fe_coor

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fe_coor

Purpose

Coordinate transformation matrices for Component Mode Synthesis problems.

Syntax

[t] = fe_coor(cp)
[t,nc] = fe_coor(cp,opt)

Description

The different uses of fe_coor are selected by the use of options given in the argument opt which contains [type method] (with the default values [1 3]).

type=1	(default) the output t is a basis for the kernel of the constraints cp range([T]_{N× (N-NC)})=ker([c]_{NS × N}) NC£ NS is the number of independent constraints.
type=2	the output argument t gives a basis of vectors linked to unit outputs followed by a basis for the kernel T = [[T_U]_{N × NS} [T_K]_{N × (N-NS)}] with [c]_{NS × N}[T]=[[^\ I _\ ] [0]_{NS × (N-NS)}] If NC<NS such a matrix cannot be constructed and an error occurs.
method	the kernel can be computed using : 1 a singular value decomposition svd (default) or 3 a lu decomposition. The lu has lowest computational cost. The svd is most robust to numerical conditioning problems.

Usage

fe_coor is used to solve problems of the general form

[Ms²+Cs+K]{q(s)}=[b] {u(s)}

{y(s)}= [c] {q(s)}

with [c_int]{q(s)}=0

which are often found in CMS problems (see section 6.1.6 and [37]).

To eliminate the constraint, one determines a basis T for the kernel of [c_int] and projects the model

[T^TMTs²+T^TCTs+T^TKT]{q_R(s)}=[T^Tb] {u(s)}

{y(s)}= [cT] {q_R(s)}