Resumo em Inglês:

Abstract This article presents a numerical model and analyses of the dynamic response of structures supported by groups of piles. The model uses a finite element discretization to represent arbitrarily-shaped structures, and a coupled finite-boundary element scheme to represent the embedded pile group. This scheme properly takes into account the energy transferred from the structure to the piles and between piles through the soil, so that the effect of dynamic pile-soil-pile interaction in the response of the structure can be studied. The model is used to analyze the dynamic response of a wind turbine tower and foundation blocks of various designs. The results show that some common design approximations may result in considerable misrepresentation of the response of these structures. The model is also used to analyze cases in which the only source of excitation to a structure comes through the soil from neighboring structures. The results showed that the farther the structure is from the source of vibration, the lower its amplitude of vibration and that the taller the structure, the lower its resonant frequencies. These analyses are only possible with models like the one presented in this article, which are able to describe the energy exchanged through the soil by the piles in a group.

Resumo em Inglês:

Abstract Accurately measuring a crack length is a crucial aspect of experimental fracture tests. In this work, we present an innovative application of the A* (A-star) shortest path methodology to track different shapes of cracks from numerical simulations. This approach is highly efficient, significantly improving the speed and accuracy of crack length measurements. Furthermore, we introduce a modified weight cost function that follows the crack path in the damage field, enhancing the accuracy of our method. The effectiveness of the proposed procedure is shown by fabricating damage fields with different geometry and good agreement when compared to the exact values. In addition, we evaluate a time-dependent crack propagation case, achieving high accuracy. We present all features and steps of the procedure to showcase its efficacy in accurately measuring the length of a crack path. Finally, we validate our method using a phase-field fracture framework and compare it with the compliance technique. The results show that the proposed method is applicable in finite element analyses with recovering accurate results.

Resumo em Inglês:

Abstract Recent research on structural dynamics has steered towards elastic metamaterials, as band gap phenomena can be explored to mitigate vibration. A challenge in their design is the determination of configurations resulting in wider band gaps in lower frequency ranges. Since some level of damping is unavoidable in any real engineering structure, it is necessary to extend the current methodology of optimal design to provide a deeper understanding of how damping may affect the desired performance. Therefore, the main objective of this article is to propose and evaluate a numerical procedure for the optimization of band gaps in damped metamaterials. Specifically, a modified objective function that incorporates an evanescence index integral is used and two optimization schemes are implemented, each reflecting whether the structure is undamped or damped. It is shown that the optimal damped metamaterial has wider range of attenuation than the undamped optimal one, but with decreased attenuation levels. The optimization procedure is validated numerically for a finite structure, demonstrating reduced transmissibility of wave motions.

Resumo em Inglês:

Abstract A metaheuristic approach for variable axial composites considering multiobjective optimization is investigated. The proposed methodology is based on the combination of three main parts: a methodology for defining the orientation of the fibers in the laminate, a structural analysis program (based on the Finite Element Method) and an optimization algorithm. It is important to highlight that a radial basis function (RBF), which describes a smooth fiber pattern, is generated using control points. The novelties of the present methodology consist of a proposal for a generalized parameterization technique, which allows the investigation of mechanical strength and stress concentration of variable axial composites. Thus, NSGA-II multiobjective genetic algorithm is used as optimization tool to define the fiber orientations. Besides, ax metaheuristic approach is used in situations when it is desirable to simultaneously minimize the stress concentration factor (Kt) and a failure criterion index (FI or Φ). Two case studies are investigated: a double notched plate and a tube with a transverse hole.

Resumo em Inglês:

Abstract Optimization methods for curvilinear reinforcements placement aims to improve mechanical response of structure. Whenever a gradient-based method is used to optimization, it is necessary arbitrate an initial placement for the fibers. This initial guess has influence on the result. This work aims to observe the influence of the initial positioning of straight carbon fiber in epoxy resin plates, which had their compliance minimized by Sequential Linear Programming. The maximum displacement is observed too, even if it is not an objective function. The case studies were carried out on the same structure and the number of fibers and its slope were changed. Variation of the force slope was also evaluated. The results confirmed an influence of the initial slope in results. The addition of a greater number of fibers does not always cause a better performance in the design. To achieve the best results, it is essential that the initial arrangement be configured in such a way as to provide proximity of the ends of the fibers and the forces and supports. It's important to try to place the fibers with axial directions close to the axial direction of the force.

Resumo em Inglês:

Abstract It is well known that boundary integral equations are exact mathematical representations of the governing differential equations of a boundary value problem when the integrals are written over a closed-shape boundary representation (B-representation) of the domain, usually reffered to as a watertight B-representation. However, practical geometric design technics (namely, NURBS surfaces) often do not render a watertight B-representation. Non-watertight geometric models with small gaps and overlaps are often generated in the design stage of projects. Based on a proposed surface-independent discretization approach, the present study investigates how unsought gaps affect the response of boundary element models of linear elasticity problems. The developed surface-independent discretization is applied to discretize multiple-patches NURBS B-representation geometries. Linear triangular and quadrilateral elements are adopted to discretize the independent surfaces. Generalized discontinuous elements at the edges of the visible areas of the NURBS parametric spaces are detected by a Level Set function. An offset collocation strategy is adopted for the nodes at the edges of the visible part of the parametric spaces. Thus, singularities and near singularities due to collocation are avoided in the BEM equations. The influence of gaps in the convergence of the L2-norm of boundary displacement error is verified in a 3D example with an available analytical solution. A second example with available numerical solution is analyzed with a non-watertight BEM discretization for qualitative boundary field validation. Finally, a non-watertight B-representation geometry of a crane hook is analyzed. The obtained results have pointed out that, as long as the gaps (and overlaps) are small enough, BEM models built up from non-watertight geometries may produce valuable solutions for practical purposes.

