In this paper, we investigate the dynamic behavior of bridges and pipelines, which, due to their repetitive spatial configuration, can be modelled as periodic structures composed of elastic beams and equally spaced elastic/inertial supports. To account for both shear deformation and rotational inertia effects, the Timoshenko-Ehrenfest beam theory is employed. The dynamic characteristics of these periodic systems are determined through their dispersion relations, calculated using a method based on the transfer matrix. Independent finite element simulations of full three-dimensional engineering models, specifically a bridge and a suspended pipeline, are performed to study their eigenvalue properties. Comparison between analytical and numerical dispersion curves reveals very good agreement when using the Timoshenko-Ehrenfest theory, whereas significant discrepancies arise with the classical Euler–Bernoulli beam theory. The results quantify the frequency range and dispersion branches beyond which the Euler–Bernoulli theory becomes inadequate, highlighting that the Timoshenko–Ehrenfest theory provides an accurate and computationally efficient analytical tool for medium- and high-frequency design and analysis of three-dimensional periodic structures. • Periodic systems of Timoshenko-Ehrenfest beams and regular supports are studied. • The analytical formulation is based on the Transfer Matrix Method. • Two examples of periodic structures are investigated: bridges and pipelines. • Finite element simulations are performed on full 3D structural models. • Analytical and numerical dispersion curves show excellent agreement.

• An analysis of variance (ANOVA) on the influence of the tool-related uncertainties, geometrical deviations and misalignment, in cylindrical cup deep drawing was performed. • Identification and quantification of the dominant uncertainties on the punch force evolution, cup profile and thickness distribution • Initial blank thickness and friction dominate overall responses, while tool misalignment and geometrical deviations affect local results. • The influence of uncertainty sources evolves spatially and temporally throughout the forming process, highlighting the need for robust, uncertainty-aware process design. Finite element analysis has become a widely used tool in the design and optimization of forming processes. Nevertheless, its use often neglects the uncertainties present in real industrial environments. This work evaluates the importance of integrating these uncertainties into the forming simulations. For that, deep drawing of a cylindrical cup was selected as test case, in order to evaluate the influence of multiple uncertainty factors on the forming results, such as the earing profile, thickness distribution, and punch force evolution. An ANOVA sensitivity analysis was performed based on simulations of the forming process to investigate the impact of the uncertainties. These included geometric and process-related parameters such as, the initial blank thickness, die and punch misalignments, geometric setup deviations, coefficient of friction, and blank holder force. The results highlight how specific factors affect different regions of the formed cup at different stages of the process. In particular, changes in the cup geometry and thickness along the cup are linked to die misalignment and the coefficient of friction, while force evolution is mainly influenced by the initial thickness and the coefficient of friction during early and intermediate punch displacements. The findings contribute to a better understanding of the role of uncertainty in sheet metal forming processes and support the development of more robust and reliable forming processes.

Composite materials are employed in engineering due to their high strength-to-weight ratios and versatility. However, they are susceptible to low-velocity impacts, which presents notable challenges. Traditional techniques for damage assessment, such as non-destructive testing and numerics-based methods, often face obstacles including high costs, material-specific limitations, and computational demands. To address these issues, we introduce an innovative machine learning-based framework designed to diagnose damage and anticipate structural responses in composite plates experiencing low-velocity impacts. This methodology employs a convolutional neural network to characterize damage, and a feed-forward neural network to predict the maximum deflection of composite plates under various impact scenarios. The framework was validated against experimental tests on composite plates made with different combinations of aramid and S2-glass fibers. Damage was accurately characterized following data augmentation and hyperparameter tuning, enabling precise predictions of damage presence, extent and position. Similarly, the structural response was satisfactorily predicted, with an average prediction error of 2.95% and 1.89% over two stacking sequences not seen during training. This approach marks a significant progression in composite material diagnostics and performance prediction by offering rapid predictions, thus bridging the existing gap between experimental constraints and computational efficiency.

A geometrically exact, dimensionally reduced model is developed to describe the nonlinear deformation of thin magnetoelastic shells. The classical Kirchhoff–Love assumptions for the mechanical fields are extended to the magnetic variables, yielding a consistent two-dimensional theory derived rigorously through a variational framework. Unlike traditional approaches that rely on mid-surface kinematics, the full deformation map is adopted as the primary variable, and the influence of the surrounding free space due to the Maxwell stress on the shell’s upper and lower surfaces is accommodated through a novel application of Green’s theorem. The governing equations are solved in closed form for the canonical case of a hyperelastic thin flat plate and for an infinite cylindrical magnetoelastic shell, to illustrate the capabilities of the model and elucidate the non-standard variables arising in the modified variational formulation.