Humberto Breves Coda

The size effect, defined as the reduction in nominal structural strength with increasing size, is a critical phenomenon in concrete and other quasi-brittle materials, governed by fracture processes such as crack initiation, propagation, and localization within the fracture process zone (FPZ). As the structural size increases, the relative influence of the FPZ diminishes, resulting in more brittle behavior. Although several numerical approaches have advanced the understanding of size effects, challenges still remain in accurately and efficiently capturing fracture processes and size-dependent behavior. In this context, the present study applies a recently developed approach, namely the position-based mesh fragmentation technique, which employs high-aspect-ratio solid elements to explicitly simulate concrete fracture. The study investigates size effects in concrete beams subjected to three-point bending under both pure Mode I and mixed-mode loading conditions, considering unnotched and notched specimens with different notch-to-depth ratios. The numerical results are complemented by a comprehensive statistical analysis, including quality indicators that provide a benchmark reference for future comparisons. Average computational times are also reported, providing benchmark values for efficiency comparisons that are rarely addressed in the literature. Moreover, the study provides insights into the influence of the FPZ and boundary conditions on structural strength and failure modes, establishing an efficient and statistically validated numerical framework for predicting size effects in concrete structures. Additionally, the numerical and experimental results are compared using Bažant’s size effect law, allowing the assessment of the numerical framework in terms of its capability to reproduce the scaling behavior of nominal strength with increasing structural size.

This study introduces a novel educational software for the analysis of 2D truss structures using a position‐based Finite Element Method (FEM). The software, named Truss Positional Finite Element Method Program (TPFEM), employs a Half‐Edge data structure to efficiently manage the geometric and topological information of truss elements. This combination enhances computational performance and supports a dynamic graphical user interface (GUI), allowing users to interactively manipulate and visualize truss structures in real time. Designed specifically for educational purposes, TPFEM offers a platform for students to explore both geometric and physical nonlinearities, going beyond traditional linear analysis. Unlike existing educational tools, which typically rely on classical displacement‐based FEM, TPFEM uniquely integrates a positional FEM approach, providing a more intuitive understanding of geometric nonlinearities in truss systems. The program can perform static, transient dynamic, and free vibration analyses, as well as nonlinear physical simulations using a one‐dimensional plasticity model. Additionally, TPFEM is built with usability in mind, ensuring accessibility for both students and educators. The software's capabilities are demonstrated through several examples, highlighting its potential as a valuable educational tool in structural engineering. By combining positional FEM with the Half‐Edge data structure in an interactive educational environment, TPFEM provides a unique and intuitive approach to learning nonlinear structural behavior. The software and its documentation are available on its website ( GitHubRepository ).

Although in many situations it is possible to consider civil structures as supported on immovable foundations, in situations of moderate settlement it is necessary to consider the interaction between the soil and the structure, considering both flexible. Soil deformability can cause considerable changes in support reactions and stresses, which are fundamental for structural design. In turn, this change in the loads transmitted to the soil causes the deformations presented by the soil to change. Thus, this work deals with coupling a formulation for nonlinear analysis of spatial trusses with a solution to the problem of settlements in stratified soils. The truss analysis follows the positional formulation of the finite element method (FEM), as presented in Coda (2018), while the soil domain analysis is based on fundamental cases of elasticity theory, as presented in Pinto (2006), Mundim, Cruvinel and Cavalcanti (2014), and in Poulos and Davis (1980), considering the characteristics of the soil based on geotechnical field tests. The calculation of soil deformation considers both the influence of direct loads on the support considered and the indirect effects of tensions due to adjacent supports, considering the variation in tension spatially, that is, along the depth of the soil below the foundation and of the adjacent region. The computational code for dynamic analysis of three-dimensional trusses is verified using analytical and numerical examples from the literature, showing compatible results. In the context of soil mechanics, the code is also verified through examples, considering homogeneous, stratified soils with three-dimensional stress propagation. Finally, examples are studied considering the soil-structure interaction, where the degree of influence of the soil-structure interaction on the results of the requesting efforts is evaluated.