a b s t r a c tThis paper presents an analytical model for the study of 2D linear-elastic non-prismatic beams. Its principal aim is to accurately predict both displacements and stresses using a simple procedure and few unknown variables. The approach adopted for the model derivation is the so-called dimensional reduction starting from the Hellinger-Reissner functional, which has both displacements and stresses as independent variables. Furthermore, the Timoshenko beam kinematic and appropriate hypotheses on the stress field are considered in order to enforce the boundary equilibrium. The use of dimensional reduction allows the reduction of the integral over a 2D domain, associated with the HellingerReissner functional, into an integral over a 1D domain (i.e., the so-called beam-axis). Finally, through some mathematical manipulations, the six ordinary differential equations governing the beam structural behaviour are derived. In order to prove the capabilities of the proposed model, the solution of the six equations is obtained for several non-prismatic beams with different geometries, constraints, and load distributions. Then, this solution is compared with the results provided by an already existing, more expensive, and refined 2D finite element analysis, showing the efficiency of the proposed model to accurately predict both displacements and stresses, at least in cases of practical interest.

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The National Research Council Canada (NRC) has worked on the development of structural health monitoring (SHM) test platforms for assessing the performance of sensor systems for load monitoring applications. The first SHM platform consists of a 5.5 m cantilever aluminum beam that provides an optimal scenario for evaluating the ability of a load monitoring system to measure bending, torsion and shear loads. The second SHM platform contains an added level of structural complexity, by consisting of aluminum skins with bonded/riveted stringers, typical of an aircraft lower wing structure. These two load monitoring platforms are well characterized and documented, providing loading conditions similar to those encountered during service. In this study, a micro-electro-mechanical system (MEMS) for acquiring data from triads of gyroscopes, accelerometers and magnetometers is described. The system was used to compute changes in angles at discrete stations along the platforms. The angles obtained from the MEMS were used to compute a second, third or fourth order degree polynomial surface from which displacements at every point could be computed. The use of a new Kalman filter was evaluated for angle estimation, from which displacements in the structure were computed. The outputs of the newly developed algorithms were then compared to the displacements obtained from the linear variable displacement transducers connected to the platforms. The displacement curves were subsequently post-processed either analytically, or with the help of a finite element model of the structure, to estimate strains and loads. The estimated strains were compared with baseline strain gauge instrumentation installed on the platforms. This new approach for load monitoring was able to provide accurate estimates of applied strains and shear loads.