Letters to the Editor

Letters to the Editor short open tubes. Thus, I draw M. Mordellet's attention to Eq. (26)-(28), FIGS. (10)·(17), the statements of the non-applicability of the clas­ sical flexural axis conception and its experi­ mental verification. This is the novel contribu­ tion in no way appearing in Wagner's and other The Open Tube associate work. 7. M. Mordellet is gravely mistaken when he states that the generality of Bodet's work is due to his having used the energy approach. This is To the Editor he should have selected the contents of Appen­ a fallacious and wholly mathematical idea. The dix A for sole consideration, I feel that they do energy approach is not more general, but in this DEAR SIR, not represent the real substance of my article. case definitely more clumsy and unimaginative I wish to make the following comments on the The following remarks may clarify the points than the more elegant direct use of equilibrium article entitled 'The Open Tube'; AIRCRAFT in question. and kinematic conditions. This may explain why ENGINEERING, Vol. XXVI, No. 302, April 1954, Mordellet's presentation of Bodet's ideas on 1. The article of M. Mordellet in AIRCRAFT pp. 102-112, by Dr John Argyris. torsion-bending in 1950 strikes one as so much ENGINEERING, November 1950, on Bodet's work In this paper the autho r makes a clear synthetic more cumbersome than the work of previous on torsion-bending I had not noticed previously, exposition of the torsion-flexure theory, little authors. but even if I had seen it I would not have found understood, at large, until recently, although of Although critical of some of the statements it necessary to give it as a reference. The simple prime importance to the designer of semi- of M. Mordellet I am nevertheless happy that reason being that the paper in question represents, monocoque structures. the so interesting subject of 'open tube' should in my opinion, a retrograde step after the basic As the autho r points out, Wagner was first and have found in him such an eager student. work starting in 1929 of Wagner, Kappus, foremost when lie solved the problem in 1929; Yours faithfully, Goodier and Argyris-Dunne on Open Tubes. but his solution, as the author states, was actually J. H. ARGYRIS One of the main points of M. Mordellet is that a 'St Venant solution' of the very long open beam, Department of Aeronautics he presented there also a synthesis of E.T.B. this complement to St Venant's solution for long Imperial College of Science and Technology and torsion-bending, apparently also due to beams arising merely because the contour of the University of London Bodet in 1937. However, it is not really a synthesis shell is 'open'. However, the connexion with London, S.W.7 in the sense I used this term, but merely an 'E.T.B.' was not noticed then, either because of May 24, 1954 obvious addition of E.T.B. and torsion-bending. the manner in which it was arrived at, or because In this connexion, may I draw M. Mordellet's it was not apparent in the symbols used. As far attention to the geometric and loading relations as the author of this note is aware, the first ROTOR BLADE MOTION of Appendix A—e.g. Eq. (A 14), (A 16), (A 19), synthetic solution of the shell problem is to be ellipse of reference points R and FIG. (18) — In the correspondence on this subject published found in the work of Pol Bodet. A short exposi­ which do not appear in either Wagner or any of on p. 203 of the June issue the letter from Mr tion of this was made by the author of this note the notes referred to by M. Mordellet. H. H. Rosenbrock is the original version received in AIRCRAFT ENGINEERING, Vol. XXII, No. 261, In M. Mordellet's reasoning of 1950 there are from him. This version should have been amended November 1950, pp. 335-7, under the title: also one or two mistakes, not affecting the final as indicated below before publication. Mr P. R. A Solution to the Problem of Torsion-flexure. result. In particular, his derivation of the equi­ Payne was informed of these alterations before This article was precisely aimed at showing that librium condition on a small tube element hap­ he framed his reply. the St Venant bending and Wagner torsion- pens to be correct only because two serious bending solutions are merely two facets of a The material alterations occur after Eq. (iv), errors happily cancel each other. Furthermore, and the correct version is as follows: general solution for the very long shell. Thus, no mention of the effect of J is made and no at least with a great degree of implicity, in the 'M r Payne puts α = –A/(B2+C2), ф=π/2, but discussion of deformations and the effects of opinion of the author of this note, P. Bodet was these values do- not satisfy (iv). The correct shear strains is given. the first to produce a synthetic solution (1937). values are Moreover, his solution comprises also the case 2. In all fairness it must be stated that M. α = –A/C√(B2+C2) of the short shell and ultimately the shell at a Mordellet was in 1950—if one judges from the ф such that sin ф = C/√(B2 + C2), built-in end, for which he gave the 'static solution' references, or rather lack of proper references, cos ф = B/√(B2+C2) as put forward by Dr Argyris himself in 1947. in his article—completely unaware of what The degree of generality of P. Bodet's solution Thus x=[A/(B2+C2)] [1 - important work had been done in the last 21 years. is, of course, due to the Energy approach, which {√/(B2+C2)/C2)C}e-Bt sin (Ct + ф)] .. (v) Thus, Wagner's name does not appear once. I am = [A/(B2 + C2)] (1 -{√(B2-+C2)/C}x has made possible many a 'sweeping statement' glad that he accepts him now as the originator in all fields of Physics. P. Bodet's work was e_Bt(sin Ct cos ф + cos Ct sin ф)] of torsion-bending. = [A/(B2+C2)] [1-e-Bt cos Ct- published in French, apart from the above cited paper, which apparently escaped the attention 3. It is true that the article of M. Mordellet (B/C) e-Bt sin Ct] (vi) as I gave before.' of Dr. Argyris. In 1953 the author of this note, contains also some remarks on combined flexure From there on the published version is correct. in a Canadair Ltd. Internal Report (Structures) and torsion of closed tubes. However, his data entitled Approximate Analysis of Flexible Frames are quite frankly trivial knowledge given even in Cylindrical Shells of Any Shape has made before the war in undergraduate courses at explicit the unified treatment of bending and Technical Universities. torsion-bending for routine stress office work. 4. The spirited defence by M. Mordellet of This long-shell distribution is taken as a basis the original work of Pol Bodet on torsion- for the computation of the effect of the frame AIRCRAFT SERVICING AND bending in 1937 is appreciated and praiseworthy. flexibility. As this is also the basic approach in However, I cannot trace it, since appropriate the work of Dr. Argyris, this part is reproduced MAINTENANCE literature references are given neither in his article here*, with the kind permission of Canadair Ltd., nor in his letter. Its having been written in French Montreal. The phrases within brackets have been The City and Guilds of London Institute has pre­ would naturally not preclude its careful con­ added in order to make this extract self-contained. pared a five year part-time course in Aircraft Servicing sideration, but a s I mentioned before M. Mordel­ and Maintenance which is intended to meet the needs Yours very truly, let's presentation of it does not add anything new of craftsmen and technicians engaged in servicing ROGER MORDELLET to what was already widely known in 1937. aircraft in industry and in H.M. Forces. It is framed Stress Engineer with the object of supplementing the student's in­ The author's comments on the further work of Canadair Ltd. dustrial or service experience and so improving his Pol Bodet are frankly unintelligible. skill and understanding. Montreal, Canada 5. The attached note of M. Mordellet is, in The course is arranged in two stages, Intermediate May 5, 1954 and Final, and the syllabuses allow for specialization in general, a reiteration of what he attempted to either airframes or power plant. The Intermediate say in 1950 and represents what has now been Dr Argyris's Reply course is planned to cover a period of three years standard knowledge for many years. part-time study, and the Final course a further period DEAR SIR , 6. Since the major part of my article, i.e. of two years. The scheme will operate from the com­ mencement of the Session 1954/55. Thank you for the interesting comment of section 4, seems to have escaped M. Mordellet's Examinations at the Intermediate and Final levels M. Roger Mordellet. I am afraid, however, that attention, I ought to point out that my paper was will be held annually, and the first examinations will he appears to be rather confused on the issues not only concerned in giving due credit to the be offered in 1955. he raises. Moreover, whilst being flattered that past work on this subject—and M. Mordellet's Full particulars of the course can be obtained in comments and work in 1950 prove to me how pamphlet form from the City and Guilds of London *The note enclosed with this letter has had to be omitted because necessary this was—but also to point out the Institute, Department of Technology, 31 Brechin of shortage of space, but it was sent to Dr. Argyris for him to study important effect of shear strain deformation in Place, London, S.W.7. price 6tl. before be prepared his reply. July 1954 229 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aircraft Engineering and Aerospace Technology Emerald Publishing

