Lower bounds to the collapse load of composite laminates

Composite laminates are nowadays employed in many engineering applications, especially in nautical and aeronautical fields, where high strength-to-weight and stiffness-to-weight ratios are required. For structures made of composite laminates a crucial task for design purpose is to numerically define their load bearing capacity, also in order to minimize economical efforts in producing and testing prototypes. The present study is focused on the evaluation of the load bearing capacity of orthotropic pinned-joints. The problem is treated at a macro structural level by means of a limit analysis approach. The examined structural elements are composite laminates obeying, by hypothesis, to a Tsai-Wu type yield criterion defined as a second order tensor polynomial form of the Tsai-Wu failure criterion for composite laminates [1]. The potentialities of two well known FE-based procedures for limit analysis are investigated. The two numerical procedures, namely the Linear Matching Method (LMM) [2,3] and the Elastic Compensation Method (ECM) [4], are appropriately modified and rephrased, in the context of anisotropic materials, to define a range of load levels bracketing the effective load value which produce the joint collapse. As known, the general lack of associativity of an anisotropic composite material, even if can be handled by a non standard limit analysis approach, see e.g. [5], generates an unavoidable gap between the upper and the lower limit load values, gap that must be ascertained to make effective the proposed approach. The latter is also able to locate the collapse zone eventually identifying the related collapse mode. For sake of brevity, only the fundamentals of the modified LMM and ECM methods are briefly summarized in the next section. The reader can refer to previous works of the Authors [see e.g. 3,6 and references therein] to acquire all the details of the numerical procedures. Finally, few numerical results are presented to highlight the effectiveness and the limits of the proposed method.