Engineering Transactions, 20, 4, pp. 555–576, 1972

Statyka Podłużnie Niejednorodnej Płyty Reissnera o Zmiennej Grubości

A. Gawęcki
Politechnika Poznańska, Poznań
Poland

The fundamental equations of the problem indicated in the title are obtained by means of the E. Reissner variational theorem applied to the orthotropic, linearly elastic body. The equations are written in terms of displacements, the unknown functions being the following three averaged displacements: two angles of rotation of the linear elements normal to the middle surface of the plate and its deflection. The displacement equations form a coupled system of linear partial differential equations with variable coefficients. Analysis of the boundary value problem yields 8 variants of homogeneous boundary conditions.
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

Л. Я. Ашола, Об уточненных meopunx пластинок muna PeUccnepa, «TeopIDI оболочек и шистю-ю, Труда IV Bcec. конф. rro Teop.IDI оболочек Iii rmaciIiiIii, Ереван 1962, Изд. A.H. Арм. CCP., 171-177, 1964.

C. A. Амбар^^мн, Теория анизотропных пластин, Наука, Москва 1967.

В. M. Арановот, К определению напряжений в заделке толстых консольных пластан, Узв. Вьют. УГ. 3aB., Мшосоежйе, 4, 18-22, 1966.

G. D. BIRKHOFF, Circular plates of variable thickness, Phil. Mag. ser. 6, 43, 953 - 962, 1922.

I. N. BRONSZTEJN, K. A. SIEMIENDIAJEW, Matematyka. Poradnik encyklopedyczny, PWN, Warszawa 1968.

1. Г. B. Хаберлаш', Обработка данных фотоупругого uccAedoeanun nAacmuu c учетом теории Peuccnepa, C6. Поларизац. оишч. метод IiiccJI. ишр. ЛенШграД Ута, 570-597, 1966.

V. Z. CHIEN, The intritisic theory of thin shells and plates, Quart. Appl. Mech., 1, 4, 2, 1 - 2, 1944.

L. H.DONNEL, A theory of thick plates, Proc. 2nd. U .S. Nat. Congr. of Appl. Mech., 369 - 373, 1954.

F. ESSENBURG, Ort axially symmetrical plates of variable thickness, J. Appl. Mech., 25, 4, 1958.

F. ESSENBURG, P. M. NAGHDI, On elastic plates of variable thickness, Proc. 3rd U. S. Nat. Congr. Appl. Mech., 313 -319, 1958.

S. FERSHT, An extended Reissner thin plate theory, Israel J. Techn., 2, 3, 3.12- 317, 19154.

D. FREDERICK, Thick rectangular plates on an elastic foundation, Proc. Am. Soc. Civ. Eng., 81, 818, 1955.

R. GANOWICZ, Wybrane zagadnienia z teorii płyt Reissnera i teorii płyt trójwarstwowych, Mech. Teor. i Stos. 3, 55 - 95, J 966.

K. GIRKMANN, R. BEER, Anwendung der verscharften Plattebtheorie nach Eric Reissner auf orthotropeb Platteb; Oster. lng.-Archiv. 12, 101, 1958.

А. Л. Гольцсняетер, K meopuu U3zu6a пластинок Peücmepa, Из6в. A.H. CCCP, отд. T. H., 4, 102-109, 1958.

A. Л. Гольденвейзер, Построение приближетюй meopuu изгиба rnacmmm методом асимптотического интегрирования ypammeStiii meopuu ynpycocmu, IIMMA 26, 668-686, 1962.

A. E. GREEN, 011 Reissner's theory of bending of elastic plates, Quart. Appl. Math., 7, 2, 1949.

A. E. GREEN, The elastic equilibrium of isotropic plates and cylinders, Proc. Roy. Soc., Ser. A, 195, 1949, 533 - 552.

A. E. GREEN, P. M. NAGHDI, The linear theory of an elastic Cosserat plate, Proc. Cambr. Phil. Soc., 63, 2, 1967.

M. HAIMOVICI, Ort the bending of elastic plates, Bull. PAN, 14, 11/12, 605 - 615, 1966.

R. J. HARTRANFT, On same problems involving singularities in Reissner's theory of plate bending, Doct. diss., Lehigh Univ., 1966.

K. BATA, On circular thick p[ate stressed by the generally distributed normal load, Proc. 2nd Jap. Nat. Congr. Appl. Mech., l17 -120, 1953.

H. HENCKY, Uber die Berucksichagwtg der Schubverzerrung in eberten Platten, Ing. Archiv., 16, 72, 1947.

Z. KĄCZKOWSKI, The influence of the shear forces and rotatory inertia on the vibration of an anisotropic plate, Arch. Mech. Stos., 12, 4, 53r - 552, 1960.