Letters to the Editor

Aircraft Engineering and Aerospace Technology, Volume 26 (7): 1 – Jul 1, 1954

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Emerald Publishing
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Copyright © Emerald Group Publishing Limited
ISSN
0002-2667
DOI
10.1108/eb032445
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Abstract

short open tubes. Thus, I draw M. Mordellet's attention to Eq. (26)-(28), FIGS. (10)·(17), the statements of the non-applicability of the clas­ sical flexural axis conception and its experi­ mental verification. This is the novel contribu­ tion in no way appearing in Wagner's and other The Open Tube associate work. 7. M. Mordellet is gravely mistaken when he states that the generality of Bodet's work is due to his having used the energy approach. This is To the Editor he should have selected the contents of Appen­ a fallacious and wholly mathematical idea. The dix A for sole consideration, I feel that they do energy approach is not more general, but in this DEAR SIR, not represent the real substance of my article. case definitely more clumsy and unimaginative I wish to make the following comments on the The following remarks may clarify the points than the more elegant direct use of equilibrium article entitled 'The Open Tube'; AIRCRAFT in question. and kinematic conditions. This may explain why ENGINEERING, Vol. XXVI, No. 302, April 1954, Mordellet's presentation of Bodet's ideas on 1. The article of M. Mordellet in AIRCRAFT pp. 102-112, by Dr John Argyris. torsion-bending in 1950 strikes one as so much ENGINEERING, November 1950, on Bodet's work In this paper the autho r makes a clear synthetic more cumbersome than the work of previous on torsion-bending I had not noticed previously, exposition of the torsion-flexure theory, little authors. but even if I had seen it I would not have found understood, at large, until recently, although of Although critical of some of the statements it necessary to give it as a reference. The simple prime importance to the designer of semi- of M. Mordellet I am nevertheless happy that reason being that the paper in question represents, monocoque structures. the so interesting subject of 'open tube' should in my opinion, a retrograde step after the basic As the autho r points out, Wagner was first and have found in him such an eager student. work starting in 1929 of Wagner, Kappus, foremost when lie solved the problem in 1929; Yours faithfully, Goodier and Argyris-Dunne on Open Tubes. but his solution, as the author states, was actually J. H. ARGYRIS One of the main points of M. Mordellet is that a 'St Venant solution' of the very long open beam, Department of Aeronautics he presented there also a synthesis of E.T.B. this complement to St Venant's solution for long Imperial College of Science and Technology and torsion-bending, apparently also due to beams arising merely because the contour of the University of London Bodet in 1937. However, it is not really a synthesis shell is 'open'. However, the connexion with London, S.W.7 in the sense I used this term, but merely an 'E.T.B.' was not noticed then, either because of May 24, 1954 obvious addition of E.T.B. and torsion-bending. the manner in which it was arrived at, or because In this connexion, may I draw M. Mordellet's it was not apparent in the symbols used. As far attention to the geometric and loading relations as the author of this note is aware, the first ROTOR BLADE MOTION of Appendix A—e.g. Eq. (A 14), (A 16), (A 19), synthetic solution of the shell problem is to be ellipse of reference points R and FIG. (18) — In the correspondence on this subject published found in the work of Pol Bodet. A short exposi­ which do not appear in either Wagner or any of on p. 203 of the June issue the letter from Mr tion of this was made by the author of this note the notes referred to by M. Mordellet. H. H. Rosenbrock is the original version received in AIRCRAFT ENGINEERING, Vol. XXII, No. 261, In M. Mordellet's reasoning of 1950 there are from him. This version should have been amended November 1950, pp. 335-7, under the title: also one or two mistakes, not affecting the final as indicated below before publication. Mr P. R. A Solution to the Problem of Torsion-flexure. result. In particular, his derivation of the equi­ Payne was informed of these alterations before This article was precisely aimed at showing that librium condition on a small tube element hap­ he framed his reply. the St Venant bending and Wagner torsion- pens to be correct only because two serious bending solutions are merely two facets of a The material alterations occur after Eq. (iv), errors happily cancel each other. Furthermore, and the correct version is as follows: general solution for the very long shell. Thus, no mention of the effect of J is made and no at least with a great degree of implicity, in the 'M r Payne puts α = –A/(B2+C2), ф=π/2, but discussion of deformations and the effects of opinion of the author of this note, P. Bodet