Additional flags

Additional options can be passed to the macroelement through further flags, all optional:

-density $rho -cmass -pDelta -intWeights $wI $wE $wJ

• -density: followed by the density of the material. Passes the density to the element for computing the mass matrix (relevant for dynamic analysis and for the application of "self weight" type loads). If not specified, no mass is assigned. It cannot be used in combination with the "custom" definition of the macroelement: in this case "-mass" flag can be used, followed by the value of mass per unit length (which is a definition usable also in any other case, left for compatibility with the other beam elements in OpenSees).

• -cmass: consistent mass matrix formulation.

• -pDelta: P-Δ formulation of compatibility relations. For the formulation of the macroelement, it is not possible to attach to it a pre-defined geometrical transformation, as done for beam elements. If omitted, geometrical nonlinearity is not accounted for.

• -intWeights: integration weights to be applied, respectively, to the base, element and end sections. They should be positive and sum up to 1 to obtain a correct response, but this condition is not enforced directly by the element. Multiplied by the element height, these weights constitute a characteristic length that can be considered when regularising the response, if softening materials are assigned to a fibre section model. Defaults depend on the type of element that is created: when Tremuri-equivalent or fiber section definitions are used, the set {0.495, 0.01, 0.495} is set to replicate the response of the Tremuri macroelement. Otherwise, the set {1/6, 2/3, 1/6} is the default. The latter, equivalent to a Gauss-Lobatto integration scheme, ensures the exact integration of polynomials of order 3. As a consequence, rotations and displacements of a quadratic curvature profile, including the elastic linear solution, are integrated exactly. The provided solution is equivalent to the one of a force-based nonlinear beam with three integration points.

 

 

back to macroelement definition / to element loads / home