Nondestructive detection of cavities by an inverse elastostatics boundary element method

Kassab, Alain J.; Moslehy, F.A.; Daryapurkar, A.

doi:10.1016/0955-7997(94)90006-x

Cited by 35 publications

(34 citation statements)

References 4 publications

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“…Mellings and Aliabadi [30] presented a dual boundary element formulation for the identification of the location and size of internal flaws in two-dimensional structures. Kassab et al [24] and Ulrich et al [37] investigated the non-destructive detection of internal cavities in the inverse elastostatic problem using the BEM. The level set method and a regularization technique related to the perimeter of the unknown inclusion were employed by Ben Ameur et al [7] for the numerical reconstruction of a void from a single Cauchy data.…”

Section: Introductionmentioning

confidence: 99%

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

Karageorghis

Lesnic

Marin

2016

Computers & Structures

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We investigate the numerical reconstruction of smooth star-shaped voids (rigid inclusions and cavities) which are compactly contained in a three-dimensional isotropic linear elastic medium from a single set of Cauchy data (i.e. nondestructive boundary displacement and traction measurements) on the accessible outer boundary. This inverse geometric problem in three-dimensional elasticity is approximated using the method of fundamental solutions (MFS). The parameters describing the boundary of the unknown void, its centre, and the contraction and dilation factors employed for selecting the fictitious surfaces where the MFS sources are to be positioned, are taken as unknowns of the problem. In this way, the original inverse geometric problem is reduced to finding the minimum of a nonlinear least-squares functional that measures the difference between the given and computed data, penalized with respect to both the MFS constants and the derivative of the radial coordinates describing the position of the star-shaped void. The interior source points are anchored and move with the void during the iterative reconstruction procedure. The feasibility of this new method is illustrated in several numerical examples.

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Section: Introductionmentioning

confidence: 99%

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

Karageorghis

Lesnic

Marin

2016

Computers & Structures

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“…Typically, the over-specified conditions are provided by measuring a field variable at the exposed boundary, as in the case of the inverse geometric problem. However, in some inverse problems, the over-specified condition can be provided by internal measurements of field variable via embedded sensors (Divo et al [1], Ulrich et al [2], Kassab et al [3]). In this paper, such measurements, along with accompanying noise, are simulated numerically.…”

Section: Introductionmentioning

confidence: 99%

“…This inverse problem has applications in the identification of surfaces flaws and cavities and in shape optimization problems (Divo et al [1,5,[7][8][9], Ulrich et al [2], Kassab et al [3,4], Bialecki et al [6]). The computational burden is intensive due to the inherent nature of the solution of inverse problem which requires numerous forward problems to be solved, regardless of whether a numerical or analytical approach is taken to solve the associated direct problem.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of the inverse geometric problem, that concerns this study, is to determine the hidden portion of the system geometry by using over-specified boundary conditions on the exposed portion. This problem has gained importance in thermal and solid mechanics applications for nondestructive detection of subsurface cavities (Ulrich et al [2], Kassab et al [3,4], Divo et al [5]). In thermal applications, the method requires over-specified boundary conditions at the surface, i.e., both temperature and flux must be given, Divo et al [1].…”

Section: Introductionmentioning

confidence: 99%

“…In elastostatics applications, the over-specified conditions are provided in terms of surface displacements and tractions. Generally, surface tractions are known boundary conditions, while the surface displacements are experimentally determined by measurements, (see Ulrich et al [2], Kassab et al [3]). …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Singular superposition elastostatics BEM/GA algorithm for cavity detection

Ojeda¹,

́amez²,

Divo³

et al. 2007

WIT Transactions on Modelling and Simulation, Vol 44

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A method for the efficient solution of the inverse geometric problem for cavity detection using a point load superposition technique in the elastostatics boundary element method (BEM) is presented in this paper. The superposition of point load clusters to simulate the presence of cavities offers tremendous advantages in reducing the computational time for the elastostatics field solution as no boundary re-discretization is necessary throughout the inverse problem solution process. The inverse solution is achieved in two steps: (1) fixing the location and strengths of the point loads, (2) locating the cavity(ies) geometry(ies). For a current estimated point load distribution, a first objective function measures the difference between BEM-computed and measured deformations at the measuring points. A Genetic Algorithm (GA) is employed to automatically alter the locations and strengths of the point sources to minimize the objective function. The GA is parallelized and dynamically balanced. Upon convergence, a second objective function is defined and minimized to locate the cavity(ies) location(s) indicated as traction-free surface(s). Results of cavity detection simulations using numerical experiments and simulated random measurement errors validate the approach in regular and irregular geometrical configurations with single and multiple cavities.

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A BEM sensitivity and shape identification analysis for acoustic scattering in fluid-solid problems

Mallardo¹,

Aliabadi

1998

Int. J. Numer. Meth. Engng.

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In this paper a boundary element formulation for the sensitivity analysis of structures immersed in an inviscide fluid and illuminated by harmonic incident plane waves is presented. Also presented is the sensitivity analysis coupled with an optimization procedure for analyses of flaw identification problems. The formulation developed utilizes the boundary integral equation of the Helmholtz equation for the external problem and the Cauchy-Navier equation for the internal elastic problem. The sensitivities are obtained by the implicit differentiation technique. Examples are presented to demonstrate the accuracy of the proposed formulations.1998 John Wiley & Sons, Ltd.

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Nondestructive detection of cavities by an inverse elastostatics boundary element method

Cited by 35 publications

References 4 publications

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

Singular superposition elastostatics BEM/GA algorithm for cavity detection

A BEM sensitivity and shape identification analysis for acoustic scattering in fluid-solid problems

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