Solution of identification inverse problems in elastodynamics using semi-analytical sensitivity computation (original) (raw)
Related papers
Computer Methods in Applied Mechanics and Engineering, 2007
Model-based nondestructive testing (NDT) requires fast and accurate solutions of the response of the mechanical model including the defect as well as the sensitivity of this response to the variation of the parameters describing the defect. For modelling crack-type defects under dynamic conditions, like vibration analysis or ultrasonics, the boundary element method (BEM) is especially well suited, in particular due to the hypersingular formulation. The present work presents the stress sensitivity boundary integral equation, dqBIE, and its use for the solution of the inverse problem when coupled to gradient-based minimization algorithms. The capability of solving numerically a NDT problem such as the location and characterization of cracks by measuring the dynamic response at an accessible boundary of the specimen is evaluated. For that, the accuracy and convergence of the sensitivity from the dqBIE is verified. Then, comprehensive convergence tests are made for the initial guess, the amount of supplied measurements, and simulated errors on measurements, geometry, elastic constants and frequency.
Optimization algorithms for identification inverse problems with the boundary element method
Engineering Analysis with Boundary Elements, 2002
In this paper the most suitable algorithms for unconstrained optimization now available applied to an identi®cation inverse problem in elasticity using the boundary element method (BEM) are compared. Advantage is taken of the analytical derivative of the whole integral equation of the BEM with respect to the variation of the geometry, direct differentiation, which can be used to obtain the gradient of the cost function to be optimized.
TOPICAL REVIEW: Inverse problems in elasticity
Inverse Problems, 2005
This article is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters, or buried objects such as cracks. These inverse problems are considered mainly for threedimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e. fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.
An inverse method for determining elastic material properties and a material interface
International Journal for Numerical Methods in Engineering, 1992
A numerical procedure which integrates optimization, finite element analysis and automatic finite element mesh generation is developed for solving a two-dimensional inverse/parameter estimation problem in solid mechanics. The problem consists of determining the location and size of a circular inclusion in a finite matrix and the elastic material properties of the inclusion and the matrix. Traction and displacement boundary conditions sufficient for solving a direct problem are applied to the boundary of the domain. In addition, displacements are measured at discrete points on the part of the boundary where the tractions are prescribed. The inverse problem is solved using a modified Levenberg-Marquardt method to match the measured displacements to a finite element model solution which depends on the unknown parameters. Numerical experiments are presented to show how different factors in the problem and the solution procedure influence the accuracy of the estimated parameters.
Identification of Elastic Parameters by Treating the Inverse Problem
International Journal of Computer Applications, 2014
The aim of this work is to lay the groundwork for identifying digital mechanical parameters of materials with elastic. Most of the tests do not allow identifying these parameters automatically. The use of the finite elements of calculations for sizing works is thus limited by a poor understanding of the mechanical properties. In this context, it raises the issue of inverse analysis [1] [2]. From this information about the parameters of the laws of material behavior, is it possible to obtain the displacement field from in situ measurements and how does digital technology obtain a determination of these parameters accurately and systematically? In this work we present a new approach by providing a formulation is easily used by treating the inverse problem. It is based on the finite element method, which, in a direct problem, gives the displacement field knowing the mechanical properties and an inverse problem gives the mechanical knowledge of the field trips. The resolution of the direct problem has yielded results. The latter is in agreement with the simulation code of commercial calculation. This allowed us to address the inverse problem with no understanding by offering an alternative identification using a database previously determined [3].
WIT transactions on modelling and simulation, 2002
elasticity are presented. of sensitivitiesof displacements and tractions by a Boundary Integral Equation in is necessary for minimization algorithms. Some recent results on the computation Equation provides a means to compute the gradient of any cost functional, which respect to the geometry, is presented. The ensuing sensitivity Boundary Integral In this communication, a sensitivity of the hypersingular integral equation with l Introduction is a part of the geometry (a). among which the Identificaion IP will be dealt with, in which the unknown on R, the nature of the unknown yields a classification of inverse problems a generic direct problem (not necessarily elastic) is defined as L (k) u = q known, for example a part of the geometry, or its mechanical properties. If this, an inverse problem is one in which part of the information above is not boundary conditions (some known values of U and q). As a counterpart of ometry (fl), mechanical properties (k),behavior model (operator L) and displacements U and stress vectors q) in a specific body defined by its ge-A direct problem can be stated as the calculation of the response (certain propagates inside it and manifests on an accessible part of i t may be studied When seeking defects or flaws inside a body, any physical magnitude that
Shape Sensitivity of the Anisotropic Elastic Response
2003
Flaw identification with non destructive experimental techniques can be mo- delled through the so-called inverse problem. This communication deals with problems where the unknowns are the location and shape of cavities embedded in a linear elastos- tatic domain. The unknowns are sought as to achieve the best fit between measured and computed values of some physical quantities (response of the system). This usually leads to the minimization of a cost functional. The most efficient non-linear minimization al- gorithms need the computation of the gradient of objective function under changes in the unknown parameters of the problem, in this case, the geometry of the model. There are several approaches to calculate this shape sensitivity, here it is em- phasized the effectiveness of the Adjoint Variable Method, which establishes a formula expressed in terms of boundary integrals, suitable for Boundary Element Method imple- mentation. Numerical results are presented for plane problems wit...
Inverse problems in elasticity
Inverse problems
This article is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters, or buried objects such as cracks. These inverse problems are considered mainly for threedimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e. fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.
An inverse technique based on the boundary element method (BEM) and elastostatic experiments for identification of elastic constants of orthotropic and general anisotropic 2D bodies is presented. Displacements at several points on the boundary of the body, obtained by a few known load cases are used in the inverse analysis to find unknown elastic constants of the body. Using data from more than one elastostatic experiment results in a more accurate and stable solution for the identification problem. In the inverse analysis, sensitivities of displacements of only boundary points with respect to the elastic constants are needed. Therefore, the BEM is a very useful and effective method for this purpose. An iterative Tikhonov regularization method is used for the inverse analysis. A method for appropriate selection of the regularization parameter appearing in the inverse analysis is also proposed. Convergence and accuracy of the presented method with respect to measurement errors and number of load cases are investigated by presenting several examples.