Crack identification in two-dimensional unilateral contact mechanics with the boundary element method

Alessandri, Claudio; Mallardo, Vincenzo

doi:10.1007/s004660050442

Cited by 17 publications

(6 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The LCP can be formulated only in terms of the pressure derivatives p ;m referred to the nodes of the matrix-inclusion system in contact but with zero contact pressures (Alessandri and Tralli, 1995a;Alessandri and Mallardo, 1999). Besides, by splitting r ;m into its positive and negative parts, and by doubling the differentiated equilibrium equations, it is possible to write the new LCP as:…”

Section: Sensitivity Problem: Idm and Lcpmentioning

confidence: 99%

“…With reference to their recent experiences (Mallardo and Aliabadi, 1998a;Mallardo and Aliabadi, 1998b;Alessandri and Mallardo, 1999;Mallardo and Alessandri, 1999), the authors present in this paper a BEM numerical procedure to solve some inverse problems concerning constrained linear elastic solids with internal inclusions in unilateral frictionless contact at the interface.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Inverse problems in the presence of inclusions and unilateral constraints: a boundary element approach

Mallardo

Alessandri

2000

Computational Mechanics

Self Cite

View full text Add to dashboard Cite

The authors present a boundary element method (BEM) numerical procedure for the solution of 2D nondestructive identi®cation problems in the presence of unilateral boundary conditions. Firstly, the position of a deformable inclusion in frictionless unilateral contact with the matrix is identi®ed on the basis of measurements surveyed at some sensor points on the external boundary where given static loads are applied (identi®cation problem). Then the procedure used is extended to the identi®cation of the position which a rigid/deformable inclusion must occupy within the matrix in order to maximise the structural stiffness of the matrix-inclusion system under prescribed external loads (optimisation problem). Matrix and deformable inclusion are both considered linear elastic. A minimisation problem is stated with design variables representing the size and the shape of the inclusion. The cost function is an error function that evaluates the difference between computed and observed displacements at the sensor points in the identi®cation problem and the strain energy accumulated by the matrixinclusion system in the optimisation problem. The minimisation is performed by using a ®rst-order nonlinear optimisation technique in which the cost function gradient is computed by implicit differentiation. Some simple but meaningful examples are presented and discussed in order to show the applicability of the proposed technique.

show abstract

Section: Sensitivity Problem: Idm and Lcpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inverse problems in the presence of inclusions and unilateral constraints: a boundary element approach

Mallardo

Alessandri

2000

Computational Mechanics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Previous work by the research community involving exact⧵implicit derivatives of BEM formulations have focused on 2D structures, 1,3,[21][22][23][24][25][26][27][28] with some work conducted on 3D structures, 13,29 and one work so far on plate structures. 20 One notable example is Huang et al in which the implicit derivatives for the 2D dual boundary element method (DBEM), a version of BEM effective at modeling cracks, were developed for the first time and used to estimate the reliability of 2D structures using the First-Order Reliability Method (FORM).…”

Section: Introductionmentioning

confidence: 99%

Manufacturing cost and reliability‐based shape optimization of plate structures

Morse

Mallardo

Aliabadi

2022

Numerical Meth Engineering

View full text Add to dashboard Cite

A novel methodology is presented for the manufacturing cost and reliability-based optimization of plate structures with the boundary element method (BEM), with the aim of improving the accuracy, robustness, and efficiency of the optimization of aircraft structures. The BEM plate formulations with respect to plate thickness are derived for the first time, and used as part of an implicit differentiation method (IDM), enabling the full shape optimization of plate structures with the BEM. These implicit derivatives are validated against derivatives obtained from the finite difference method (FDM) and from an analytical solution. Results indicate that the IDM is more robust than the FDM and in excellent agreement with the analytical solution, and more accurate than the FDM for most of the step-sizes investigated. To demonstrate the full shape optimization of plates with the newly developed IDM, a numerical example involving reliability-based design optimization and manufacturing cost optimization is presented for a plate structure. Results show that the newly developed IDM is more efficient than the FDM when performing this optimization.

show abstract

“…Mellings and Aliabadi used the steepest descent and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton methods as well as the Dual BEM to identify flaws via displacement or stress measurements [5]. Similar studies have also been carried out in [6][7][8][16][17][18][19] using either gradient-based optimization techniques (e.g., line search methods and quadratic programming) or heuristic algorithms (e.g., genetic algorithms (GAs) and evolutionary algorithms (EAs)) integrated with BEM, through elasto (e.g., displacement and stress) or thermo (e.g., temperature) measurements. Apart from flaw detection in elastomechanics, these methods have also been used in other engineering identification areas.…”

Section: Introductionmentioning

confidence: 99%

Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm

Sun

Waisman

Betti

2013

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYWe present a novel algorithm based on the extended finite element method (XFEM) and an enhanced artificial bee colony (EABC) algorithm to detect and quantify multiple flaws in structures. The concept is based on recent work that have shown the excellent synergy between XFEM, used to model the forward problem, and a genetic‐type algorithm to solve an inverse identification problem and converge to the ‘best’ flaw parameters.In this paper, an adaptive algorithm that can detect multiple flaws without any knowledge on the number of flaws beforehand is proposed. The algorithm is based on the introduction of topological variables into the search space, used to adaptively activate/deactivate flaws during run time until convergence is reached. The identification is based on a limited number of strain sensors assumed to be attached to the structure surface boundaries. Each flaw is approximated by a circular void with the following three variables: center coordinates (xc, yc) and radius (rc), within the XFEM framework. In addition, the proposed EABC scheme is improved by a guided‐to‐best solution updating strategy and a local search (LS) operator of the Nelder–Mead simplex type that show fast convergence and superior global/LS abilities compared with the standard ABC or classic genetic algorithms.Several numerical examples, with increasing level of difficulty, are studied in order to evaluate the proposed algorithm. In particular, we consider identification of multiple flaws with unknown a priori information on the number of flaws (which makes the inverse problem harder), the proximity of flaws, flaws having irregular shapes (similar to artificial noise), and the effect of structured/unstructured meshes. The results show that the proposed XFEM–EABC algorithm is able to converge on all test problems and accurately identify flaws. Hence, this methodology is found to be robust and efficient for nondestructive detection and quantification of multiple flaws in structures. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

Crack identification in two-dimensional unilateral contact mechanics with the boundary element method

Cited by 17 publications

References 25 publications

Inverse problems in the presence of inclusions and unilateral constraints: a boundary element approach

Inverse problems in the presence of inclusions and unilateral constraints: a boundary element approach

Manufacturing cost and reliability‐based shape optimization of plate structures

Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm

Contact Info

Product

Resources

About