Nhận diện vết nứt với dữ liệu biên không đầy đủ trong đàn hồi tuyến tính bằng phương pháp khoảng cách đối ngẫu

Computational Mechanics - Tập 67 - Trang 1559-1579 - 2021
R. Ferrier1, M. Kadri2, P. Gosselet3
1LMA, Université Aix-Marseille, Marseille, France
2LAMSIN, ENIT, Université El Manar, Tunis, Tunisia
3Bâtiment ESPRIT, Cité Scientifique, LaMcube, Université de Lille, Villeneuve-d’Ascq, France

Tóm tắt

Bài báo này đề xuất và nghiên cứu ba phương pháp nhận diện vết nứt trong các thân đàn hồi tuyến tính. Các phương pháp này dựa trên nguyên tắc chênh lệch đối ngẫu mà chúng mở rộng đến trường hợp dữ liệu biên phần nào bị dư thừa. Tất cả các phương pháp đều được đánh giá trên một trường hợp 2D học thuật, sau đó phương pháp hấp dẫn nhất được phân tích sâu hơn và minh họa trên một bài kiểm tra 3D.

Từ khóa

#nhận diện vết nứt #đàn hồi tuyến tính #phương pháp khoảng cách đối ngẫu #dữ liệu biên không đầy đủ

Tài liệu tham khảo

Alessandrini G, Rondi L, Rosset E, Vessella S (2009) The stability for the Cauchy problem for elliptic equations. Inverse Probl 25(12):123004 Amstutz S, Horchani I, Masmoudi M (2005) Crack detection by the topological gradient method. Control Cybern 34(1):81–101 Andrieux S (2015) The reciprocity likelihood maximization: a variational approach of the reciprocity gap method. J Mech Mater Struct 10(3):219–237 Andrieux S, Baranger T (2012) Emerging crack front identification from tangential surface displacements. Comptes Rendus Mécanique 340(8):565–574 Andrieux S, Baranger T, Ben Abda A (2006) Solving Cauchy problems by minimizing an energy-like functional. Inverse Probl 22(1):115 Andrieux S, Ben Abda A (1993) The reciprocity gap: a general concept for flaws identification problems. Mech Res Commun 20(5):415–420 Andrieux S, Ben Abda A, Bui HD (1999) Reciprocity principle and crack identification. Inverse Probl 15(1):59 Andrieux S, Ben Abda A, Jaoua M (1998) On the inverse emergent plane crack problem. Math Methods Appl Sci 21(10):895–906 Avril S, Bonnet M, Bretelle A-S, Grediac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco E et al (2008) Overview of identification methods of mechanical parameters based on full-field measurements. Exp Mech 48(4):381 Ben Abda A, Ameur HB, Jaoua M (1999) Identification of 2D cracks by elastic boundary measurements. Inverse Probl 15(1):67 Ben Abda A, Delbary F, Haddar H (2005) On the use of the reciprocity-gap functional in inverse scattering from planar cracks. Math Models Methods Appl Sci 15(10):1553–1574 Ben Abda A, Kallel M, Leblond J, Marmorat J-P (2002) Line segment crack recovery from incomplete boundary data. Inverse Probl 18(4):1057 Ben Belgacem F (2007) Why is the Cauchy problem severely ill-posed? Inverse Probl 23(2):823–836 Ben Belgacem F, El Fekih H (2005) On Cauchy’s problem: I. A variational Steklov-Poincaré theory. Inverse Problems 21(6):1915 Cakoni F, Colton D (2003) The linear sampling method for cracks. Inverse Probl 19(2):279 Cimetiere A, Delvare F, Jaoua M, Pons F (2001) Solution of the Cauchy problem using iterated Tikhonov regularization. Inverse Probl 17(3):553–570 Ern A, Guermond J-L (2013) Theory and practice of finite elements, volume 159. Springer Science & Business Media Ferrier R, Kadri ML, Gosselet P (2018) The Steklov-Poincaré technique for data completion: preconditioning and filtering. Int J Numer Methods Eng 116(4):270–286 Ferrier R, Kadri ML, Gosselet P (2019) Planar crack identification in 3D linear elasticity by the Reciprocity Gap method. Comput Methods Appl Mech Eng 355:193–215 Geuzaine C, Remacle J-F (2009) Gmsh: a 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng 79(11):1309–1331 Kadri ML, Ben Abdallah J, Baranger T (2011) Identification of internal cracks in a three-dimensional solid body via Steklov-Poincaré approaches. Comptes Rendus Mécanique 339(10):674–681 Kozlov VA, Maz’ya VG (1989) Iterative procedures for solving ill-posed boundary value problems that preserve the differential equations. Algebra i Analiz 1(5):144–170 O’Leary DP (1980) The block conjugate gradient algorithm and related methods. Linear algebra and its applications 29:293–322 Santosa F, Vogelius M (1991) A computational algorithm to determine cracks from electrostatic boundary measurements. Int J Eng Sci 29(8):917–937 Shifrin E, Shushpannikov P (2013) Identification of small well-separated defects in an isotropic elastic body using boundary measurements. Int J Solids Struct 50(22):3707–3716 Shifrin EI, Kaptsov AV (2017) Identification of multiple cracks in 2D elasticity by means of the reciprocity principle and cluster analysis. Inverse Probl 34(1):015009 Steinhorst P, Kaltenbacher B (2013) Application of the reciprocity principle for the determination of planar cracks in piezoelectric material. In Advanced finite element methods and applications, pp 325–353. Springer