Abstract

Large finite-element mathematical models are developed to calculate the deformations induced by the supports of a 4.2-m aperture 3.2-focal ratio primary mirror of an optical telescope. It is supported axially on three rings of pneumatic cylinders and radially by a system of transverse level weights, an arrangement only possible in a telescope that uses an altazimuth mounting. The stress distributions in the mirror when lifted by a central lifter and when resting on its axial flotation system are shown. A comparison is made between the results using classical flat-plate theory and the finite-element models.

© 1980 Optical Society of America

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References

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  1. A. Couder, Bull. Astron. 7, 14 (1931).
  2. G. Schwesinger, J. Opt. Soc. Am. 44, 417 (1954).
    [CrossRef]
  3. L. A. Selke, Appl. Opt. 9, 149 (1970).
    [CrossRef] [PubMed]
  4. A. J. Malvick, E. T. Pearson, Appl. Opt. 7, 1207 (1968).
    [CrossRef] [PubMed]
  5. A. S. Day, Engineer 219, 218 (1965).
  6. J. R. H. Otter, A. C. Cassell, R. E. Hobbs, Proc. Inst. Civ. Eng. 35, 633 (1966).
    [CrossRef]
  7. O. C. Zienckiewicz, The Finite Element Method in Engineering Science (McGraw-Hill, New York, 1971).
  8. B. K. Ionnisiani, Izv. Spetsial Astrofiz. Obs., 3 (1971).
  9. H. C. King, The History of the Telescope (Criffin, London, 1955).
  10. J. D. Pope, “A 4.2 Metre Altazimuth-Mounted Telescope,” in ESO Conference Proceedings, Optical Telescopes of the Future (ESO, Geneva, 1977), p. 67.
  11. A. J. Malvick, Appl. Opt. 11, 575 (1972).
    [CrossRef] [PubMed]

1972 (1)

1971 (1)

B. K. Ionnisiani, Izv. Spetsial Astrofiz. Obs., 3 (1971).

1970 (1)

1968 (1)

1966 (1)

J. R. H. Otter, A. C. Cassell, R. E. Hobbs, Proc. Inst. Civ. Eng. 35, 633 (1966).
[CrossRef]

1965 (1)

A. S. Day, Engineer 219, 218 (1965).

1954 (1)

1931 (1)

A. Couder, Bull. Astron. 7, 14 (1931).

Cassell, A. C.

J. R. H. Otter, A. C. Cassell, R. E. Hobbs, Proc. Inst. Civ. Eng. 35, 633 (1966).
[CrossRef]

Couder, A.

A. Couder, Bull. Astron. 7, 14 (1931).

Day, A. S.

A. S. Day, Engineer 219, 218 (1965).

Hobbs, R. E.

J. R. H. Otter, A. C. Cassell, R. E. Hobbs, Proc. Inst. Civ. Eng. 35, 633 (1966).
[CrossRef]

Ionnisiani, B. K.

B. K. Ionnisiani, Izv. Spetsial Astrofiz. Obs., 3 (1971).

King, H. C.

H. C. King, The History of the Telescope (Criffin, London, 1955).

Malvick, A. J.

Otter, J. R. H.

J. R. H. Otter, A. C. Cassell, R. E. Hobbs, Proc. Inst. Civ. Eng. 35, 633 (1966).
[CrossRef]

Pearson, E. T.

Pope, J. D.

J. D. Pope, “A 4.2 Metre Altazimuth-Mounted Telescope,” in ESO Conference Proceedings, Optical Telescopes of the Future (ESO, Geneva, 1977), p. 67.

Schwesinger, G.

Selke, L. A.

Zienckiewicz, O. C.

O. C. Zienckiewicz, The Finite Element Method in Engineering Science (McGraw-Hill, New York, 1971).

Appl. Opt. (3)

Bull. Astron. (1)

A. Couder, Bull. Astron. 7, 14 (1931).

Engineer (1)

A. S. Day, Engineer 219, 218 (1965).

Izv. Spetsial Astrofiz. Obs. (1)

B. K. Ionnisiani, Izv. Spetsial Astrofiz. Obs., 3 (1971).

J. Opt. Soc. Am. (1)

Proc. Inst. Civ. Eng. (1)

J. R. H. Otter, A. C. Cassell, R. E. Hobbs, Proc. Inst. Civ. Eng. 35, 633 (1966).
[CrossRef]

Other (3)

O. C. Zienckiewicz, The Finite Element Method in Engineering Science (McGraw-Hill, New York, 1971).

H. C. King, The History of the Telescope (Criffin, London, 1955).

J. D. Pope, “A 4.2 Metre Altazimuth-Mounted Telescope,” in ESO Conference Proceedings, Optical Telescopes of the Future (ESO, Geneva, 1977), p. 67.