was these values do- not satisfy (iv). The correct shear strains is given. the first to produce a synthetic solution (1937). values are Moreover, his solution comprises also the case 2. In all fairness it must be stated that M. α = –A/C√(B2+C2) of the short shell and ultimately the shell at a Mordellet was in 1950—if one judges from the ф such that sin ф = C/√(B2 + C2), built-in end, for which he gave the 'static solution' references, or rather lack of proper references, cos ф = B/√(B2+C2) as put forward by Dr Argyris himself in 1947. in his article—completely unaware of what The degree of generality of P. Bodet's solution Thus x=[A/(B2+C2)] [1 - important work had been done in the last 21 years. is, of course, due to the Energy approach, which {√/(B2+C2)/C2)C}e-Bt sin (Ct + ф)] .. (v) Thus, Wagner's name does not appear once. I am = [A/(B2 + C2)] (1 -{√(B2-+C2)/C}x has made possible many a 'sweeping statement' glad that he accepts him now as the originator in all fields of Physics. P. Bodet's work was e_Bt(sin Ct cos ф + cos Ct sin ф)] of torsion-bending. = [A/(B2+C2)] [1-e-Bt cos Ct- published in French, apart from the above cited paper, which apparently escaped the attention 3. It is true that the article of M. Mordellet (B/C) e-Bt sin Ct] (vi) as I gave before.' of Dr. Argyris. In 1953 the author of this note, contains also some remarks on combined flexure From there on the published version is correct. in a Canadair Ltd. Internal Report (Structures) and torsion of closed tubes. However, his data entitled Approximate Analysis of Flexible Frames are quite frankly trivial knowledge given even in Cylindrical Shells of Any Shape has made before the war in undergraduate courses at explicit the unified treatment of bending and Technical Universities. torsion-bending for routine stress office work. 4. The spirited defence by M. Mordellet of This long-shell distribution is taken as a basis the original work of Pol Bodet on torsion- for the computation of the effect of the frame AIRCRAFT SERVICING AND bending in 1937 is appreciated and praiseworthy. flexibility. As this is also the basic approach in However, I cannot trace it, since appropriate the work of Dr. Argyris, this part is reproduced MAINTENANCE literature references are given neither in his article here*, with the kind permission of Canadair Ltd., nor in his letter. Its having been written in French Montreal. The phrases within brackets have been The City and Guilds of London Institute has pre­ would naturally not preclude its careful con­ added in order to make this extract self-contained. pared a five year part-time course in Aircraft Servicing sideration, but a s I mentioned before M. Mordel­ and Maintenance which is intended to meet the needs Yours very truly, let's presentation of it does not add anything new of craftsmen and technicians engaged in servicing ROGER MORDELLET to what was already widely known in 1937. aircraft in industry and in H.M. Forces. It is framed Stress Engineer with the object of supplementing the student's in­ The author's comments on the further work of Canadair Ltd. dustrial or service experience and so improving his Pol Bodet are frankly unintelligible. skill and understanding. Montreal, Canada 5. The attached note of M. Mordellet is, in The course is arranged in two stages, Intermediate May 5, 1954 and Final, and the syllabuses allow for specialization in general, a reiteration of what he attempted to either airframes or power plant. The Intermediate say in 1950 and represents what has now been Dr Argyris's Reply course is planned to cover a period of three years standard knowledge for many years. part-time study, and the Final course a further period DEAR SIR , 6. Since the major part of my article, i.e. of two years. The scheme will operate from the com­ mencement of the Session 1954/55. Thank you for the interesting comment of section 4, seems to have escaped M. Mordellet's Examinations at the Intermediate and Final levels M. Roger Mordellet. I am afraid, however, that attention, I ought to point out that my paper was will be held annually, and the first examinations will he appears to be rather confused on the issues not only concerned in giving due credit to the be offered in 1955. he raises. Moreover, whilst being flattered that past work on this subject—and M. Mordellet's Full particulars of the course can be obtained in comments and work in 1950 prove to me how pamphlet form from the City and Guilds of London *The note enclosed with this letter has had to be omitted because necessary this was—but also to point out the Institute, Department of Technology, 31 Brechin of shortage of space, but it was sent to Dr. Argyris for him to study important effect of shear strain deformation in Place, London, S.W.7. price 6tl. before be prepared his reply. July 1954 229

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Aircraft Engineering and Aerospace TechnologyEmerald Publishing

Published: Jul 1, 1954

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