fe_coor

Contents Functions

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 6.2.6 and [40]).

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)}