Specify physical connections between components of mechss
model
specifies physical couplings between components sysCon
= interface(sys
,c1,nodes1,c2,nodes2)c1
and
c2
in the second-order sparse model sys
.
nodes1
and nodes2
contain the indices of shared
nodes relative to the nodes of c1
and c2
. The physical
interface is assumed rigid and satisfies the standard consistency and equilibrium
conditions. sysCon
is the resultant model with the specified physical
connections. Use showStateInfo
to get the list of all available components of sys
.
Dual Assembly
interface
uses
the concept of dual assembly to physically connect the nodes of the model
components. For n
substructures in the physical domain, the sparse matrices
in block diagonal form are:
where, f is the force vector dependent on time and g is the vector of internal forces at the interface.
Two interfaced components share a set of nodes in the global finite element mesh q: the subset N1 of nodes from the first component coincides with the subset N2 of nodes from the second component. The coupling between the two components is rigid only if:
The displacements q at the shared nodes are the same for both components.
The forces g one component exerts on the other are opposite (by the action/reaction principle).
This relation can be summarized as:
where, H is a localisation matrix with entries 0, 1, or -1. The equation Hq = 0 is equivalent to q(N1) = q(N2), and the equation g = −HT λ is equivalent to g(N1) = −λ and g(N2) = λ. These equations can be combined in the differential-algebraic equation (DAE) form:
This DAE model is called the dual assembly model of the overall structure. While the principle was explained for two components, this model can accommodate multiple interfaces, including interfaces involving more than two components.
Nonrigid interface
In non-rigid interfaces, the displacements q1(N1) and q2(N2) are allowed to differ and the internal force is given by:
This models spring-damper-like connections between nodes N1 in the first component and nodes N2 in the second component. Going from rigid to non-rigid connection eliminates the algebraic constraints Hq = 0 and explicitates the internal forces. Then, eliminate λ to obtain:
This is the set of the primal-assembly equations for non-rigid
coupling form that remains symmetric when the uncoupled model is symmetric. A drawback of this
form is that the coupling terms and may cause fill-in. To avoid this, interface
instead
constructs the dual-assembly form: