The paper describes the Field Boundary Element Method applied to the fracture analysis of a 2D rectangular plate made of Functionally Graded Material to calculate Mode I Stress Intensity Factor. The object of the Field Boundary Element Method is the transversely isotropic plane plate. Its material presents an exponential variation of the elasticity tensor depending on a scalar function of position, i.e., the elastic tensor results from multiplying a scalar function by a constant taken as a reference. Several examples using a parametric representation of the structural response show the suitability of the method that constitutes a sight of Stress Intensity Factor evaluation of Functionally Graded Materials plane plates even in the case of more complex geometries.

Safety assessment of structures can be obtained employing limit design to overcome uncertainties concerning actual response due to inelastic constitutive behavior and more generally to non-linear structural response and loads’ random variability. The limit analysis is used for evaluating the safety of the structures directly starting from load level without any knowledge of the load history. In the paper, the lower bound calculation is proposed where a new strain-based approach is used that allowed describing the residual stress and displacement in terms of permanent strain. The strategy used the permanent strain as the effective parameters of the procedure so that it was possible to assess the ductility requirements for the complete load program developed till collapse or shakedown. The procedure is compared to experimental results obtained on aluminum beams in shakedown.

The calculation of the collapse load of spherical domes is addressed using a semi-analytical approach under the hypotheses of small displacements and perfect plasticity. The procedure is based on the numerical approximation of the self-stress that represents the projection of the balance equilibrium null space on a finite dimensional manifold. The so obtained self-equilibrated stress span is superimposed to a finite element linear elastic solution to the prescribed loads yielding to the statically admissible set accordingly to Melan’s theorem. The compatibility of the stress with the constitutive law of the material has been enforced using linearized limit domain in terms of generalized stress, namely axial force and bending moment along the local spherical curvilinear coordinates. The procedure has been tested with reference to numerical and experimental data from the literature confirming the accuracy of the proposed method. The comparison with the literature confirms that the buckling load is much greater than the plastic collapse loads both calculated through the proposed procedure and reported in the quoted literature.

This work presents preliminary experimental results advancing non-destructive testing methods for detecting steel bars in concrete structures via contactless investigation in the X-band spectrum. The study reveals the field’s penetration into concrete, extracting insights into embedded bars through scattered data. Applying a quasi-quadratic inverse scattering technique to numerically simulated data yields promising results, confirming the effectiveness and reliability of the proposed approach. In this realm, using a higher frequency allows the use of lighter equipment and smaller antennas. Identified areas for improvement include accounting for antenna behavior and establishing undeformed target morphology and precise orientation. Transitioning from powder-based and sand specimens to real solid reinforced concrete structures is expected to alleviate laboratory challenges. Although accurately determining concrete properties such as relative permittivity and conductivity is essential, it remains beyond the scope of this study. Finally, overcoming these challenges could significantly enhance non-invasive testing, improving structural health monitoring and disaster prevention.