Comparison of experimental testing and finite element modelling of a replica of a section of the Vasa warship to identify the behaviour of structural joints

Modelling in design of new support systems necessitates the joint stiffness of the existing wooden structures. In valuable structures, e.g. in cultural heritage, or structures with inaccessible joints, these stiffness values must be estimated, e.g. by testing joints in tailored replicas of the original parts. Although a simplified structure, the replica, can call for finite element (FE) modelling to capture the stiffness parameters. The first step in such a process is to compare FE predictions with experimental tests, for validation purposes. The reasons for unavoidable differences in load-displacement behaviour between model predictions and experimental test should be identified, and then possibly remedied by an improved model. Underlying causes like the complex shape of joints, geometrical uncertainties, contact mechanisms and material nonlinearity are generally too computationally expensive to be included in a full-scale model. It is therefore convenient to collect such effects in the contact penalty stiffness in the joint contact areas where stresses are high, which influences the resulting joint stiffness. A procedure for this is here illustrated for the case of the 17th century Vasa shipwreck. A replica of a section of the ship has been constructed, and its joints were tested in bending-compression, in-plane shear and rotation. The FE simulations showed stiffer behaviour than the experimental results. Therefore, a normal penalty stiffness in contact surfaces of the joint were introduced, and used as a calibration parameter to account for the simplifying assumptions or indeliberate imprecision in the model, e.g. concerning boundary conditions, material properties and geometrical detail. The difference between numerical predictions and experimental results could then be significantly reduced, with a suitable normal penalty stiffness value. Once an acceptable finite element model has been obtained, it is shown how this can be used to identify stiffness values for joints in the physical structure with compensation for degradation of material properties due to aging and conservation treatment.