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The problem of solving complex engineering problems has always been a major topic in all industrial fields, such as aerospace, civil and mechanical engineering. The use of numerical methods has increased exponentially in the last few years, due to modern computers in the field of structural mechanics. Moreover, a wide range of numerical methods have been presented in the literature for solving such problems. Structural mechanics problems are dealt with using partial differential systems of equations that might be solved by following the two main classes of methods: Domain-decomposition methods or the so-called finite element methods and mesh-free methods where no decomposition is carried out. Both methodologies discretize a partial differential system into a set of algebraic equations that can be easily solved by computer implementation. The aim of the present Special Issue is to present a collection of recent works on these themes and a comparison of the novel advancements of both worlds in structural mechanics applications.

direction field --- tensor line --- principal stress --- tailored fiber placement --- heat conduction --- finite elements --- space-time --- elastodynamics --- mesh adaptation --- non-circular deep tunnel --- complex variables --- conformal mapping --- elasticity --- numerical simulation --- numerical modeling --- joint static strength --- finite element method --- parametric investigation --- reinforced joint (collar and doubler plate) --- nonlocal elasticity theory --- Galerkin weighted residual FEM --- silicon carbide nanowire --- silver nanowire --- gold nanowire --- biostructure --- rostrum --- paddlefish --- Polyodon spathula --- maximum-flow/minimum-cut --- stress patterns --- finite element modelling --- laminated composite plates --- non-uniform mechanical properties --- panel method --- marine propeller --- noise --- FW-H equations --- experimental test --- continuation methods --- bifurcations --- limit points --- cohesive elements --- functionally graded materials --- porosity distributions --- first-order shear deformation theory --- shear correction factor --- higher-order shear deformation theory --- equivalent single-layer approach --- n/a