Analysis of effective elastic properties for shell with complex geometrical shapes

Abstract

The manuscript offers a methodology to solve the local problem derived from the homogenization technique, considering composite materials with generalized periodicity and imperfect spring contact at the interface. The general expressions of the local problem for an anisotropic composite with perfect and imperfect contact at the interface are derived. The analytical solutions of the local problems are obtained by solving a system of partial differential equations. In order to validate the model, the effective properties of the structure presented in the literature are obtained as particular cases. The solution of the local problem is used to extend the study to more complex structures, such as, wavy laminates shell composites with imperfect spring type contact at the interface. Also, the results are compared with the results for perfect and imperfect contact models available in the literature.

An approach for modeling non-ageing linear viscoelastic composites with general periodicity

“…3). According to geometrical configuration of the structure, the two-steps homogenization scheme in different directions can be used to estimate the overall effective behavior (see Otero et al 2003 [47] and Guinovart-Sanjuán et al 2018 [48]). In this example, elastic fibers (glass) are embedded in a viscoelastic matrix (epoxy).…”

A hierarchical asymptotic homogenization approach for viscoelastic composites

“…(44a-44c) and the effective coefficients Eqs. (35) and (48) for each level of organization. The procedure can be used in order to solve a linear elastic problem (t ¼ 0) in composites with the same structural characteristics.…”

“…(32) and (45), the effective coefficients Eqs. (35) and (48) can be written, respectively, as follows…”

A model of heterogeneous thermoviscoplastic material preserving uniform normal strains under combined compression, tension (or compression) and shearing. Instability and homogenization results

“…For two different points of view on homogenization of non-linear laminated composites we refer to Omri et al, 2000, Lopez-Realpozo et al, 2008, Zhu et al, 2018. For the analysis of effective behavior of elastic structures with non-linear periodicity we refer to Guinovart-Sanjuan et al, 2018 andDong et al, 2018. For an application of the finite-volume homogenization to nanoporous materials with cylindrical voids we refer to Chen et al, 2018b. The homogenization result of the present paper can eventually be used in manufacturing processes of layered materials with functionally graded interfaces, for which prescribed uniform normal strains are desired under combined biaxial normal stress and shearing.…”