Static condensation

Fig. 16. Example of a A s.p. = f(t) relation, manifesting surface potential changes in a nickel-hydrogen system as a function of time and amount of hydrogen introduced onto a surface of a nickel film deposited at liquid nitrogen temperature hydrogen-nickel film interactions were studied by Tompkins-Eberhagen static condenser method at liquid nitrogen temperature. After Dus (60). Each dose of H2 — 2.5 X 10 molecules.

A glass adsorption cell used for the static condenser method is shown in Fig. 14. The condenser is formed from two concentric cylinders separated by a 2 mm gap. 

Fig. 14. Cell for the measurement of contact potential difference by the static condenser method.

For static analysis, a straightforward technique is the static condensation of the stiffness matrix. For dynamic analysis, several approaches can be used, none of them being mathematically exact. 

For technical reasons, only two out of four degrees of fireedom (DoFs) were included in the pseudo-dynamic tests those of floors 2 and 4. The other two DoFs were statically condensed. One-half of the tributary mass of 43,375 kg of each one of the 1st and 3rd floors was lumped to the nearest DoF. 

The lateral stiffness k of the frame can be obtained by static condensation since there is no force acting on DOF 2 and 3 ... 

Eliminate the three rotational DOFs by static condensation to obtain... 

Natural mode after using static condensation... 

Natural mode after calculating rotations using static condensation equations ... 

Statically condense joint rotations in the stiffness matrix of Problem 17.6 ... 

For the remaining case of unidirectional electric flux density confined to the component D3, the transverse electric field strength components E, E2 may be expressed in terms of the shear strains 731, 723. Therewith Ei and E2 can be eliminated from the constitutive equations by static condensation. Thus, this modification of Eqs. (4.20) represents a purely mechanical interaction with strengthened shear stiffnesses as the result of the piezoelectric effect ... 

All integrations may be performed symbolically. To avoid the implications of the effect, which might appear in the context of the description of the Timoshenko beam, a reduced integration scheme is applied, see for example Hughes [101]. Alternatively, one may start off from four nodes per element for the transverse displacements and rotations using cubic Lagrange polynomials for the interpolation and then reduce the degrees of freedom by means of a static condensation, see Knothe and Wessels [113]. 

In all the DD methods described in this section, no reduction in the total number of degrees of freedom is made. Therefore, the error associated with static condensation of component mode synthesis where a set of degrees of freedom is eliminated firom the calculation does not appear here. However, approximations arise from usage of iterative solvers. The main goal here is to reduce the total computational cost by distributing the total computational burden among a... 

A more formal procedure for the static condensation introduced in the previous sections can be described as follows (Cook et al. 2002). Let equation = F be the global system of equations for a given substructure. Then, this equation can be rearranged in the following manner... 

Finite element model after static condensation. Finite element nodes are symbolized by black circles ( ]... 

---