Nonlinear Dynamic Analysis of Plates Subjected to Explosive Loads

Reis, Ana Waldila de Queiroz Ramiro; Burgos, Rodrigo Bird; Oliveira, Maria Fernanda Figueiredo de

doi:10.1590/1679-78256706

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Latin American Journal of Solids and Structures

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ORIGINAL ARTICLE • Lat. Am. j. solids struct 19 (1) • 2022 • https://doi.org/10.1590/1679-78256706 copy

Nonlinear Dynamic Analysis of Plates Subjected to Explosive Loads

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Blast loads have been increasingly studied in the past decades, especially regarding civil structures. Until recently, the negative phase of these loads has been disregarded, but studies concluded that the effect of suction must be included. In the case of plates, nonlinearity plays an important role, and the membrane effect should also be considered. This work focuses on the influence of nonlinearity in plates subjected to blast loads. Equations were developed for the calculation of blast load parameters, considering that positive and negative phases are approximated by the Friedlander equation and cubic polynomial, respectively. The plate is modeled as a SDOF system using von Karman's theory of large displacements. The development of the nonlinear dynamic differential equation is reviewed, considering a simply supported plate, and its solution is based on fourth order Runge-Kutta numerical method. A reference example is used as a benchmark and then parametric studies are conducted, in which the influence of scaled distance, mass of explosive, and the consideration or not of the negative phase is analyzed.

Keywords:
Plates; Dynamic Analysis; Nonlinearity; von Karman; Blast Load; Runge-Kutta

Graphical abstract

Case	$x = \pm a / 2$	$y = \pm b / 2$
Stress Free	$ϕ_{, y y} = ϕ_{, x y} = 0$	$ϕ_{, x x} = ϕ_{, x y} = 0$
Immovable	$u_{x} = ϕ_{, x y} = 0$	$u_{y} = ϕ_{, x y} = 0$
Movable	$P_{x} = ϕ_{, x y} = 0$	$P_{y} = ϕ_{, x y} = 0$

Case	$p_{x}^{'}$	$p_{y}^{'}$
Stress Free	0	0
Immovable	$\frac{π^{2} E h^{2} (β^{2} ν + 1)}{8 a^{2} (1 - ν^{2})}$	$\frac{π^{2} E h^{2} (β^{2} + ν)}{8 a^{2} (1 - ν^{2})}$
Movable	0	0

Case	$K_{3}$	$K_{1}$
Stress Free	$\frac{2 π^{4} E h^{2} β^{2} (Φ_{0,1} + Φ_{1,0})}{a^{6} ρ}$	$\frac{π^{4} D {(β^{2} + 1)}^{2}}{a^{4} h ρ}$
Immovable	$\frac{π^{4} E h^{2} [(β^{4} + 1) (ν^{2} - 3) ν^{2} - 4 β^{2} ν]}{16 a^{4} ρ (1 - ν^{2})}$
Movable	$\frac{π^{4} E h^{2} (β^{4} + 1)}{16 a^{4} ρ}$

Parameters	Valor
Dimension (a x b)	0.508 m x 0.508 m
Thickness (h)	0.0034 m
Young’s modulus (E)	207 GPa
Poisson’s coefficient (ν)	0.3
Mass density (ρ)	7770 kg/m³

Parameters	Valor
P_max	57086.0019 Pa
P_min	15420.247 Pa
t_d	0.002026061 s
i_d	37.3129 Pa.s
i_m	40.536 Pa.s
t_m	0.004673336 s

Parameter	Value
Dimension (a x b)	1.397 m x 1.448 m
Thickness (h)	0.00963 m
Young’s modulus (E)	72 GPa
Poisson’s coefficient (ν)	0.25
Mass density (ρ)	2500 kg/m³

Parameters	Valor
Z	0 – 39.64 m / kg^1/3
W	10 kg and 100 kg

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