Abstract in English:Abstract The topological derivative measures the sensitivity of a shape functional with respect to an infinitesimal singular domain perturbation, such as the insertion of holes, inclusions or source-terms. The topological derivative has been successfully applied in obtaining the optimal topology for a large class of physics and engineering problems. In this paper the topological derivative is applied in the context of topology optimization of structures subject to multiple load-cases. In particular, the structural compliance under plane stress or plane strain assumptions is minimized under volume constraint. For the sake of completeness, the topological asymptotic analysis of the total potential energy with respect to the nucleation of a small circular inclusion is developed in all details. Since we are dealing with multiple load-cases, a multi-objective optimization problem is proposed and the topological sensitivity is obtained as a sum of the topological derivatives associated with each load-case. The volume constraint is imposed through the Augmented Lagrangian Method. The obtained result is used to devise a topology optimization algorithm based on the topological derivative together with a level-set domain representation method. Finally, several finite element-based examples of structural optimization are presented.
Abstract in English:Abstract For many practical applications in engineering, a complex structure shows linear elastic behavior over almost all its extension, but exhibits confined plasticity contained in some small critical regions, e.g. stress concentrations in fillets and sharp internal corners. The behavior of C0- and Ck-GFEM is investigated in this class of problems. The first goal of this study is to verify the actual formulation of the Ck-GFEM for two-dimensional elastoplasticity, as a modification of the C0-GFEM formulation. The Ck-GFEM is based on a set of basis functions with Ck continuity over the domain. The approximation functions are constructed from a Ck continuous partition of unity, over which polynomial enrichment functions (or any special function) can be applied, in the same fashion as in the usual C0-GFEM. In this way, the finite element approximations show continuous responses for both displacements and stresses across inter-element interfaces. An investigation is performed to assess the behavior of higher-regularity partitions of unity against conventional C0 counterparts. The irreversible response and hardening effects of the material is represented by the rate independent J2 plasticity theory with linear isotropic hardening of material and von Mises yield criteria, being considered only monotonic loading and the kinematics of small displacements and small deformations. The focus herein is to enlighten any possible advantage of smoothness in the presence of plastification phenomena, seeking for improvements in capturing the evolution of the process zone.
Abstract in English:Abstract The Modified Global Green's Function Method (MGGFM) is an integral technique that is characterized by good accuracy in the evaluation of boundary fluxes. This method uses only projections of the Green's Function for the solution of the discrete problem and this is the origin of the term 'Modified' of its name. In this paper the local strategy for calculating the projections of Green's function using de Finite Element Method (FEM) are detailed. The numerical examples show some aspects of the method that had not yet been observed and good results for the flux in all nodes of the mesh.
Abstract in English:Abstract The propagation of compaction waves in a stationary foam block subjected to an impact by a small mass is studied in order to examine the mechanism of compaction within the primary and reflected stress waves. The analysis is focused on aluminium strain rate insensitive foam that exhibits strain hardening under quasistatic compression. A theoretical approach is applied using a uniaxial model of compaction in which the compacted strains, being functions of the velocity variation, are not predefined but are obtained as a part of the solution. The present approach allows one to obtain the strain histories and strain distributions within the primary compaction wave as well as within the reflected wave, which propagates in a media with non-uniform density increasing monotonically in the direction of loading. FE simulations considering aluminium based foam Cymat with density 411.5 kg/m3 are carried out in order to verify the proposed theoretical model. A comparison between the impact velocity attenuation predicted by the present model and classical Rigid Perfectly-Plastic Locking material model for cellular materials is discussed.
Abstract in English:Abstract This work presents a new methodology for the parametric optimization of piezoelectric actuators installed in laminated composite structures, with the objective of controlling structural vibrations. Problem formulation is the optimum location of a Macro Fiber Composite (MFC) actuator patch by means the maximization of the controllability index. The control strategy is based on a Linear Quadratic Regulator (LQR) approach. For the structural analysis, the modeling of the interaction between the MFC and the structure is made taking into account the active material as one of the orthotropic laminate shell layers. The actuation itself is modeled as an initial strain arising from the application of an electric potential which deforms the rest of the structure. Thereby, modeling the electric field and the electromechanical coupling within the actuator is avoided because these effects are considered analytically. Numerical simulations show that the structural model presents good agreement with numerical and experimental results. Furthermore, the results show that optimizing the location of the actuator in the structure helps the control algorithm to reduce induced structural vibration.
Abstract in English:Abstract This work reviews the developments of Boundary Element Method formulations to solve several types of plate bending problems, including non-linear bending. The formulation is developed and solved using the standard BEM procedure, and different integration approaches were discussed and tested. Object oriented implementation issues are commented. Results were obtained for linear and non-linear elastic bending as well as buckling of selected cases of thick plates, including cases of step variation in thickness under large displacements regime.
Abstract in English:Abstract The application of gradient-based methods to structural optimization problems usually requires the determination of displacement sensitivities with respect to design variables. In this regard, it is important to have at hand comprehensive methods for sensitivity analysis, which show stability, efficiency and accuracy. Particularly, application of the semi-analytical method for linear and nonlinear problems is generally a good trade-off between formulation simplicity and accuracy. In spite of that, semi-analytical methods are known to behave pathologically for shape design variables when the structure is subjected to rigid rotations. A large number of solutions for this problem have been presented in last years, although the formulation involved is generally not trivial, especially in the nonlinear case. A recent method, which adopts the semi-analytical approach and uses complex variables has rendered very promising results for all the aforementioned aspects: stability, efficiency and accuracy. Additionally, it is simple to codify. The present contribution is concerned with the application of this sensitivity analysis method to geometrically nonlinear truss problems. To this end, a finite element formulation is presented and displacement sensitivities are evaluated with respect to material and shape design variables. The results are compared to those obtained using the semi-analytical method with real variables and to global finite differences. An example demonstrates the potentiality of this new approach.