SUMMARYA 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.
SUMMARYA finite element method (FEM) is presented for calculating the surface tractions on a body from internal measurements of displacement at discrete sensor locations. The solution algorithm employs a sensitivity analysis which minimizes the difference between the calculated and measured displacements at each sensor location. Spatial regularization is one technique employed to stabilize the minimization process by imposing various degrees of smoothness on the solution. It also allows the problem to be solved with fewer sensors than traction boundary nodes. As an alternative to spatial regularization, a method based on 'keynodes' is introduced which assumes that each component of the boundary traction distribution can be described by a polynomial of specified order. The methods are applied to several two-dimensional examples including a rolling contact problem. The effects of parameters such as the number of sensors, the location of the sensors and the error in the sensor displacements are discussed.
SUMMARYThis paper is concerned with solution by the boundary element method (BEM) of a certain class of inverse linear elastic problems using the spatial regularization method. More specifically, the problem of calculating the boundary and internal conditions on a deformed specimen given approximate information on the displacements at discrete 'sensor locations' in the specimen is discussed. The solution algorithm employs a sensitivity analysis and a least-squares minimization of the difference between the calculated and measured displacements at each sensor location. The ideas presented here can be applied to contact problems where measurements of the deformation at the contact area are difficult.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.