HESAM Université

The main goal of this work involves conducting numerical simulations to determine the vibrational behavior of composite shell structures. The introduction of doubly-curved laminated shells plays a pivotal role in diverse engineering applications, offering an expanded design space and the potential to enhance mechanical performance. However, the analysis of this kind of structures poses significant challenges due to the need to account for the curvature of the shell mid-surface. Moreover, the aspect ratio strongly influences the structural response in terms of free vibrations, also affecting the accuracy of the numerical solution. To address these complexities, this work employs the Carrera’s unified formulation, a well-established methodology for evaluating composites structural behavior which allows to set the expansion order of through-the-thickness polynomials as a free parameter of the simulation. In this context, the governing equations of the problem are derived through pure displacement and mixed formulations, within a finite element framework, ensuring a robust and adaptable analysis approach. This study extends the application of the unified formulation to complex shell geometries featuring non-uniform curvatures along the mid-surface principal directions. Free vibration analyses are performed to determine fundamental frequencies and mode shapes, with results benchmarked against 3D models from Abaqus and classical theoretical predictions. The comparison demonstrates the effectiveness of the proposed approach, establishing its efficacy for advanced structural investigation of fiber-reinforced shells with spatially varying curvatures, regardless of the considered slenderness ratio. • Carrera’s unified formulation is adopted for the modal analysis of curved shells. • Governing equations are derived using displacement-based and mixed theories. • Numerical results are validated against three-dimensional Abaqus reference models. • Lower-order models show accurate results for thin shells at reduced numerical cost. • Layer-wise mixed models achieve top accuracy.

Summary Bioleaching is a biologically facilitated process that helps to dissolve valuable metals in order to extract them from the mineral gangue. Applied in the field to heap ores, its efficiency mainly depends on solution flow inside the heterogeneous heaps, which is often tortuous and can remain stagnant in the pores and crevices between the particles. Methodologies that can help to monitor the bioleaching processes are therefore needed to improve operational efficiency. In this article, we present for the first time preliminary laboratory-scale investigations on spectral induced polarization (SIP) during the bioleaching of chalcopyrite (CuFeS2) containing ore material from a mine in Chile. Two column experiments representing different stages of the bioleaching process were monitored under un-saturated and highly acidic environment (pH ~2). Our objective was to explore the feasibility of SIP for detecting changes in electrical properties potentially associated with bioleaching-induced mineral dissolution and alteration. The results show a rapid decrease in SIP phase shift and imaginary conductivity during the early stage of bioleaching, while the real conductivity remains relatively stable. At a more advanced stage of bioleaching, the phase response is weaker and more stable. A relaxation time distribution (RTD) analysis was applied to further investigate changes in polarization mechanisms. Prior to bioleaching, the RTD exhibits a well-defined peak consistent with polarization controlled by sulfide mineral grains, whereas after one month of bioleaching the RTD broadens and shifts toward larger relaxation times, accompanied by a decrease in chargeability. This combined evolution suggests bioleaching-induced modifications of electrochemically active surfaces, potentially related to mineral dissolution and the formation of passivation layers. Estimated particle sizes derived from the RTD analysis are consistent with scanning electron microscopy observations. Although, the absence of a dedicated abiotic control column prevents us from attributing these changes unambiguously to bioleaching alone, these results highlight the potential of SIP as a non-invasive, real-time and integrative tool to monitor leaching processes and to identify zones that may remain weakly affected by leaching.

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