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1

Dynamic crushing behavior of closed-cell aluminum foams based on different space-filling unit cells

Talebi S., Hedayati R., Sadighi M.

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 3

231--245

EN

Closed-cell metal foams are cellular solids that show unique properties such as high strength to weight ratio, high energy absorption capacity, and low thermal conductivity. Due to being computation and cost effective, modeling the behavior of closed-cell foams using regular unit cells has attracted a lot of attention in this regard. Recent developments in additive manufacturing techniques which have made the production of rationally designed porous structures feasible has also contributed to recent increasing interest in studying the mechanical behavior of regular lattice structures. In this study, five different topologies namely Kelvin, Weaire–Phelan, rhombicuboctahedron, octahedral, and truncated cube are considered for constructing lattice structures. The effects of foam density and impact velocity on the stress–strain curves, first peak stress, and energy absorption capacity are investigated. The results showed that unit cell topology has a very significant effect on the stiffness, first peak stress, failure mode, and energy absorption capacity. Among all the unit cell types, the Kelvin unit cell demonstrated the most similar behavior to experimental test results. The Weaire–Phelan unit cell, while showing promising results in low and medium densities, demonstrated unstable behavior at high impact velocity. The lattice structures with high fractions of vertical walls (truncated cube and rhombicuboctahedron) showed higher stiffness and first peak stress values as compared to lattice structures with high ratio of oblique walls (Weaire–Phelan and Kelvin). However, as for the energy absorption capacity, other factors were important. The lattice structures with high cell wall surface area had higher energy absorption capacities as compared to lattice structures with low surface area. The results of this study are not only beneficial in determining the proper unit cell type in numerical modeling of dynamic behavior of closed-cell foams, but they are also advantageous in studying the dynamic behavior of additively manufactured lattice structures with different topologies.

2

Existence results for Kirchhoff type systems with singular nonlinearity

Firouzjai A., Afrouzi G. A., Talebi S.

Opuscula Mathematica

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2018

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Vol. 38, no. 2

187--199

EN

Using the method of sub-super solutions, we study the existence of positive solutions for a class of singular nonlinear semipositone systems involving nonlocal operator.

3

On PC solutions of PARMA (p, q) models

Miamee A. G., Talebi S.

Probability and Mathematical Statistics

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2005

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Vol. 25, Fasc. 2

279--288

EN

This note is concerned with the existence of periodically correlated solutions for the PARMA (p, q) system xn = φ1n xn – 1 + φ2n xn – 2 +...+ φpn xn – p + ξn + θ1n ξn-1… + θqn ξn-q, n ∈ Z, where ξn is a white noise and the varying coefficients φin and θin are periodic in n with period T. Conditions which ensure the existence of periodically correlated solutions for such systems are obtained.