Plastic limit analysis of cylindrically orthotropic circular plates Guowei Ma * , Bazle A. Gama, John W. Gillespie Jr. Center for Composite Materials, University of Delaware, Newark, DE 19711, USA Abstract The plastic limit analysis of cylindrically orthotropic circular plates is developed using a piecewise linear orthotropic yield cri- terion. The yield criterion is a modification of an isotropic formulation that consists of a series of weighted piecewise linear components. The piecewise linear yield criterion enables an analytical solution for the plastic limit load of cylindrically orthotropic circular plates. Plastic limit analysis for both simply supported and clamped circular plates under uniformly distributed load are carried out. Parametric studies are conducted to investigate the sensitivity of the plastic limit loads to material orthotropy and influences of orthotropic ratio and chosen yield criteria on the plastic limit loads of the circular plates are discussed. It is found that the plastic limit loads of the orthotropic circular plates are affected significantly by the orthotropic ratio. Enhancement of the circumferential yield moment will increase dramatically the plastic limit load of the plates. Moment and velocity fields of the plates in plastic limit state are also derived and discussed. The results obtained from the present study are helpful in understanding the failure mechanism of orthotropic circular plates and is useful for design. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Circular plate; Plastic limit load; Orthotropy; Yield criterion; Moment field; Velocity field 1. Introduction Structures are sometimes designed with enhanced strength in a certain direction to resist external load. Traditionally, stiffeners are the most commonly used method to increase stiffness and strength at minimal weight. Mechanical orthotropy may also arise from cold forming process of material. Some single crystal mate- rials such as BCC iron, and textured polycrystalline materials exhibit anisotropic properties due to their in- herent atomic structures. Fiber reinforced composites offer much higher strength-to-weight and stiffness-to- weight by combining structural fibers and a more flexi- ble matrix (e.g. glass fibers in synthetic resins). It has been found that the strength in the fiber direction of unidirectional fiber reinforced composites can be an order of magnitude higher than in the transverse direc- tion [1]. Some composites such as metal matrix rein- forced by metal fibers, plastics reinforced by Kevlar or glass fibers, not only have high strength and high stiff- ness, but also undergo plastic flow and considerable ductility. Plastic limit analysis of these kinds of ortho- tropic plates should be updated based on the yield properties of the plates. The yield behavior of an orthotropic plate is always represented by a proper criterion. Numerous ortho- tropic yield criteria have been published over the past decades. One typical orthotropic yield criterion is re- ferred to as Tsai–Hill criterion, which is an extension of the Hill anisotropic criterion to predict failure in an orthotropic, transversely isotropic lamina [2]. The cri- terion simplifies to the von Mises criterion for isotropic materials. Unfortunately, these criteria as well as many other commonly used orthotropic criteria have qua- dratic or polynomial forms and cannot be used straightforwardly to analytically derive the plastic limit load of a plate. A pioneering work that investigated the plastic limit behavior of cylindrically orthotropic circu- lar plate under various loading cases has been carried out by Markowitz and Hu [3] who employed a modified Tresca criterion. The criterion, similar to the Tresca criterion for isotropic materials, has a piecewise linear form. The plastic limit solution given in their study satisfies both statical and kinematical admissible re- quirements, and is an exact solution. Save [4] and Save et al. [5] summarized the plastic limit solutions obtained for orthotropic circular plates. It is noticed that all the derivations for the plastic limit load of orthotropic cir- cular plate in the previous studies were based on the modified Tresca criterion. Unfortunately, the Tresca criterion has obvious limitations because the effect of the intermediate principal stress on material strength is Composite Structures 55 (2002) 455–466 www.elsevier.com/locate/compstruct * Corresponding author. Fax: +1-302-831-8525. E-mail address: mag@ccm.udel.edu (G. Ma). 0263-8223/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0263-8223(01)00174-X