A general solution for moments around holes in symmetric laminates V.G. Ukadgaonker * , D.K.N. Rao Department of Mechanical Engineering, Indian Institute of Technology, Powai, Mumbai 400 076, India Abstract The survey of literature revealed that very few solutions are available for bending of anisotropic plates containing holes. In this paper, a general solution is given for bending of symmetric laminates with holes based on the formulations of Lekhnitskii and Savin that considers any shape of hole in symmetric laminates subjected to remotely applied bending or twisting moments. The results obtained are in good agreement with those in the available literature. Moments around circular, elliptical, triangular, square, rectangular and several irregular shaped holes in cross-ply and angle ply symmetric laminates are obtained. The study on stacking sequence revealed that the moments around the hole will decrease for laminates with large number of ply groups and vice versa. The results also revealed that the magnitude of moments and symmetry of distribution depend on the combined eect of all the pa- rameters, viz., hole geometry, loading, YoungÕs moduli and PoissonÕs ratios of the material and ¯exural moduli of the lami- nates. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Stress concentrations; Bending of anisotropic plates; Moments around holes www.elsevier.com/locate/compstruc Composite Structures 49 (2000) 41±54 Notation B  1 ; B 0  1 ; C 0  1 loading condition constants D  ij normalized o-axis ¯exural moduli k, N numbers associated with terms of the mapping function K 5 ±K 8 , K 5 ± K 8 complex constants and their conjugates M 0 applied moment about y 0 -axis at in®nity ms normal moment on the hole contour M q , M h , M qh moments around the hole in curvilinear coordinates M x , M y , M xy moments around the hole in Cartesian coordinates ps transversal force on the hole contour p j ; q j j  1; ... ; 4 complex constants Q ij stiness coecients Q x , Q y components of transversal plate forces R constant denoting the size of the hole S ij i; j  1; 2; 6 o-axis compliance coecients s j j  1; ... ; 4 complex parameters of anisotropy z coordinate in the thickness direction z j complex coordinates in an- isotropic case, z j  x  s j y /z 1 ; wz 2  stress functions of given plate problem / 1 z 1 ; w 1 z 2  stress functions of ®rst stage solution / 0 z 1 ; w 0 z 2  stress functions of second stage solution / 0 z 1 ; w 0 z 2  ®rst derivatives of the stress functions x j f mapping function in anisotropic case * Corresponding author. Tel.: +91-22-576-7543; fax: +91-22-578- 3480. E-mail address: vgu@me.iitb.ernet.in (V.G. Ukadgaonker). 0263-8223/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 8 2 2 3 ( 9 9 ) 0 0 1 2 4 - 5