mws_civ_dif_txt_discrete_examples

# mws_civ_dif_txt_discrete_examples - Chapter 02.03...

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Unformatted text preview: Chapter 02.03 Differentiation of Discrete Functions-More Examples Civil Engineering Example 1 To find the stress concentration around a hole in a plate under a uniform stress, a finite difference program has been written that calculates the radial and tangential displacements at different points in the plate. To find the stresses and hence the stress concentration factor, one needs to find the derivatives of these displacements. In Table 1 the radial displacements are given along the u y-axis. The radius of the hole is 1.0 cm. a) At x , if the radial strain r is given by r u r , find the radial strain at cm 1 . 1 using the forward divided difference method. r b) If the tangential strain at 90 , cm 1 . 1 r is given to you as 0029733 . , find the hoop stress, , at 90 , cm 1 . 1 r if ) ( 1 2 E r , where 3 . and GPa 200 E . Table 1 Radial displacement as a function of location. ) cm ( r ) cm ( u 1.0 – 0.0010000 1.1 – 0.0010689 1.2 – 0.0011088 1.3 – 0.0011326 1.4 – 0.0011474 1.5 – 0.0011574 1.6 – 0.0011650 1.7 – 0.0011718 1.8 – 0.0011785 1.9 – 0.0011857 Solution a) 02.03.1 02.03.2 Chapter 02.03 r u u r u i i r 1 1 . 1 i r 2 . 1 1 i r i i r r r 1 1 . 1 . 1 2 . 1 0011088 . 1 i u 0010689 . i u r u u i i r 1 cm/cm 000399 . 1 . ) 0010689 . ( 0011088 . b) ) ( 1 2 r E ) 0029733 . 3 . 000399 . ( 3 . 1 10 2 2 11 Pa 10 35 . 108 6 Example 2 To find the stress concentration around a hole in a plate under a uniform stress, a finite difference program has been written that calculates the radial and tangential displacements at different points in the plate. To find the stresses and hence the stress concentration factor, one needs to find the derivatives of these displacements. In Table 2 the radial displacements one needs to find the derivatives of these displacements....
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mws_civ_dif_txt_discrete_examples - Chapter 02.03...

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