55。57 53。 1 2

39。37 37。57

22。 5 30。12 28。89

15 20。29 19。66

7。5 10。 1 5 9。98

0 0 0

— 19。03 — 19。66

— 27。b5

— 30 — 3 5。bS

— 45 — 50。 37

— 60 — 63。91 — 66。55

— 75 — 77。00 — 78。63

values of b and 9)。 They are compared with those which would occur for the ellipse of revolution (e —— 0) having the same values of u and 6 (see also Table 1)。 The stress distributions for the ellipsoid are symmetric about b = 0, with the circumferential stress greatest (46。20 N/mm’) at § = 0。 Those for the assumed egg shape are no longer symmetric about /J — 0, the maximum (48。05 N/mm') still being in the circumferential ( J I direction but occurring near /J = 20 , and 4% higher than for the ellipsoid。 For the same values of a and b an increase in e will lead to an increases in maximum stress。 For example, if e/h is increased from 0。 1778 to 0。2667 the maximum stress will be 7% higher than for the ellipsoid。论文网

As an approximation, it may  be  thought  that  the maximum  stress would  be  similar to  that in a spherical shell of the same thickness but of radius a。 However this value would be a significant underestimate, i。e。 42。8 N/mm’ but an overestimate (48。6 M, mm') would be given by an equivalent sphere radius of a + e。

The finite element analysis, which effectively solved the full shell equations [3), allowing for compatibility as well as for equilibrium, gave direct stress distributions which were almost identical with the membrane analysis distributions for the example quoted, but small additional bending stresses  were  present。  These  were  most  significant  in  the  w  direction  at  /J = 90"  (maximum

+ 0。95 N/mm'  with  tension  on the inside surface), less so at  b = 90  (maximum   + 0。45 N/m    2

with the tension on the inside) and much less so near /J = 20 (maximum + 0。22 N/mm’  with tension on the outside)。

For the assumed dimensions the membrane analysis thus predicted the maximum stress to within

0。5 % of that calculated from the complete shell equations。

It may appear surprising that the stress distribution in an egg shell (a naturally occurring structure) is so variable along a meridian。 However, internal pressure is not likely to be the critical naturally occurring load which the shell has to withstand while required to remain in tact。 The only time when, in its natural life, it would be subjected to a load approximating to uniform internal pressure is when a chick is about to be hatched。 Under these circumstances the shell is required to fracture, and is observed to do so at a position corresponding approximately to that where the calculated maximum stress occurs。摘要：数形代表提出家禽的鸡蛋壳和外壳进行应力分析所受到的内部压力。代数表达式的膜解决方案被认为接近完整的分析。版权©1996爱思唯尔科学有限公司