Finite Element Analysis of Some Inverse Elasticity Problems

This paper is concerned with the solution of some inverse elasticity problems of practical significance to experimental mechanics. More specifically, the boundary tractions and displacements in an elastically deformed two-dimensional body are calculated using experimentally determined or specified displacements or strains at a finite number of internal points in the body. A brief description of what inverse problems are and why they are important is given. The finite element method is used with regularization techniques to solve the inverse deformation problems of concern here. Some illustrated numerical examples are presented to demonstrate the method. Through these examples, the effect of the error in the internal data and of the number of measurement points and their location is examined and reported. In addition, potential applications for the method are discussed.

[1]  A new NDT: Evaluation of plastic strains in bulk from displacements on surfaces , 1985 .

[2]  James V. Beck,et al.  Parameter Estimation in Engineering and Science , 1977 .

[3]  N. Zabaras,et al.  AN ANALYSIS OF TWO-DIMENSIONAL LINEAR INVERSE HEAT TRANSFER PROBLEMS USING AN INTEGRAL METHOD , 1988 .

[4]  H. R. Busby,et al.  Numerical solution to a two‐dimensional inverse heat conduction problem , 1985 .

[5]  I. Frank.  An application of least squares method to the solution of the inverse problem of heat conduction. , 1963 .

[6]  J. M. Weathers,et al.  Integration of laser-speckle and finite-element techniques of stress analysis , 1985 .

[7]  S. Mukherjee,et al.  An analysis of inverse heat transfer problems with phase changes using an integral method , 1988 .

[8]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[9]  J. Beck.  Criteria for comparison of methods of solution of the inverse heat conduction problem , 1975 .

[10]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[11]  D. M. Trujillo.  Application of dynamic programming to the general inverse problem , 1978 .

[12]  Computer-Aided Nondestructive Measurements of Plastic Strains from Surface Displacements , 1986 .

[13]  L. Payne,et al.  Improperly Posed Problems in Partial Differential Equations , 1987 .

[14]  J. Beck.  Surface heat flux determination using an integral method , 1968 .

[15]  V. Romanov.  Inverse problems of mathematical physics , 1986 .

[16]  O. M. Alifanov,et al.  Regularized numerical solution of nonlinear inverse heat-conduction problem , 1975 .

[17]  J. Sládek,et al.  Stress analysis by combination of holographic interferometry and boundary-integral method , 1983 .

[18]  J. Beck.  Nonlinear estimation applied to the nonlinear inverse heat conduction problem , 1970 .

[19]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[20]  H. R. Busby,et al.  SOLUTION OF INVERSE HEAT CONDUCTION PROBLEMS USING AN EIGENVALUE REDUCTION TECHNIQUE , 1986 .

[21]  Ray W. Ogden,et al.  Nonlinear Elastic Deformations , 1985 .

[22]  R. Hills,et al.  ONE-DIMENSIONAL NONLINEAR INVERSE HEAT CONDUCTION TECHNIQUE , 1986 .

[23]  Krzysztof Grysa,et al.  An inverse temperature field problem of the theory of thermal stresses , 1981 .

[24]  J. Beck,et al.  EFFICIENT SEQUENTIAL SOLUTION OF THE NONLINEAR INVERSE HEAT CONDUCTION PROBLEM , 1982 .

[25]  J. V. Beck,et al.  Combined function specification-regularization procedure for solution of inverse heat conduction problem , 1984 .

[26]  G. M. L. Gladwell,et al.  Inverse Problems in Vibration , 1986 .

[27]  J V Beck.  NON – LINEAR ESTIMATION APPLIED TO THE NON – LINEAR HEAT CONDUCTION PROBLEM , 1970 .