PSI - Issue 26

Panagiotis N. Lymperopoulos et al. / Procedia Structural Integrity 26 (2020) 263–268 Panagiotis N. Lymperopoulos, Efstathios E. Theotokoglou/ StructuralIntegrity Procedia 00 (2019) 000 – 000

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Antiseismic buildings’ design is an essential factor during the building design process. Seismic waves appear to have amplitude at about 12 mm for a seismic activity of about 7 Richer (Shearer (2009)). Therefore, pentamodes should confront such displacements.

Nomenclature G

shear modulus of pentamode shear strength of pentamode shear strength of a typical isolator stiffness strength of pentamode small diameter of pentamode big diameter of pentamode

G c G r

K

d

D

α

main dimension of pentamode In this research, an initial approach on the design of pentamodes related to a computational analysis is taken place. A finite element model is proposed in order to confront typical seismic wave’s displacements. According to the proposed computational study, small and large displacements finite element analyses have been considered. From our study results that the proposed pentamodes can confront seismic displacements.

2. Basic Study

Pentamodes are under research in order to replace isolators for the antiseismic design. Critical for the pentamodes design is the ratio of the shear modulus of pentamode G over the stiffness strength of pentamode K, (G/K). Analytical approaches have been proposed by (Norris A. (2014)), (Fabbrocino et.al. (2015)) and (Kadic et.al. (2012)), in order to calculate the ratio G/K, which is very important for pentamodes design. A numerical approach is also considered in this study for the ratio G/K. In addition, a computational analysis is also taken under consideration for small and large displacements.

2.1. Materials In our study two different materials have been used in order to model metamaterials. The materials that have been considered are given in Table 1.

Table 1.Materials tab. Material

Young Modulus [GPA]

Density [kg/m 3 ]

Steel (Fabbrocino et.al. (2015)) Polymer (Amendola et.al (2017))

206

8000 1300

1.4

3. Computational Analysis

A typical pentamode structure that has been modelled in our numerical study is shown in Figure 1. Pentamode structures have been modeled using the Finite Element Program ANSYS (ANSYS (2019)). The element which has been used in our analysis is the BEAM89 element, which is a typical 2 node linear beam element. In order to better model each rod, 4 finite elements have been used. In our analysis, a constant displacement (15mm) at nodes at the top of the pentamode structure is considered. The nodes at the bottom of the pentamode are fully constrained. In order to calculate the displacements, small and large displacements approaches ((ANSYS, 2019)) have been considered.