Z. KĄCZKOWSKI, Płyty. Obliczenia statyczne, Arkady, 1968.

S. KALISKI, Pewne problemy brzegowe dynamicznej teorii sprężystości ciał i ciał niesprężystych, Biul. WAT, 6, 28, 3 - 306, 1957.

S. KALISKI i in., Drgania i fale, PWN, Warszawa 1966.

И. A. KBJihlfeBCKHH, Обобщение coepeMenuoft meopuu o6ono!feK, Пр^м, Мат. Mex., 2, 4, 1939.

A. B. KoJioc, 06 oóJlacmu npuMeHenun npu6m;JJcemtbtx meopuu. uszu6a flJ!acmuH muna meopuu Peüccnepa, Труда VI Bcec. Kott

E. KOPPE, Die dicke Platte mit nichtUnear Spmtnungs VerteUung, ZAMM, 3, 37, 1 - 2, 1957.

A. KROMM, Verollgemeinerte Theorie der Plattenstatik, lng.RArchiv, 21, 266-286, 1953.

C. Г. Лехнмлш, K meopuu attusomponntix толстых irntm, №B. AH CCCP, 2, 142-145, 1959.

C. W. LEE, A three dimensional solution for simply supported thick rectangular plates, Nucl. Eng. Design, 6, 2, 155 -162, 1967.

A. E. H. LOVE, Mathematical theory of elasticity, Cambridge 1934.

S. J. MEDWADOWSKI, A refined theory of elastic, orthotropic plates, J. Appl. Mech., 25, 4, 437 - 443, 1958.

R. D. MINDLIN, M. FORRAY, Thickness-shear and flexural vibrations of contoured crystal plates, J. Appl. Phys., 25, 12-20, 1954.

J. MOSSAKOWSKI, Równania teorii Reissnera dla płyt ortotropowych, Księga Jubileuszowa W. Wierzbickiego, PWN, 145 - 155, Warszawa 1959.

M. MymTapu, Teopun изгиба nitum cpedHeü mollUJunm, Изв. AH CCCP, 2, 107-113, 1959.

NEGORO SHOSABURO, On a method of solving elastic problems of plates, Proc. 4th Jap. Nat. Congr. Appl. Mech., 1954, 153 -156, Tokio 1955.

V. PANE, Verscharfte Theorie der elastfschen Platte, Ing. Archiv., 33, 6, 1964.

V. V. PONIATOWSKII, Theory for plates of medium thickness, J. Appl. Math., 26, 2, 1962.

E. L. REISS, Symmetric bending of thick circular plates, J. Soc. Ind. and Appl. Math., 10, 4, 1962.

E. REISSNER, On the theory of bending of elastic plates, J. Math. Phys., 23, ·184-191, 1944.

E. REISSNER, The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech., 12, A 69 - A 77, 1945.

E. REISSNER, On bending of elastic plates, Quart. Appl. Math., 5, 55 - 68, 1947.

E. REISSNER, On a variational theorem in elasticity, J. Math. Phys., 29, 90-95, 1950.

W. I. SMIRNOW, Matematyka wyższa, 2, PWN, Warszawa 1960.

M. SOKOŁOWSKI, The bending of transversally nonhomogeneous moderately thick plates, Bull. Acad. Polon. Sci., serie Sci. Techn., 6, 4, 1958.

C. STANESCU, Consideratii asupra - unci teorii a placilor, Studii si cercetari mec. apl. Acad. RSR, 25, 3, 1967, 527 - 537.

J. J. STOKER, Mathematical problems connected with the bending and bucking of elastic plates, Bull. Am. Math. Soc., 48, 247 - 261, 1942.

M. Г. TeperynoB, K meopuu пластин средней толгципы, Труды Конф, no теорйй nnacTHU и o6ono"IeK, 367-375, Ka3aHb 1961.

R. TIFFEN, P. G. LOWE, At exact theory of generally loaded elastic plates in terms of moments of the fundamental equations, Proc. London Math. Soc., 13, 3, 1963.

R. TIFFEN, E.P. SAYER, A moment theory of elastic plates, Mathematika, 9, ll-24, 1962.

S. TIMOSHENKO, S. WOYN0WSKY-KRUGER, Teoria płyt i powłok, Arkady, Warszawa 1962.

E. Ф. BrracoB, 06 ypaeuenunx meopuu изгиба nnacmtmoK, H3B. AH CCCP, 12, 57-60, 1957

K. H. ZIMMER, Ein Beitrag zur nichtlinearen Plattentheorie, Wiss. Z. Techn. Univ. Dresden, 15, 5, 1017 - 1022, 1966.