On the Use of Fundamental Solutions in Trefftz Method for Potential and Elasticity Problems

Patterson, C.; Sheikh, Mohammad

doi:10.1007/978-3-662-11273-1_4

Cited by 27 publications

(15 citation statements)

References 6 publications

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“…For elasticity, previous work was reported by Patterson and Sheikh [16], Redekop [17] and Murashima et al [8] for planar problems and Karageorghis and Fairweather [18] and Redekop and Thompson [19] for axisymetric problems and by Patterson and Sheikh et al [9,12], Wearing and Sheikh [11], Redekop and Cheung [20] and Poullikas et al [21] for three-dimensional problems.…”

Section: Introductionmentioning

confidence: 88%

The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

Fam

Rashed

2005

Comput Mech

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This paper presents the Method of Fundamental Solutions for three-dimensional elastostatics with body forces. The gravitational body loading is considered as an example for the treated body forces. A new set of particular solutions corresponding to such loading is derived using Ho¨rmander operator-decoupling technique, and the relevant particular solution expressions for displacements, tractions and stresses are derived and given explicitly. Several examples are tested and the results confirm the validity and efficiency of the presented method.

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Section: Introductionmentioning

confidence: 88%

The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

Fam

Rashed

2005

Comput Mech

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“…= i h * ( Q X 4(Q) = h * ( Q ) (23) where (') denotes the differentiation with respect to the specified value on the boundary. i r is calculated from equation (11).…”

Section: ( Q )mentioning

confidence: 99%

An application of Trefftz method to the sensitivity analysis of two‐dimensional potential problem

Kita

Kamiya

Ikeda

1995

Numerical Meth Engineering

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SUMMARYThis paper presents a new formulation for the sensitivity analysis with the help of the Trefftz boundary-type solution procedure. Direct differentiation of the expressions of the field variables leads to the expressions of the sensitivities. Since the field variables are approximated by linear combination of regular T-complete functions, the analytical expressions of the sensitivities are also regular. Sensitivity analysis schemes with respect to variations of dimensions of the object and boundary conditions are explained in detail. Twodimensional potential problems in the bounded region are considered as a numerical example in order to confirm its validity.

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“…However, it should be noted that, in all the examples carried out by the authors, the range of acceptable final results was broader than the range of stable e K . Relative solution error (21) and relative measure of generalized energy density error (22) with its average value…”

Section: N -Cqmentioning

confidence: 99%

“…Such HT-H elements have been widely investigated and applied to plane elasticity [ 14, 151, Poisson equation [17], various kinds of plates [12,22], and shells [28]. However, as it was shown for the standard Trefftz method [4,21,24,30,32] and 3D axisymmetric problems of elasticity [29], the second type of shape functions can also be effectively used. The authors carried out a series of numerical experiments to compare the two types of solutions.…”

Section: Alternative Shape Functionsmentioning

confidence: 99%

Alternative T‐complete systems of shape functions applied in analytical Trefftz finite elements

Szybiński

Zieliński

1995

Numerical Methods Partial

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The authors compare the behavior of hybrid Trefftz p-elements with two different types of shape functions identically fulfilling governing differential equations. Numerical examples include several boundary problems for Laplace, Poisson, and plane elasticity equations. Accuracy of the solutions, convergence properties, numerical stability and sensitivity for mesh distortion are investigated. It is shown that both systems of the functions can be efficiently applied, although they have different properties. 0 1995 John Wiley & Sons. Inc.

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On the Use of Fundamental Solutions in Trefftz Method for Potential and Elasticity Problems

Cited by 27 publications

References 6 publications

The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

An application of Trefftz method to the sensitivity analysis of two‐dimensional potential problem

Alternative T‐complete systems of shape functions applied in analytical Trefftz finite elements

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