# stiffness matrix

## stiffness matrix

[′stif·nəs ‚mā·triks]
(mechanics)
A matrixKused to express the potential energy V of a mechanical system during small displacements from an equilibrium position, by means of the equation V = ½q T Kq, whereqis the vector whose components are the generalized components of the system with respect to time andq T is the transpose ofq. Also known as stability matrix.
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References in periodicals archive ?
Therefore the spring stiffness is characterized through the stiffness matrix [k] defined as
The constant mass matrix can be obtained using variable separation; however, the expressions of elastic potential energy and the stiffness matrix become more complex.
A small stiffness coefficient corresponding to the drilling degrees is added to the stiffness matrix to avoid equation singularity.
In general, [tau] = [K.sub.q][DELTA] and D = J(q)[DELTA] where A is the vector of the joint deformations, and [K.sub.q] = diag([K.sub.1], [K.sub.2], ..., [K.sub.n]) is the joint stiffness matrix. From (13) and (14), the generalized compliance matrix for the pelvic support mechanism can be derived as
where [{[delta]}.sup.e] is the displacement at the node, {[delta](x, y)} is the displacement at any place in the unit, {[sigma]} is the stress at any place in the unit, {[epsilon]} is the strain at any place in the unit, [[K].sup.e] is the stiffness matrix of the unit, [B] is the strain matrix of the unit, [D] is the elastic matrix of the unit, and [S] is the stress matrix of the unit, t is the thickness of the unit, the general value is 1.
Substituting (7) into (3), with respect to the displacement q, the expression of the stiffness matrix of the element is obtained as
[11] proposed a static reanalysis method given the modification of supports by using modified master stiffness matrices, a rank-one decomposition of the corresponding incremental stiffness matrix, and a sparse Cholesky rank-one update/downdate algorithm.
They found that only the stiffness proportional damping coefficient that is related to the stiffness matrix is essential to damping out high-frequency oscillations, and the low-frequency oscillation is damped out automatically in an implicit dynamic approach, HHT-[alpha] approach, which they used in their study [24, 25].
where [bar.Q] is a reduced stiffness matrix obtained by the rotation of the original stiffness matrix Q:
In general, a cohesive element can be differentiated to a continuum element by a reduced stiffness matrix based on reduced sectional stresses, Figure 2.
The nondimensional mass matrix is reduced to the unity matrix [I], and the stiffness matrix [[K.sup.SS.sub.N]], combining the effects of the extensional and spiral springs, obtained by addition of the Winkler soil stiffness matrix and the spiral spring matrix, for the simply supported case, can be presented as follows [9]:
where [c.sup.E] is the elastic stiffness matrix, the superscript T denotes transpose, E is the electric field vector, D is the electric displacement vector, [[epsilon].sup.S] is the dielectric constant matrix, and e is the piezo stress/charge constant.

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