On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

Due to the conflict between equilibrium and constitutive requirements, Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest. As an alternative, the stress-driven model has been recently developed. In this paper, for higher-order shear deformation beams, the ill-posed issue (i.e., excessive mandatory boundary conditions (BCs) cannot be met simultaneously) exists not only in strain-driven nonlocal models but also in stress-driven ones. The well-posedness of both the strain- and stress-driven two-phase nonlocal (TPN-StrainD and TPN-StressD) models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded (FG) materials. The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions. By using the generalized differential quadrature method (GDQM), the coupling governing equations are solved numerically. The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

Ἰουδαϊσμός – ἰουδαΐζειν – ἰουδαϊκῶς Sprachliche und semantische Überlegungen im Blick auf Gal 1,13 f. und 2,14

Since late antiquity there has been diversity in the particulars of the interpretation of the Greek term Ἰουδαϊσμός in Galatians 1,13–14, but the prevailing notion in most cases is that Ἰουδαϊσμός signifies “Judaism”, the religion of the Jewish people. On the contrary, in a provocative article Steve Mason proposed a radical revision of this reading of Ἰουδαϊσμός and its cognates (cf. Gal 2,13–15; 3,28). According to him (and other scholars) there was no category of “Judaism” in the Graeco-Roman World, no “religion” too, and that the Ἰουδαῖοι were understood as an ethnic group comparable to other ethnic groups. Consequently Mason claims that the substantive adjective Ἰουδαῖος has always the ethnic-regional sense “Judean”, never the religious sense “Jew”. To my opinion this view is partly right and partly wrong. Starting from the grammatical and semantic data provided by 2 and 4 Maccabees and attested in the epigraphic record this essay aims at two points: It is argued, first, that due to the fact that Ἰουδαϊσμός and its cognates obviously denote also a religious dimension it seems very unlikely to hold the view of a purely ethnic centered conception of Jewish identity. Further, that the Galatian controversy and the incident at Antioch, described in Gal 2,11–14, reflect a quarrel within the early church about the crucial question concerning the constitutive requirements in regard to the construction, formation, and performance of Christian identity.