On a two-level Newton-type procedure applied for solving non-linear elasticity problems

2000 ◽  
Vol 49 (12) ◽  
pp. 1479-1493 ◽  
Author(s):  
Owe Axelsson ◽  
Alexander Padiy
Keyword(s):  
Linear Elasticity ◽  
Non Linear ◽  
Elasticity Problems

scholarly journals The Solution of Inverse Non-Linear Elasticity Problems That Arise When Locating Breast Tumours

2005 ◽  
Vol 6 (3) ◽  
pp. 143-149 ◽  
Author(s):  
Jonathan P. Whiteley
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Elasticity Theory ◽  
Linear Elasticity ◽  
Simple Approach ◽  
Linear Elasticity Theory ◽  
Wide Range ◽  
Non Linear ◽  
Elasticity Problems ◽  
Free Body

Non-linear elasticity theory may be used to calculate the coordinates of a deformed body when the coordinates of the undeformed, stress-free body are known. In some situations, such as one of the steps in the location of tumours in a breast, the coordinates of the deformed body are known and the coordinates of the undeformed body are to be calculated, i.e. we require the solution of the inverse problem. Other than for situations where classical linear elasticity theory may be applied, the simple approach for solving the inverse problem of reversing the direction of gravity and modelling the deformed body as an undeformed body does not give the correct solution. In this study, we derive equations that may be used to solve inverse problems. The solution of these equations may be used for a wide range of inverse problems in non-linear elasticity.

scholarly journals Solving Non-linear Elasticity Problems by a WLS High Order Continuation

2020 ◽  
pp. 266-279
Author(s):  
Oussama Elmhaia ◽  
Youssef Belaasilia ◽  
Bouazza Braikat ◽  
Noureddine Damil
Keyword(s):  
Linear Elasticity ◽  
High Order ◽  
Non Linear ◽  
Elasticity Problems

The Boundary Contour Method for Three-Dimensional Linear Elasticity

1996 ◽  
Vol 63 (2) ◽  
pp. 278-286 ◽  
Author(s):  
A. Nagarajan ◽  
S. Mukherjee ◽  
E. Lutz
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Boundary Contour ◽  
Boundary Contour Method ◽  
Novel Variant ◽  
Elasticity Problems ◽  
Element Method

This paper presents a novel variant of the boundary element method, here called the boundary contour method, applied to three-dimensional problems of linear elasticity. In this work, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. Thus, in this formulation, only line integrals have to be numerically evaluated for three-dimensional elasticity problems—even for curved surface elements of arbitrary shape. Numerical results are presented for some three-dimensional problems, and these are compared against analytical solutions.

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