Determination of stress and displacement state in the circular annulus steel sheet with Cartesian orthotropy

Abstract

This paper deals with determination of stress, strain and displacement state of a circular annulus which is made of material with Cartesian orthotropic rheological behaviour. There is a continuous and constant load on the inner and/or outer edge. Stress and strain state in the circular annulus is in the elastic domain. Stress state is determined on the basis of an Airy stress function, where all boundary conditions have to be fulfilled. The Ritz's method was applied to determine unknown parameters of the Airy function. References F. Kosel. The stress and deflection state in the circular annulus with Cartesian orthotropy. Proceedings 14th Canadian Congress of Applied Mechanics , volume 2, pages 493--494. CANCAM, 1993. Pistonesi, C. and Laura, P. A. A., Forced vibrations of a clamped, circular plate of rectangular orthotropy, J. Sound Vibr. , 228 , 1999, 712--716. Tahan, N., PavloviE, M. N. and Kotsovos, M. D., Orthotropic rectangular plates under in-plane loading part 1: closed-form solutions for stresses, Compos. Struct. , 33 , 1995, 35--48. Wu, Z. J. and Wardenier, J., Further investigation on the exact elasticity solution for anisotropic thick rectangular plates, Int. J. Solids Struct. , 35 , 1998, 747--758. Adewale, A. O., Application of the singularity function method to semi-infinite orthotropic rectangular plates on an elastic foundation, Int. J. Mech. Sci. , 43 , 2001, 2261--2279. Bhaskar, K. and Kaushik, B., Simple and exact series solutions for flexure of orthotropic rectangular plates with any combination of clamped and simply supported edges, Compos. Struct. , 63 , 2004, 63--68. S. G. Lekhnitskii. Theory of elasticity of an anisotropic body . Mir Publishers, Moscow, 1981.