4.2.6.12. HDR¶

This command is used to construct an HDR bearing element object in three-dimension. The 3D continuum geometry of an high damping rubber bearing is modeled as a 2-node, 12 DOF discrete element. This is the third element in the series of elements developed for analysis of base-isolated structures under extreme loading (others being ElastomericX and LeadRubberX). The major difference between HDR element with ElastomericX is the hysteresis model in shear. The HDR element uses a model proposed by Grant et al. (2004) to capture the shear behavior of a high damping rubber bearing. The time-dependent values of mechanical properties (e.g., vertical stiffness, buckling load capacity) can also be recorded using the “parameters” recorder.

element('HDR', eleTag, *eleNodes, Gr, Kbulk, D1, D2, ts, tr, n, a1, a2, a3, b1, b2, b3, c1, c2, c3, c4, <<x1, x2, x3>, y1, y2, y3>, <kc>, <PhiM>, <ac>, <sDratio>, <m>, <tc>)

For 3D problem

`eleTag` (int)	unique element object tag
`eleNodes` (list (int))	a list of two element nodes
`Gr` (float)	shear modulus of elastomeric bearing
`Kbulk` (float)	bulk modulus of rubber
`D1` (float)	internal diameter
`D2` (float)	outer diameter (excluding cover thickness)
`ts` (float)	single steel shim layer thickness
`tr` (float)	single rubber layer thickness
`n` (int)	number of rubber layers
`a1` `a2` `a3` `b1` `b2` `b3` `c1` `c2` `c3` `c4` (float)	parameters of the Grant model
`x1` `x2` `x3` (float)	vector components in global coordinates defining local x-axis (optional)
`y1` `y2` `y3` (float)	vector components in global coordinates defining local y-axis (optional)
`kc` (float)	cavitation parameter (optional, default = 10.0)
`PhiM` (float)	damage parameter (optional, default = 0.5)
`ac` (float)	strength reduction parameter (optional, default = 1.0)
`sDratio` (float)	shear distance from iNode as a fraction of the element length (optional, default = 0.5)
`m` (float)	element mass (optional, default = 0.0)
`tc` (float)	cover thickness (optional, default = 0.0)