Boundary elements applied to three dimensional elastodynamic properties
Boundary elements applied to three dimensional elastodynamic properties
This work shows the use of the Direct Boundary Element Method in solving practical problems in three-dimensional, linear, steady-state elastodynamics in the frequency domain. Boundary integral equations for bounded bodies and external problems in infinite domains were reviewed. The boundary integral equations were solved numerically or semi-analytically and the problem boundary was discretized using discontinuous constant and linear triangular elements for both displacements and tractions. The choice of discontinuous triangular elements over continuous triangular ones has been discussed in detail. Integrations on a field element (i.e. an element which does not contain any source node) were performed using Hammer's numerical integration formula for triangular areas. However, integrations on a source element (i.e. an element containing one or more source nodes) were solved using two different approaches: one semi-analytical and the other numerical through element sub-division. The semi-analytical approach involves the use of a numerical procedure originally presented by H.R. Kutt and later modified by P.S. Theocaris for evaluating two-dimensional Cauchy principal value integrals. In the entirely numerical approach, the source element was divided into sub-elements, then the Hammer's numerical integration scheme was applied to approximate the integrals on each sub-element. The above formulations were implemented in computer programs written in Fortran. Numerical solutions, when compared with published analytical results, indicate that the semi-analytical approach produced more accurate solutions. They also show that the Direct Boundary Element Formulation using discontinuous triangular elements can be used for solving practical elastodynamic problems. (D71899/87)
University of Southampton
1986
Chang, Ooi-Voon
(1986)
Boundary elements applied to three dimensional elastodynamic properties.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
This work shows the use of the Direct Boundary Element Method in solving practical problems in three-dimensional, linear, steady-state elastodynamics in the frequency domain. Boundary integral equations for bounded bodies and external problems in infinite domains were reviewed. The boundary integral equations were solved numerically or semi-analytically and the problem boundary was discretized using discontinuous constant and linear triangular elements for both displacements and tractions. The choice of discontinuous triangular elements over continuous triangular ones has been discussed in detail. Integrations on a field element (i.e. an element which does not contain any source node) were performed using Hammer's numerical integration formula for triangular areas. However, integrations on a source element (i.e. an element containing one or more source nodes) were solved using two different approaches: one semi-analytical and the other numerical through element sub-division. The semi-analytical approach involves the use of a numerical procedure originally presented by H.R. Kutt and later modified by P.S. Theocaris for evaluating two-dimensional Cauchy principal value integrals. In the entirely numerical approach, the source element was divided into sub-elements, then the Hammer's numerical integration scheme was applied to approximate the integrals on each sub-element. The above formulations were implemented in computer programs written in Fortran. Numerical solutions, when compared with published analytical results, indicate that the semi-analytical approach produced more accurate solutions. They also show that the Direct Boundary Element Formulation using discontinuous triangular elements can be used for solving practical elastodynamic problems. (D71899/87)
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Published date: 1986
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Local EPrints ID: 460736
URI: http://eprints.soton.ac.uk/id/eprint/460736
PURE UUID: 7bc4c762-4bba-4d40-b558-d721bcf1549d
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Date deposited: 04 Jul 2022 18:28
Last modified: 04 Jul 2022 18:28
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Author:
Ooi-Voon Chang
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