Research Papers

Multistable Cosine-Curved Dome System for Elastic Energy Dissipation

[+] Author and Article Information
Mansour Alturki

Department of Civil and Environmental Engineering,
Michigan State University,
1208 Engineering Building,
East Lansing, MI 48824-1226
e-mail: alturki1@msu.edu

Rigoberto Burgueño

Department of Civil and Environmental Engineering,
Department of Mechanical Engineering,
Michigan State University,
3574 Engineering Building,
East Lansing, MI 48824-1226
e-mail: burgueno@msu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received February 14, 2019; final manuscript received May 16, 2019; published online June 10, 2019. Assoc. Editor: Pedro Reis.

J. Appl. Mech 86(9), 091002 (Jun 10, 2019) (10 pages) Paper No: JAM-19-1071; doi: 10.1115/1.4043792 History: Received February 14, 2019; Accepted May 16, 2019

This paper presents a new energy dissipation system composed of multistable cosine-curved domes (CCD) connected in series. The system exhibits multiple consecutive snap-through and snap-back buckling behavior with a hysteretic response. The response of the CCDs is within the elastic regime and hence the system's original configuration is fully recoverable. Numerical studies and experimental tests were conducted on the geometric properties of the individual CCD units and their number in the system to examine the force–displacement and energy dissipation characteristics. Finite element analysis (FEA) was performed to simulate the response of the system to develop a multilinear analytical model for the hysteretic response that considers the nonlinear behavior of the system. The model was used to study the energy dissipation characteristics of the system. Experimental tests on 3D printed specimens were conducted to analyze the system and validate numerical results. Results show that the energy dissipation mainly depends on the number and the apex height-to-thickness ratio of the CCD units. The developed multilinear analytical model yields conservative yet accurate values for the dissipated energy of the system. The proposed system offered reliable high energy dissipation with a maximum loss factor value of 0.14 for a monostable (self-recoverable) system and higher for a bistable system.

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Fig. 1

The MCCD system: (a) cross-section of a single CCD unit, (b) schematic force–displacement response of a single CCD, (c) MCCD composed of multiple CCDs, and (d) schematic hysteretic response of an MCCD system. Note that δ is the local CCD displacement, while Δ is the global system displacement.

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Fig. 2

Geometric parameters of a typical CCD: (a) cross-section at the apex and (b) idealized system

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Fig. 3

(a) Normalized Fδ response for monostable and bistable CCDs and (b) multilinear approximation of the Fδ response of a CCD

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Fig. 4

Possible configurations of CCD units in the vertical direction: (a) parallel stacking (np = 2) and (b) series stacking (ns = 2)

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Fig. 5

F–Δ curves for CCDs in (a) parallel configuration and (b) series configuration

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Fig. 6

The idealized MCCD system

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Fig. 7

Force–deformation curves from FEA for MCCD systems: (a) monostable and (b) bistable

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Fig. 8

Number of CCDs in regions I, II, and III during loading stages for a system of ns = 4

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Fig. 9

(a) Schematic F–Δ response of the MCCD system with quantities used to develop the multilinear model and (b) actual and multilinear Fδ responses of a CCD unit

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Fig. 10

F–Δ curves from FEA and analytical model using (a) linear equations and (b) nonlinear equations to calculate keI, keIII, Fbdi,and Fndi

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Fig. 11

Test setup for an MCCD system with ten CCDs (ns = 10)

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Fig. 12

F–Δ curves for MCCD system from experimental tests and the analytical model

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Fig. 13

Experimental F–Δ curves for an MCCD system at varying loading rates: 1, 3, 9, and 15 mm/s

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Fig. 14

(a) Normalized Fδ curve for a CCD with h/t = 2.75 under force and displacement control conditions and (b) loss factor with h/t for different ns values

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Fig. 15

(a) F–Δ curves for MCCDs with h/t = 2.5 and ns = 8 and 14 and (b) loss factor with ns for different h/t ratios



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