Saint-Venant’s problem for Cosserat shells with voids

Minimum Energy Characterizations for the Solution of Saint-Venant's Problem in the Theory of Shells

“…Using a method established by Iezan [12,13] in the context of three-dimensional elasticity, Bîrsan [14] has given a solution of the relaxed Saint-Venant's problem in the theory of Cosserat shells. As remarked in [15], the solution obtained is in accordance with the corresponding results previously known in the theories of shells and plates derived from the three-dimensional equations of linear elasticity.…”

“…¼ O C ð Þ; 8 ¼ O D ð Þ: ð5:27ÞIn[15], the identification (5.26), (5.27) has been used in order to compare the solution of Saint-Venant's problem for Cosserat shells presented in Section 3 with the corresponding results from the classical shell theory. Thus, the formulae for torsion (3.12) 3 and (3.17) reduce to…”

On the theory of elastic shells made from a material with voids

“…In order to describe the porosity of a Cosserat shell with voids, we consider two independent scalar fields m(h a , t) and v(h a , t) called the volume fraction fields (0 < m 6 1). We mention that, in the previous approaches of the theory of Cosserat shells with voids (see Bîrsan, 2000aBîrsan, , 2005, only one porosity field has been admitted, corresponding to m(h a , t), which permits for the characterization of the changes in volume fraction along the middle surface of the three-dimensional shell. In this paper, we introduce an additional porosity field, namely v(h a , t), which will give us information about the volume fraction variations along the shell thickness.…”

“…A theory for Cosserat shells with voids was first presented by Bîrsan (2000a,b) and was employed recently to determine the solution of Saint-VenantÕs problem for porous cylindrical shells (see Bîrsan, 2005). This theory accounts for the variations of the volume fraction field along the middle surface of the shell, but not for the changes in porosity along the shell thickness.…”

On the theory of loaded general cylindrical Cosserat elastic shells

“…Interesting results related to this problem have been obtained by different approaches in several studies, such as Berdichevsky et al (1992), Ladevèze et al (2004), Librescu and Song (2005). A comparison between the results of the Cosserat theory and those predicted by the classical theory of shells for Saint-Venant's problem has been presented in Bîrsan (2005b).…”