2009
DOI: 10.1016/j.ijsolstr.2009.09.006
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A numerical study on the solution of the Cauchy problem in elasticity

Abstract: a b s t r a c tThis work deals with the Cauchy problem in two-dimensional linear elasticity. The equations of the problem are discretized through a standard FEM approach and the resulting ill-conditioned discrete problem is solved within the frame of the Tikhonov approach, the choice of the required regularization parameter is accomplished through the Generalized Cross Validation criterion. On this basis a numerical experimentation has been performed and the calculated solutions have been used to highlight the… Show more

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Cited by 44 publications
(37 citation statements)
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References 48 publications
(47 reference statements)
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“…the stiffnesses of the springs and the strain thresholds, used to build the numerical model since the performances of the model depend significantly on their values. In this perspective it is definitely helpful a sensitivity analysis on the parameters by using the tools reported, shortly, in the review paper [43] and, in depth, in [44][45][46][47][48][49] and applied in problems concerning huge and innovative structures as those described e.g. in [50,51].…”
Section: Discussionmentioning
confidence: 99%
“…the stiffnesses of the springs and the strain thresholds, used to build the numerical model since the performances of the model depend significantly on their values. In this perspective it is definitely helpful a sensitivity analysis on the parameters by using the tools reported, shortly, in the review paper [43] and, in depth, in [44][45][46][47][48][49] and applied in problems concerning huge and innovative structures as those described e.g. in [50,51].…”
Section: Discussionmentioning
confidence: 99%
“…From this point of view, an investigation on proper finite element (FE) simulation [21][22][23][24][25][26][27][28][29] or regularized FE [30][31][32][33][34][35][36][37] will be welcome in order to avoid, e.g., the unpleasant occurrence of instability [38][39][40][41][42][43][44][45][46][47][48][49]. Due to the high porosity, the Biot model should probably be modified, see e.g.…”
Section: Numerical Simulationsmentioning
confidence: 99%
“…The deficiencies of classical approaches when the material behavior exhibits size-scale effects are investigated in [59], and in [47] a novel invariance requirement (micro-randomness) in addition to isotropy is formulated, which implies conformal invariance of the curvature. The numerical investigation of structures of the type considered also requires special attention, and it is therefore important in the development of novel techniques [5][6][7][8][9]37,38,[48][49][50][51]65] or the proper employment of the existing ones (see, for instance, [68], where Galerkin boundary element method is used to address a class of strain gradient elastic materials).…”
Section: Introductionmentioning
confidence: 99%