Abstract
Based on the general solution of the three-dimensional problem for piezoelectric materials, the problem of a piezoelectric cone subjected to concentrated loads at its apex is solved by trial-and-error method. The displacements and stresses are explicitly given for the cases of compression in the presence of point charge, bending and torsion. These solutions are simple in form and convenient for application. When the apex angle 2α equals π, the solutions for concentrated force, point charge and torsion reduce to solutions of the half-space problem.
Similar content being viewed by others
References
Love A E H.A Treatise on the Mathematical Theory of Elasticity [M]. 4th edition, New York: Reprinted by Dover Publications, 1994
Lur'e A I.Three-Dimensional Problems of the Theory of Elastiity [M]. New York: Interscience Publishers, 1964
Lekhniskii S G.Theory of Elasticity of an Anisotropic Elastiity Body [M]. Moscow: Mir Publishers, 1981
Hu Haichang. On the three-dimensional problems of theory of elasticity of a transversely isotropic body [J].Acta Phsica Sinica, 1953,9 (2): 130–144 (in Chinese)
Chen W T. Stress in a transversely isotropic elastic cone under an asymmetric force at its vertex [J].ZAMP, 1965,16 (22): 337–344
Ding Haojiang, Zou Daoqin, Ren Yongjian. Elasticity solutions of spherically isotropic cones under concentrated loads at apes [J].Applied Mathematics and Mechanics, 1995,16 (11): 1025–1038
Sosa H A, Castro M A. On concentrated loads at the boundary of a piezoelectric half-plane [J].Journal of the Mechanics and Physics of Solids, 1994,42: 1105–1122
Ding Haojiang, Wang Guoqing, Cheng Weiqiu: General solution of plane problem of piezoelectric media expressed by “Harmonic Functions” [J].Applied Mathematics and Mechanics, 1997,18 (8): 757–764
Ding Haojiang, Chen B, Liang J. General solution for coupled equations for piezoelectric media [J].International Journal of Solids and Structures, 1996,33 (16): 2283–2298
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China; and the Natural Science Foundation of Zhejing Province
Rights and permissions
About this article
Cite this article
Haojiang, D., Fenglin, G. & Daoqin, Z. Elasticity solutions for a piezoelectric cone under concentrated loads at its apex. Appl Math Mech 20, 12–17 (1999). https://doi.org/10.1007/BF02459268
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02459268