Impact-Materia.doc

(完整版)Impact Materia
Impact Material
This command is used to construct an impact material object
uniaxialMaterial ImpactMaterial ＄matTag ＄K1 $K2 $δy $gap

＄matTag
integer tag identifying material
$K1
initial stiffness 初始刚度
＄K2
secondary stiffness 屈服后刚度
＄δy
yield displacement 屈服位移
＄gap
initial gap* 初始间隙
NOTES:
This material is implemented as a compression—only gap material。 Delta_y and gap should be input as negative values。
＄δy、$gap都为负值。
DESCRIPTION:
This material is based on an approximation to the Hertz contact model proposed by Muthukumar (See REFERENCES below）. The energy dissipated during impact is:
E = kh ＊ δm^(n+1) ＊ （1—e^2) / (N+1)
where kh is the impact stiffness parameter, with a typical value of EA/L or 25,000 k-in。-3/2； n is typically taken as 3/2 for the exponent associated with the Hertz power rule； e is the coefficient of restitution, with typical values from 0。6-0。8; and δm is the maximum penetration during the pounding event。
n：3/2 ；e:恢复系数，取值:0。6～0。8；δm：最大侵入深度（最大侵入深度为假设值,并不是实际的侵入深度）.
The effective stiffness, Keff， is： Keff = kh ＊ (δm)^0。5
The yield displacement is:
δy = a ＊ δm
where a is typically taken as 0。1。 The initial stiffness， K1, and secondary stiffness； K2, are then selected such that the Impact model dissipates an amount of energy during a pounding event that is consistent with the associated energy dissipated in the Hertz model。
K1 = Keff + E / (a*δm^2)
K2 = Keff - E / （(1-a）＊δm^2）
Response of Impact Material during a pounding event. Response of Impact Material for displacement cycles of increasing amplitude

你可参考一下文献：
A contact element approach with hystersis damping for the analysis and design of pounding in bridges
以及研究生论文：简支梁斜交梁桥非线性地震反应分析与控制