Beam Property Adaptation

Remark 10.8. The tensional stiffness Pn and the chordwise shear stiffness P22 are accepted to exhibit deviations from the application example data. 

Division of the shear stiffness coefficients of the beam, see Eq. (10.16e), by each other directly yields the cross-sectional aspect ratio 

Similarly, the bending stiffness coefficients, see Eqs. (10.16b) and (10.16c), may be divided by each other. The resulting polynomial equation has three solutions, whereof only one is real  

The results of Eqs. (10.20) and (10.21) do not agree exactly. These, as well as further discrepancies, are caused by the fact that the single-cell thin-walled box beam, naturally, is not able to represent the properties of a solid configuration with multiple materials and complicated geometry. Consequently, one or the other beam stiffness coefficient cannot be accurately matched. The prioritization of Remark 10.8 gives preference to the result of Eq. (10.21). With the values of Table B.l, the cross-sectional aspect ratio is gained  

The division of the torsional stiffness by a shear stiffness can be solved for the width h of the box beam. This can be done for each of the shear stiffness 

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In Remarks 10.3 to 10.6, the wall properties around the circumferential contour have been specihed. For the central web, however, an altered configuration may be selected. In the beam property adaptation of Section 10.2.2 for... 

Table 10.3. Diagonal entries of the beam stifftiess matrix resulting from the property adaptation with deviations from the application example data, see Table B.l.

Figure 10.35 Methods of measuring the mechanical properties of thin films (a) Nano-indentation, (b) beam deflection and (c) disc deflection. (Adapted from G.M. Pharr and W.C. Oliver, 1992, Measurement of Thin Film Mechanical Properties Using Nanoindentation , Materials Research Society Bulletin XVII (July) 28...

Figure 2. The linear polarized laser light is converted to circularly polarized light by a A/4 wave plate and then is linearly repolarized in the desired direetion by a eomputer controlled polarizer. The exeitation beam passes through a pinhole and reaehes the sample. The windows of the eryostat had to be carefully checked at the experimental temperature for depolarization properties. The lower part clarifies the definitions and orientations of the properties discussed in the text. Figure adapted from Ref. 1.

Even though carbon anodes are not confined within a steel shell like cathode, thermal expansion of the anodic beams as well as thermal shocks may lead to mechanical failure of anodes. Creep/relaxation could also play an important role, mainly in the stub-hole region where high localized stresses could be induced by irregular geometries. Anode properties are very similar to carbon cathode and ramming peste, therefore, constitutive laws developed for one of the materials can be easily adapted to the others. 

The constitutive relation of an adaptive laminated composite shell is given in Eq. (6.6). Being considered for the thin wall of the beam, the lines, respectively columns, associated with the cross-sectional strain component °(x, s) and bending curvature Ks x,s) can be dropped in accordance with Remark 7.4. To comply with the specification of a prismatic beam in Remark 7.1, also with regard to the material properties, the latter need to be constant along the lengthwise direction and thus the constitutive matrix lK(s) only depends on the cross-sectional coordinate. The constitutive relation of the wall and the corresponding formulation for the beam with the constitutive matrix P then... 

Scheme III consists of two layer pairs with opposing fiber orientations and relative polarizations. To induce warping deformation and consequently beam twist, the relative polarization around the cross-section alternates from quadrant to quadrant. Similar results could be achieved just by using lengthwise oriented fibers with such an alternating relative polarization. But without adjustable fiber orientations, it would not be possible to adapt to given stiffness properties, especially with regard to torsion.

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