By R N L Smith (Auth.)

More and more a massive box to engineering layout, this e-book offers an creation to fracture and fatigue. beneficial properties contain a chain of courses enforcing these equipment that are either important and straightforward

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3) To obtain actual stress intensity factors the Q-values should be multiplied by KQ = σ^/τα. This multiplication could be simply added to the program if desired. (4) In the first run, the crack is very small compared to the hole and should, therefore, be well approximated by an edge crack in an infinite sheet with an applied stress of three units. In other words, for small edge cracks a good estimate of SIF is simply the stress concentration factor times the edge cracked plate value. Note that very few integration points are required.

1,0 Ready S a m p l e run 2 RUN CRSS DISPLACEMENTS AND STRESSES AT DISTANCE (R), ANGLE (THETA) FROM A CRACK TIP TERMINATES IF (R) IS NEGATIVE. KI KII ? 100,0 PLANE STRESS (Y/N) ? N DISTANCE R, ANGLE THETA (DEGREES) ? 20795E-ll DISTANCE R, ANGLE THETA (DEGREES) ? 42 TXY = 0 DISTANCE R, ANGLE THETA (DEGREES) ? -1,0 Ready 29 30 Elastic Fracture Sample run 3 RUN CRSS DISPLACEMENTS AND STRESSES AT DISTANCE (R), ANGLE (THETA) FROM A CRACK TIP TERMINATES IF (R) IS NEGATIVE. KI KII ? 100,50 PLANE STRESS (Y/N) ?

It will also be useful to have an explicit expression for p(x) in the form a 0 4- a\X + a2x2 -f .... The Lagrange algorithm is therefore implemented below by expanding the brackets in each U and collecting like terms together. g Mason 1983). A program which implements the Lagrange formula for any number of data points and allows calculation of intermediate values is as follows. 2 LAG: Lagrangian interpolation 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 PRINT " LAGRANGE INTERPOLATION" DIMENSION X ( 6 ) , Y ( 6 ) , C ( 6 ) , T ( 6 ) INPUT ' NUMBER OF POINTS TO BE GIVEN';N FOR 1=1 TO N INPUT ' X I , Y I ' ; X ( I ) , Y ( I ) NEXT I REM *** FIND COEFFICIENTS OF POLYNOMIAL FOR 1=1 TO N Q=l M=0 FOR K=l TO N C(K)=1 NEXT K FOR J=l TO N IF J=I THEN 320 IF M=0 THEN 290 FOR K=M TO 1 STEP - 1 C(K+1)=-X(J)*C(K+1)+C(K) 36 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 Stress intensity factors NEXT K C(1)=-X(J)*C(1) Q=Q*(X(I)-X(J)) M=M+1 NEXT J Q=Y(I)/Q FOR K=l TO N T(K)=T(K)+C(K)*Q NEXT K NEXT I REM *** PRINT AND EVALUATE POLYNOMIAL FOR K=l TO N PRINT " COEFFICIENT OF X**";(K-l);" IS M;T(K) NEXT K INPUT ' NEW X VALUE»;XI Y1=0 FOR 1=1 TO N Y1=Y1+T(I)*X1**(I-1) NEXT I PRINT ' AT X =';X1;' Υ =';Y1 PRINT INPUT ' ANOTHER X-VALUE (Y/N)';A$ IF A$='Y' GOTO 420 END Sample run 1 RUN LAG LAGRANGE INTERPOLATION NUMBER OF POINTS TO BE GIVEN ?