Inverse analysis FOR two-dimensional structures using the boundary element method

Inverse analysis is currently an important subject of study in several fields of science and engineering. The identification of physical and geometric parameters using experimental measurements is required in many applications. In this work a boundary element formulation to identify boundary and interface values as well as material properties is proposed. In particular the proposed formulation is dedicated to identifying material parameters when a cohesive crack model is assumed for 2D problems. A computer code is developed and implemented using the BEM multi-region technique and regularisation methods to perform the inverse analysis. Several examples are shown to demonstrate the efficiency of the proposed model.

[1]  L. M. Bezerra,et al.  A boundary element formulation for the inverse elastostatics problem (iesp) of flaw detection , 1993 .

[2]  D. W. Nicholson,et al.  A boundary element solution of an inverse elasticity problem and applications to determining residual stress and contact stress , 1997 .

[3]  J. Desanto.  Mathematical and numerical aspects of wave propagation , 1998 .

[4]  Rafael Gallego,et al.  Identification of cracks and cavities using the topological sensitivity boundary integral equation , 2004 .

[5]  Sang-Youl Lee,et al.  Defect identification in laminated composite structures by BEM from incomplete static data , 2005 .

[6]  C. Brebbia,et al.  Boundary Elements IX , 1987 .

[7]  W. S. Venturini,et al.  On the description of localization and failure phenomena by the boundary element method , 2006 .

[8]  Tadeusz Burczyński,et al.  Sensitivity analysis for shape perturbation of cavity or internal crack using BIE and adjoint variable approach , 2002 .

[9]  Carlos Alberto Brebbia,et al.  Boundary Elements: An Introductory Course , 1989 .

[10]  D. Rooke,et al.  The dual boundary element method: Effective implementation for crack problems , 1992 .

[11]  S. Roux,et al.  “Finite-Element” Displacement Fields Analysis from Digital Images: Application to Portevin–Le Châtelier Bands , 2006 .

[12]  Identification of Cracks or Defects by Means of the Elastodynamic BEM , 1991 .

[13]  G. Stavroulakis,et al.  Nondestructive elastostatic identification of unilateral cracks through BEM and neural networks , 1997 .

[14]  L. M. Bezerra,et al.  Inverse boundary traction reconstruction with the bem , 1995 .

[15]  H. Watabe,et al.  Improving defects search in structure by boundary element and genetic algorithm scan method , 1997 .

[16]  M. Bonnet.  Boundary element based formulations for crack shape sensitivity analysis , 2001 .

[17]  Andrea Prosperetti,et al.  Boundary Integral Methods , 2002 .

[18]  Derek B. Ingham,et al.  Identification of material properties and cavities in two-dimensional linear elasticity , 2003 .

[19]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[20]  M. H. Aliabadi,et al.  Crack growth analysis in concrete using boundary element method , 1995 .

[21]  Vincenzo Mallardo,et al.  Crack identification in two-dimensional unilateral contact mechanics with the boundary element method , 1999 .

[22]  A. Kirsch.  An Introduction to the Mathematical Theory of Inverse Problems , 1996, Applied Mathematical Sciences.

[23]  C. Schwab,et al.  Boundary Element Methods , 2010 .

[24]  Franccois Hild,et al.  Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties – a Review , 2006 .

[25]  Regularised Boundary Integral Equations for an Inverse Problem of Crack Determination in Time Domain , 1992 .

[26]  Andrei Constantinescu,et al.  Spatial localization of the error of constitutive law for the identification of defects in elastic bodies , 2000 .

[27]  Boundary element formulation of shape sensitivity analysis for defect identification in free vibration problem , 1997 .

[28]  Derek B. Ingham,et al.  Boundary Integral Formulations for Inverse Analysis , 1997 .

[29]  John W. Hutchinson,et al.  Dynamic Fracture Mechanics , 1990 .

[30]  C. A. Brebbia.  Boundary elements ten, an introduction , 1988 .

[31]  Nobuyoshi Tosaka,et al.  Unknown defect identification in elastic field by boundary element method with filtering procedure , 1995 .

[32]  W. S. Venturini,et al.  An implicit BEM formulation for gradient plasticity and localization phenomena , 2002 .

[33]  Åke Björck,et al.  Numerical methods for least square problems , 1996 .

[34]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[35]  Genki Yagawa,et al.  NEW REGULARIZATION BY TRANSFORMATION FOR NEURAL NETWORK BASED INVERSE ANALYSES AND ITS APPLICATION TO STRUCTURE IDENTIFICATION , 1996 .

[36]  Amanda Bordelon,et al.  Fracture Behavior of Functionally Graded Concrete Materials for Rigid Pavements , 2007 .

[37]  Rafael Gallego,et al.  Hypersingular shape sensitivity boundary integral equation for crack identification under harmonic elastodynamic excitation , 2007 .

[38]  Satya N. Atluri,et al.  Computational Mechanics ’95 , 1995 .

[39]  Gene H. Golub,et al.  Calculating the singular values and pseudo-inverse of a matrix , 2007, Milestones in Matrix Computation.

[40]  G. Maier,et al.  Parameter identification of a cohesive crack model by Kalman filter , 2002 .

[41]  Bojan B. Guzina,et al.  Computational framework for the BIE solution to inverse scattering problems in elastodynamics , 2003 .

[42]  Nondestructive detection of cavities by an inverse elastostatics boundary element method , 1994 .

[43]  Boundary element method applied to some inverse problems , 1986 .

[44]  Boundary element analysis of contact problems using inverse techniques—linear and quadratic elements , 2004 .

[45]  A. Kassab,et al.  A BEM based pattern search solution for a class of inverse elastostatic problems , 1996 .

[46]  Tadeusz Burczyński,et al.  The identification of cracks using boundary elements and evolutionary algorithms , 2001 .

[47]  M. H. Aliabadi,et al.  Flaw identification using the boundary element method , 1995 .