In the 1 International Workshop, devoted to Trefftz Method, the author presented an indirect approach to Trefftz Method (Trefftz-Herrera Method), while in the Second one some of the basic ideas of how to integrate different approaches to Trefftz method were introduced. The present Plenary Lecture, corresponding to the 3 International Workshop of this series, is devoted to show that Trefftz Meth...

Professor Jirousek has been a very important driving force in the modern development of Trefftz method, contributing to its application in many different fields such as elasticity, shells and plates theory, Poisson equation and transient heat analysis. This article is dedicated to him. The focus of the paper is to incorporate Jirousek method into a very general framework of Trefftz method which...

this paper presents the bending analysis of annular plates by the indirect trefftz boundary approach. the formulation for thin and thick plates is based on the kirchhoff plate theory and the reissner plate theory. the governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. the trefftz method employs the complete set of solu...

This paper presents the bending analysis of annular plates by the indirect Trefftz boundary approach. The formulation for thin and thick plates is based on the Kirchhoff plate theory and the Reissner plate theory. The governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. The Trefftz method employs the complete set of solu...

In this chapter, the indirect Trefftz collocation method is applied to solve the inverse Cauchy problem of linear piezoelectricity. The static analysis of coupled fields in 2D piezoelectric solids is considered. The piezoelectric material is modelled as a homogenous, linear elastic, linear dielectric and transversal isotropic. The T-functions are obtained by the Stroh formalism. The inverse Cau...

The author’s algebraic theory of boundary value problems has permitted systematizing Trefftz method and expanding its scope. The concept of TH-completeness has played a key role for such developments. This paper is devoted to revise the present state of these matters. Starting from the basic concepts of the algebraic theory, Green–Herrera formulas are presented and Localized Adjoint Method (LAM...

In this paper, the direct Trefftz method is applied to solve the free-vibration problem of a membrane. In the direct Trefftz method, there exists no spurious eigenvalue. However, an ill-posed nature of numerical instability encountered in the direct Trefftz method requires some treatments. The Tikhonov's regularization method and generalized singular-value decomposition method are used to deal ...

In this paper a guaranteed upper bound of the global discretization error in linear elastic finite element approximations is presented, based on a generalized Trefftz functional. Therefore, the general concept of complementary energy functionals and the corresponding approximation methods of Ritz, Trefftz, the method of orthogonal projection and the hypercircle method are briefly outlined. Furt...

In this paper, a generalized Trefftz method in plane elasticity is developed, for solving problems in an arbitrary multiply connected domain. Firstly, the relations between Trefftz basis functions from different source points are discussed, by using the binomial theorem and the logarithmic binomial theorem. Based on these theorems, we clearly explain the relation between the T-Trefftz and the F...