Optical Methods in Experimental Solid Mechanics by Karl-Hans Laermann (eds.)

By Karl-Hans Laermann (eds.)

The e-book covers the theories and physics of complex new optical measuring tools and difficulties of experimental functionality, contemporary achievements within the easy interferometric tools holography, speckle-interferometry, shearography in addition to linear/non-linear photoelasticity and photoviscoelasticity, Moiré- and grid-techniques. It bargains with concept and alertness of electronic photo processing, equipment of knowledge recording, info processing and -visualisation, with mathematical/numerical systems for ultimate overview of digitised measured facts and the primary of hybrid thoughts. It introduces into the hot perceptions of equipment in experimental reliable mechanics and it may inspire scientists to deal intensively with the theories for extra advancements, and allows practitioners, to appreciate conception and physics of the hot achievements at the least and to use the tools in learn als good as in advancements in practice.

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To solve this equation a reduction-procedure will be applied. 3. The. reduction-procedure. 4). For further evaluation the process is split up into two phases. e. in the plane (x 1,x 2 ) are determined. 22) the following equation is obtained to calculate the components u 1 and u2 along the respective axis of evaluation. 4: Performance scheme of the reduction process. (t+l) are unknown the reduction process starts at cross-section t = 0 proceeding along the axis of evaluation parallel to axis x3 to cross-section t = n; in both these intersection points the values u~ (0) and u~ (n) are given as measured data.

11) Xj and these series are truncated after the fourth term. l +1. 1.. 11 b) at;o 1 f. = f: o + - 1+5-X· I +1 IJ I j 2! ax + • -f.. = t '1 '0 axj 1 ax/ ax} 2! 1la) by 1-oxil 1 1 3! ax} 3! 12) yields an approximate value of fi(M) and thus a rough approach of the 51 Hybrid Techniques in Experimental Solid Mechanics correlation functi~n G(Mr,M) only. 3). 15) 52 K-H. Laermann m= 1 1 2 1- 2lJ. 15) Transformation of the components ui into the reference co-ordinate system (xi) and taking the weighted mean over a sufficient number of these values of a triple, which can be regarded as a numerical integration in the R3 -space, yields the final values of the components of the displacement vector ui(M) with satisfactory accuracy.

3 9E5 _ 9Eo . x1 - c1 (1-2v)z , gz = Cz 4. 33) the stress-optical coefficient is given to [ 3 Cz (1+vi • P i(1+4VE,) ~ p ... 20), this coefficient must be independent of the applied stress. And indeed this has been confirmed by respective experiments. 3. p [kN1 &0 Eo =4160 N/mm2; v = 0 32 c1 = 01 00367 mm2/N Cz = 0,00003 (mm2/N )2 S =28 N/mm+ord. 0,2 O,t. 3. Results of material testing. 5. Examples of application. To convey an impression on the effects of non-linear material response of photoelastic model material and on the results of the evaluation of the experimental data two examples are presented.

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