Symmetry properties of the reciprocity gap functional in the linear elasticity
Source abstract
Abstract
The reciprocity gap functional for a linear elastic body with an embedded defect is considered. The functional is a bilinear functional depending on two stress states—in an elastic body with a defect and without it. It is shown that for various types of boundary conditions the functional is a symmetric one in a certain sense. Some corollaries of the symmetry properties of the functional are obtained.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Elasticity and Wave Propagation · Contact Mechanics and Variational Inequalities · Composite Material Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (9)
Show source-provided references
1. Andrieux S, Ben Abda A, Bui H (1999) Reciprocity principle and crack identification. Inverse Probl 15: 59–6510.1088/0266-5611/15/1/010 ↗
2. Bonnet V, Constantinescu A (2005) Inverse problems in elasticity. Inverse Probl. 21: R1–R5010.1088/0266-5611/21/2/R01 ↗
3. Goldstein RV (1979) Plane crack of arbitrary rupture in an elastic solid. Izvestiya AN USSR. Solid Mech 3: 111–126 (in Russian)
4. Goldstein RV, Shifrin EI, Shushpannikov PS (2007) Application of invariant integrals to the problems of defect identification. Int J Fract 147: 45–5410.1007/s10704-007-9125-y ↗
5. Goldstein RV, Shifrin EI, Shushpannikov PS (2008) Application of invariant integrals to elastostatic inverse problems. Comptes rendus Mecanique 336: 108–11710.1016/j.crme.2007.11.002 ↗
6. Hong CC, Stern M (1978) The computation of stress intensity factors in dissimilar materials. J Elast 8: 21–3010.1007/BF00044508 ↗
7. Kaptsov AV, Shifrin EI (2008) Plane crack identification in elastic solid using invariant integrals. Izvestiya RAS. Mekh Tverdogo Tela (MTT) 3: 145–163 (in Russian)
8. Shifrin EI (2009) On the relation between invariant integrals of linear isotropic elasticity and the integrals determined by the reciprocity principle. Prikladnaya Matematika I Mekhanika (PMM) 73: 325–334 (in Russian)
9. Stern M, Becker EB, Dunham RS (1976) A contour integral computation of mixed-mode stress intensity factors. Int J Fract 12: 359–36810.1007/BF00032831 ↗