A multiresolution finite wavelet domain method, that utilizes Daubechies wavelet and scaling functions for the hierarchical approximation of state variables, is presented. The multiresolution approximation yields a hierarchical set of equations of motion involving the coarse component of generalized displacements, while additional equations of finer components are subsequently added. A coarse solution is first calculated, and finer solutions can be sequentially superimposed on the coarse solution until convergence to the final solution is achieved. Moreover, it is shown that each resolution can model specific bandwidths of wavenumbers, thus providing a unique capability to separate coexisting wave modes and detect converted and reflected waves in the presence of damage. Two wavelet-based beam elements are explored, the first encompasses the Timoshenko shear beam theory and the second a high-order layerwise laminate theory for the accurate prediction of both symmetric and antisymmetric guided waves. Numerical results illustrate the inherent property of the method to a priori localize and isolate coexisting guided wave modes and their conversions, induced by different material regions and weak or debonded layer interfaces, thus demonstrating the method’s intrinsic capabilities towards the design of wave-based SHM systems.@en

The accuracy of structural analysis in composite structures depends on the proper estimation of the uncertainties mainly related to the mechanical properties of the constituent materials. On this basis, a sophisticated numerical tool is proposed, able to perform stochastic finite element analysis on composite structures with material uncertainties by distributing stochastic mechanical properties along the domain of a composite structure. The output of the analysis is a probability density function for the deformation, strain, stress and failure fields. The proposed tool exploits the Karhunen–Loève expansion and the Latin Hypercube Sampling methods for the stochastic distribution of the mechanical properties, the well-established First-Order Shear Deformation theory in conjunction with a random variable approach for the calculation of stochastic stiffness matrices, and the Puck's failure criterion for the conduction of probabilistic analysis of different failure modes in composite structures. A quasi-static tensile testing campaign was conducted with quasi-isotropic coupons in order to assess the fidelity of the method and the efficiency of the stochastic distribution algorithm is compared with the full field data acquired by the digital image correlation approach. The current paper provides a thorough presentation of the development of the proposed stochastic finite element method and validation results which ensure the efficiency of the proposed stochastic numerical tool.@en

A hybrid methodology based on numerical and non-destructive experimental schemes, which is able to predict the structural level strength of composite laminates is proposed on the current work. The main objective is to predict the strength by substituting the up to failure experiments with non-destructive experiments where the investigated specimen is loaded up to 20% of its maximum load. A significant gap exists between the 20% and the 100% load which is proposed to be treated by high fidelity physics-based numerical models, deep learning techniques, and non-catastrophic experiments. Thus, a deep learning algorithm is developed, based on the convolutional neural networks and trained by probabilistic failure analysis datasets which result from the utilization of the stochastic finite element method. Also, the Monte Carlo dropout technique is embedded into the developed convolutional neural network to estimate the uncertainty induced by the investigated variations between the simulated and experimental data. The current paper provides a thorough description of the proposed methodology and a practical example which demonstrates the validity of the method.@en