A further development of the boundary integral technique for elastostatics
A further development of the boundary integral technique for elastostatics
The field equations of plane and three-dimensional elastostatics are transformed, by a general method applicable to any elliptic equation, into boundary integral equations. For the discretisation of these equations, the boundary is represented by three- node segments with quadratic variation of geometry in the two- dimensional case, and by eight-node quadrilaterals and six-node triangles also with quadratic variation of geometry in three dimensions. Over each boundary element, displacement and traction are considered to vary linearly, quadratically or cubically with respect to the intrinsic coordinates. In three dimensions, the elastic body is divided into subregions, for each of which the integral equation is discretised. By specifying continuity and equilibrium across interfaces, a global system of equations is obtained ; this system is of banded form. The subregions may- have different. elastic properties. Gaussian quadrature formulae are used to evaluate all integrals but those of the product of the strongly singular kernel and shape functions corresponding to the functional singularity ; these integrals and the coefficient of the free term of the integral equation are calculated indirectly, by considering rigid body translations. The program for three-dimensional analysis chooses the order of integration formula for each surface element according to the rapidity of variation of the integrand. Equation coefficients are scaled so that numerical stability is such that the system may be solved by elimination without iteration on the residues. The system is reduced by block solution, all load cases being treated simultaneously. Examples of two and three-dimensional analyses are presented, and comparisons are made with results obtained experimentally and by the finite element method. It is shown that the boundary integral equation method may be used to analyse a wide range of practical problems, and that in most cases it is a relatively economical method of calculation.
University of Southampton
Lachat, Jean Claude Auguste
c3680335-0125-473f-91af-37c31c00a6e9
1975
Lachat, Jean Claude Auguste
c3680335-0125-473f-91af-37c31c00a6e9
Lachat, Jean Claude Auguste
(1975)
A further development of the boundary integral technique for elastostatics.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
The field equations of plane and three-dimensional elastostatics are transformed, by a general method applicable to any elliptic equation, into boundary integral equations. For the discretisation of these equations, the boundary is represented by three- node segments with quadratic variation of geometry in the two- dimensional case, and by eight-node quadrilaterals and six-node triangles also with quadratic variation of geometry in three dimensions. Over each boundary element, displacement and traction are considered to vary linearly, quadratically or cubically with respect to the intrinsic coordinates. In three dimensions, the elastic body is divided into subregions, for each of which the integral equation is discretised. By specifying continuity and equilibrium across interfaces, a global system of equations is obtained ; this system is of banded form. The subregions may- have different. elastic properties. Gaussian quadrature formulae are used to evaluate all integrals but those of the product of the strongly singular kernel and shape functions corresponding to the functional singularity ; these integrals and the coefficient of the free term of the integral equation are calculated indirectly, by considering rigid body translations. The program for three-dimensional analysis chooses the order of integration formula for each surface element according to the rapidity of variation of the integrand. Equation coefficients are scaled so that numerical stability is such that the system may be solved by elimination without iteration on the residues. The system is reduced by block solution, all load cases being treated simultaneously. Examples of two and three-dimensional analyses are presented, and comparisons are made with results obtained experimentally and by the finite element method. It is shown that the boundary integral equation method may be used to analyse a wide range of practical problems, and that in most cases it is a relatively economical method of calculation.
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Published date: 1975
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Local EPrints ID: 458850
URI: http://eprints.soton.ac.uk/id/eprint/458850
PURE UUID: 8298b399-c28a-4df4-8c20-f2f50d6b93c9
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Last modified: 16 Mar 2024 18:26
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Author:
Jean Claude Auguste Lachat
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