Trefftz and Essential Solution-Based Finite Element Methods

Editor Name: Qing-Hua Qin

To read the full article:

This reference explains hybrid-Trefftz finite element method (FEM). Readers are introduced to the basic concepts and general element formulations of the method. The book consists of two major parts: Part I Trefftz FEM and Part II fundamental solution based FEM. In the first part, Chapter 1 gives an introduction and overview of the hybrid-Trefftz FEM. 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 which cover the n-sided polygonal hybrid finite elements and analysis of piezoelectric resources. It includes solutions to problems in the numerical analysis of different material types and solutions to some problems encountered in civil engineering (seepage, heat transfer, etc).

This reference is suitable for Scholars at graduate and postgraduate levels in mathematics, civil engineering and materials science. Professionals involved in developing analytical tools for materials and construction testing can also benefit from the methods presented in the book.

About the Editor:

Qing-Hua Qin

Dr. Qing-Hua Qin is a Professor at Shenzhen MSU-BIT University. He received his Bachelor of Engineering degree in mechanical engineering from Chang An University and earning his Master of Science degree and PhD degree from Huazhong University of Science and Technology (HUST) in China. Both MS and PhD are in applied mechanics. He has worked in several leading Australian and Chinese institutions and was awarded a Queen Elizabeth II fellowship and professional fellowship at the University of Sydney. He was also awarded a Cheung Kong Professorship at Tianjin University from the Ministry of Education of China. His research is interdisciplinary which spans the fundamentals of solid mechanics, computational engineering, materials engineering, manufacturing and machine learning – to application areas such as functional materials, additive manufacturing, topology optimisation and integrating hybrid finite element methods with machine learning. He has published more than 300 journal papers and 8 English monographs in the field of applied mechanics.


Finite element method, Dual Reciprocity Method, Trefftz function, variational principle, Fundamental solution, piezoelectricity, Numerical analysis, Two-dimensional elasticity, functionally graded material, Heat transfer, Special purposed element, n-sided polygonal element, tapered composite shaft, Non-homogeneous parabolic problem.

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Author: Bentham Science Publishers

A major STM journal publisher of more than 100 online and print journals and related print/online book series, Bentham Science answers the information needs of scientists in the fields of pharmaceutical, biomedical, medical, engineering, technology, computer and social sciences.

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