advanced courses in mathematics and engineering (civil engineering/materials engineering). Professionals involved in developing analytical tools for materials and construction testing can also benefit from the methods presented in the book.


Scholars at the graduate and postgraduate levels in mathematics, civil engineering, and materials science; researchers and engineering professionals involved in the making of programs and numerical tools to assess problems in construction projects


- Pp. i
Qing-Hua Qin
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List of Contributors

- Pp. ii
Qing-Hua Qin
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Introduction to Hybrid-Trefftz Finite Element Method

- Pp. 1-54 (54)
Qing-Hua Qin*
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Hybrid-Trefftz Finite Elements for Non- homogeneous Parabolic Problems

- Pp. 55-102 (48)
Ionut D. Moldovan*, Ana Coutinho, Ildi Cismasiu
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Thermal Analysis of Composites with Trefftz Finite Element Methods

- Pp. 103-132 (30)
Keyong Wang*, Ze She
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Hybrid-Trefftz Finite Element Method for Heat Conduction in Functionally Graded Materials

- Pp. 133-162 (30)
Zhuo-Jia Fu*, Wen-Zhi Xu, Qiang Xi
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Introduction to Fundamental Solution Based Finite Element Methods

- Pp. 163-201 (39)
Qing-Hua Qin*
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Hybrid Fundamental Solution based Finite Element Method for Axisymmetric Potential Problems

- Pp. 202-232 (31)
Keyong Wang, Junchen Zhou*
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Rotordynamic Response of Tapered Composite Driveshafts based on Hierarchical Shaft Finite Element

- Pp. 233-267 (35)
Rajamohan Ganesan*
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n-sided Polygonal Hybrid Finite Elements with Unified Fundamental Solution Kernels

- Pp. 268-311 (44)
Wan-Qing Lin, Hui Wang*
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Hybrid Fundamental-Solution-Based FEM for Piezoelectric Materials

- Pp. 312-337 (26)
Changyong Cao*, Qing-Hua Qin
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Subject Index

- Pp. 338-344 (7)
Qing-Hua Qin
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.An Introduction to Sobolev Spaces.
.Exterior Calculus: Theory and Cases.
.The Generalized Relative Gol’dberg Order and Type: Some Remarks on Functions of Complex Variables.