## 2 Review of Discretization Concepts  
The most essential issue related to the numerical simulations of engineering systems is to generate accurate and reliable response predictions in a reasonable computational time frame. On the other hand, these numerical domains are required to have reasonable details and realistic service life conditions for the verified design processes. The conventional finite element (FE) and computational fluid dynamic (CFD) solvers have generally been employed as basic simulation techniques for solving complex systems. Overall, the concepts of spatial discretization and meshing for coordinational-space to define simpler subspaces (elements) with approximate solutions have been used in the last seventy years. Different types of the so-called meshing/gridding schemes that fragment the single numerical space into small elements/cells/particles have been developed and heavily used. Today's meshing technology is able to discretize a wide variety of complex geometries, adapt into large deformation of the engineering systems (e.g., adaptive re-meshing), and coup with non-conformal aspects of multibody grids. These novel meshing capabilities raise new challenges to the designing practice of safe engineering systems that can only be met if the design and simulation integrate so that fast optimization cycles become available. There have also been various attempts to introduce innovative discretization techniques [7; 8; 9; 10] for dynamic systems (with evolution in time, like cracking phenomena) and interfacing technology for moving grids (e.g., moving vehicles). Most of these techniques have been developed for numerical simulation of complex multi-body systems based on the solution technique (e.g., discrete and continuous), accuracy, computational time, and the degrees of complexities. Although fixed Lagrangian grid has extensively been used for domain discretization in solid mechanics [8; 9; 10], its application for systems with large deformation and internal evolutions is limited. In the Lagrangian as well as the updated Lagrangian (with adaptive re-meshing) approaches, the process of large deformation of an engineering system is simulated as a material deformation fixed to the grid, where each cell transports its own properties (such as density, among others). For history-based transient simulations, as the deformation of the system advances, its properties may change in time (e.g., softening and physical cracking). Accordingly, the procedure of simulating and tracking of material deformation by predicting the time-transient histories of each numerical cell/grid is conventionally defined as the Lagrangian description. In the Lagrangian/updated Lagrangian algorithms, each individual cell/grid within the preliminary computational domain follows its fixed material zone during the deformation of the body. On the other hand, for the Eulerian fixed/moving mesh approaches, rather than following each material cell (deformation front), the evolution of the material flow properties at every point in coordinatial space and time can be visualized. This means that the simulation of material deformation properties at a specified grid/cell depends on its spatial location (at coordinational space) and time. The computational mesh is conventionally fixed for this scheme, while the material deforms with respect to the mesh. The large deformation and distortions of the engineering systems can be simulated with more ease, but generally, it might have resolution issues for material deformation at free boundaries. Figure 1 shows a conventional Lagrangian fixed-grid finite element (FE) mesh and its stress results for gantry boom-leg joints. As both of Lagrangian and Eulerian methods have some shortcomings for real-world dynamic simulations of large structural systems, alternative hybrid techniques have also been developed [11; 12; 13; 14; 15] that combine the best features of both the Lagrangian and Eulerian approaches (arbitrary Lagrangian-Eulerian, ALE; mixed Lagrangian-Eulerian, MiLE; multi material ALE, and so on).