Resumo em Inglês:

Abstract Topology optimization research has focused on structures of a single domain or component. The single component configuration fails to capture the complexity of real multi-component structures. It is necessary to develop new methods and numerical strategies to solve multi-component systems. In this work, we propose a new approach considering a sequential method of topological optimization in multi-component systems. The proposed algorithm for topology optimization of multi-component systems is sequential. It optimizes the first component, the result found is included in the analysis of the optimization of the next component and thus it continues analyzing consecutively all the components until the last one. This methodology is the only one that performs sequential optimization using open-source tools. The implementation of sequential method is developed in four processes: development of the multi-component mesh, numerical structural analysis through the FEM, sensitivity analysis and a final optimization. A comparison is made with an optimization of multi-component systems in a normal way using three commonly seen examples.

Resumo em Inglês:

Abstract This work investigates the transient response of bar structures interacting with three-dimensional soil profiles. The structures are modeled by the Finite Element Method (FEM) and the soil models are described by a three-dimensional Boundary Element Formulation (BEM) in the frequency domain. A classic modal analysis is performed on the structure in terms of the relative displacements with respect to the soil. The dynamic response of the structure is coupled to the soil response, aiming to obtain frequency response functions (FRFs) of the soil-structure system. A new set of modal parameters are extracted from the FRFs of the coupled system. These new parameters allow for the synthesis of a set of orthogonal differential equations in the time domain. These equations are integrated by a classical numerical scheme resulting in the transient response of the structure interacting with the supporting soil. It is shown that for soil profiles that present eigenfrequencies, the system modal basis must be expanded to properly include the soil dynamics. The cases of a structure interacting with a homogeneous half-space and with a horizontal layer over a rigid stratum are considered. The results presented for both soil models are consistent.

Resumo em Inglês:

Abstract Glued-Laminated Timber (GLULAM) is a widely-used building material, popular for its strength, durability, and sustainability. It is created by bonding together layers of wood, making it a common choice for civil structures. In this study, Bi-directional Evolutionary Structural Optimization (BESO) is proposed to improve the performance of GLULAM structures. By positioning steel bars within the GLULAM structure, the objective is to increase the structure's stiffness and enhance its structural integrity. To achieve this, the study introduces the concept of a sub-design domain and utilizes optimization theory to determine the optimal placement of the steel bars. The finite element problem is solved using ANSYS software, while the topological optimization problem is solved using MATLAB software. The use of sub-design domains and optimization theory enables the optimal placement of the reinforcements to be determined. The results of this study demonstrate the potential of this approach for enhancing the structural integrity and stiffness of GLULAM structures under static loads.

Resumo em Inglês:

Abstract Deformation in polymers is highly dependent on molecular structures and motion and relaxation mechanisms, which are highly influenced by temperature and mechanical load history. These features imply that some models can fit for specific classes of polymers and not for others; moreover, these models also include several non-linearities, which turns out to be challenging for computational simulation. This work develops and simulates a thermal-structural phase-field model for the polytetrafluorethylene (PTFE) polymer. The constitutive multimechanism model used considers a non-isothermal non-linear elastoviscoplastic model, able to represent elastic molecular interactions, and viscoplastic flow from polymer segments. Material parameters for complex rheological models are addressed, through a genetic algorithm, to adjust curves from simulated models to stress-strain experiments available in literature. Results of stress-strain curves, followed by rupture, for a temperature ranging from -50° C to 150° C are plotted in comparison with experimental results, presenting a reasonable fit.

Resumo em Inglês:

Abstract This article presents novel non-singular influence functions for homogeneous media. These solutions are displacement and stress fields of a three-dimensional, isotropic full-space under time-harmonic vertical and horizontal loads, which can be used within the framework of boundary element methods to solve elastodynamics problems in engineering practice. In order to account for sharply-varying contact tractions that may occur in such problems, the solutions in this article consider a biquadratic distribution of the loads within the loaded surface. In the present derivation, sets of Fourier transforms are used to uncouple the medium's equation of motion and enable the incorporation of boundary conditions directly as traction discontinuities. The article brings selected numerical results for various geometric and constitutive parameters.

Resumo em Inglês:

Abstract A consistent model that properly captures the behavior of materials when submitted to loads and at the same time considers the influence of damage growth in the material properties is a challenging task. Specially in brittle materials, due to the mechanism of cleavage, as the damage grows, the material mechanical response is differently degraded according to the load direction considered, characterizing an anisotropic damage. A fourth-order degradation tensor is used with a phase field framework in order to model the induced damage anisotropy without the need of defining the damage principal direction a priori. The transient non-linear coupled system of equations is solved using appropriate time integration procedures. Due to the mild non-linearities, standard linearization methods are not considered. The numerical examples illustrate the model’s features and conclude that the adopted approach is able to simulate anisotropic damage totally driven by the strain state of the material.