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Figures (12)

Fig. 1
Fig. 1

Surface deflections of the 4.2-m primary mirror supported on one, two, and three rings. Curve 1: one ring fixed in R and Z at 1.553-m radius. Curve 2: two rings fixed in R and Z at 1.0697 and 1.783 m. Curve 3: three rings fixed in R and Z at 0.8, 1.336, and 1.869 m.

Fig. 2
Fig. 2

Surface deflections of the 4.2-m primary mirror on various support combinations. Curve 4: three rings, radii 0.80, 1.355, 1.870, fixed in R and Z. Curve 5: three rings, radii 0.8, 1.355, 1.875, fixed in R and Z. Curve 6: three rings, radii 0.795, 1.355, 1.885, fixed in R and Z. Curve 7: three rings, radii 0.795, 1.355, 1.87, fixed in R and Z. Curve 8: three rings, radii 0.795,1.355,1.88, fixed in Z only. Curve 9: three rings, radii 0.798, 1.355, 1.88, fixed in Z only. Reactions (in kN) for two inner radii, outer rings fixed in Z only: Curve 10: 32.174, 52.876. Curve 11: 31.98, 54.62. Curve 12: 31.98, 53.68. Curve 13: 32.05, 53.68. Curve 14: 31.167, 53.56. Curve 15: 31.49, 55.112.

Fig. 3
Fig. 3

Primary mirror cell showing axial and transverse supports.

Fig. 4
Fig. 4

Radial support force distributions that could be used for the support of a large primary mirror of an altazimuth telescope. (a) Traditional cosine push–pull. (b) Using the vertical components of (a). (c) Equal transverse force distribution, showing the location of supports in the plane of the center of gravity of the mirror. (d) Equal transverse forces acting through the centers of gravity of individual slices, showing the locations in relation to the plane of the center of gravity of the mirror.

Fig. 5
Fig. 5

The 3-D finite-element model developed to compute the deformations of the mirror due to the radial supports.

Fig. 6
Fig. 6

Poisson-ratio induced deformations of the 4.2-m primary when subject to a standard cosine push–pull support force distribution (units of 10 nm).

Fig. 7
Fig. 7

Poisson-ratio induced deformations of the 4.2-m mirror when supported by the vertical components of a cosine push–pull force distribution (units of 10 nm).

Fig. 8
Fig. 8

Poisson-ratio induced deformations of the 4.2-m primary when supported with equal vertical transverse force distribution (units of 10 nm).

Fig. 9
Fig. 9

Bending and Poisson-ratio induced deformations for the 4.2 m primary supported with equal vertical transverse forces on the mirror center of gravity (units of 10 nm).

Fig. 10
Fig. 10

Tangential stresses in the 4.2-m primary mirror and its lifter (units of kN m−2). (a) Stress distribution calculated with classical flat-plate theory. (b) Stress distribution obtained by a finite element analysis. (c) Finite-element model used to simulate the metal central lifter and the 4.2-m primary mirror.

Fig. 11
Fig. 11

Tangential stresses in the 3.8 m primary mirror (units of kN m−2). (a) Stress distribution calculated using classical flat-plate theory. (b) Stress distribution obtained by the finite-element analysis. (c) Stress distribution in the mirror when it is supported on three rings of pneumatic cylinders. (d) Stress distribution in the mirror when it is supported on three knife-edge support rings.

Fig. 12
Fig. 12

Tangential stress distribution in the 4.2-m primary mirror. (a) Stresses in the mirror when it is supported on three knife-edge rings. (b) Stresses in the mirror when supported on its three rings of pneumatic cylinders. (c) The basic finite-element model generated to calculate the stress and deflections of the 4.2 m primary mirror.

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