Trefftz method for Kirchhoff plate bending problems

Jin, Wenhe; Cheung, Y.K.; Zienkiewicz, O. C.

doi:10.1002/nme.1620360504

Cited by 52 publications

(31 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Given the fact that RBF and Tre tz share some features the reproduction of the results obtained by Jin et al [33] was deemed relevant. Amongst those common features are, for example, that both techniques lead to global approximations of the relevant variables in a way which is more closely related than with, generally speaking, ÿnite element methods and that the number of unknowns=equations is usually much lower than that of standard ÿnite element techniques for obtaining similar accuracy.…”

Section: Numerical Testsmentioning

confidence: 96%

“…The methodology chosen for presenting the results and also the tests conducted follow closely that of Jin et al [33], a reference work for Tre tz formulation (which may also be considered, up to a certain point, meshless). Given the fact that RBF and Tre tz share some features the reproduction of the results obtained by Jin et al [33] was deemed relevant.…”

Section: Numerical Testsmentioning

confidence: 99%

See 1 more Smart Citation

A meshless method for Kirchhoff plate bending problems

Leitão

2001

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYIn this work a meshless method for the analysis of bending of thin homogeneous plates is presented. This meshless method is based on the use of radial basis functions to build an approximation of the general solution of the partial di erential equations governing the Kirchho plate bending problem. In order to obtain a symmetric and non-singular linear equation system the Hermite collocation method is used. To assess the formulation a series of plates with di erent boundary conditions are analysed. Comparisons are made with other results available in the literature.

show abstract

Section: Numerical Testsmentioning

confidence: 96%

Section: Numerical Testsmentioning

confidence: 99%

A meshless method for Kirchhoff plate bending problems

Leitão

2001

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Another regular boundary type approach is the Tre tz method, which has been widely used to deal with many types of problems, such as plane elasticity problems [14], plate bending problems [15] and acoustics [16], and the ÿrst applications of various modern forms of this method can be traced back to 1978 [17]. The boundary type Tre tz method basically employs the complete set of solutions satisfying the governing equation as the beginning step.…”

Section: Introductionmentioning

confidence: 99%

Application of symmetric indirect Trefftz method to free vibration problems in 2D

Chang

Liu

Kuo

et al. 2003

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYA symmetric indirect Tre tz method is developed to solve the free vibration problem of a 2D membrane. It is proved that in this approach the spurious eigensolution exists, and an auxiliary matrix is constructed to help extraction of the spurious solution using the generalized singular-value decomposition. In addition to the spurious eigensolution, this regular formulation su ers from its ill-posed nature, i.e. the numerical instability. In order to deal with the numerical instability, the Tikhonov's regularization method, in conjunction with the generalized singular-value decomposition, is suggested. The proposed approach has some merits when compared with other regular boundary element formulations reported so far; namely the capacity of representing eigenmodes and the ability to deal with a multiply connected domain of genus 1. Several numerical examples are demonstrated to show the validity of the current approach.

show abstract

“…These unknowns are then obtained from the approximate satisfaction of the boundary conditions by means of collocation or in a weighted residual sense. Trefftz-based formulations have been studied by several authors, such as Jirousek and co-workers (of which Jirousek and Wrobleski [5] give a thorough account), Cheung et al [6], Jin et al [7], Zielinski and Zienkiewicz [8], Zielinski and Herrera [9], and Freitas and Ji [10] amongst others. Reviews on the subject may be found in Zielinski [11], Kita and Kamiya [12] and Jirousek and Wrobleski [5].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of thin circular plates by the indirect Trefftz method

Ghannadiasl

Noorzad

2009

Mesh Reduction Methods

View full text Add to dashboard Cite

The vibration of plates is important in many applications pertaining to mechanical, civil and aerospace engineering. Therefore, the vibration of plates is an important research area that has been studied by many researchers. To date, there are abundant plate vibration solutions available in the open literature based on Kirchhoff assumptions. The purpose of the present paper is free vibration analysis of thin circular plates by the indirect Trefftz method. In thin plate vibration problems, we will deal with the governing equation with the homogeneous boundary conditions. The Trefftz method basically employs the complete set of solutions satisfying the governing equation as the first step. To derive the boundary integral equation, either the reciprocity law, which is similar to those used in conventional BEMs, or the weight residual method can be used. The proposed approach has some merits when compared with other regular boundary element formulations reported so far. A main benefit for the Trefftz method is that it does not involve singular integrals due to the properties of its solution basis functions (T functions); thus, it can be categorized into the regular boundary element method. Besides, this advocated approach yields a solution that offers simultaneously the advantages of the classical FEM and BEM solutions, without having their drawbacks. Finally, several numerical examples are demonstrated to show the validity of the current approach.

show abstract

Trefftz method for Kirchhoff plate bending problems

Cited by 52 publications

References 18 publications

A meshless method for Kirchhoff plate bending problems

A meshless method for Kirchhoff plate bending problems

Application of symmetric indirect Trefftz method to free vibration problems in 2D

Free vibration analysis of thin circular plates by the indirect Trefftz method

Contact Info

Product

Resources

About