As mulheres têm passe livre para se tornarem policial militar feminina,atendendo aos mesmos requisitos que os homens. O que muda em alguns casos é a estatura mínima exigida: para homens, 1,60m. Para mulheres, 1,55m. Ambos descalços.
Interesting engineering and industrial applications of the method have been also presented. Obliviously, many other applications of the method have been reported in the literature. In this review, we limited our analysis only to the applications of PFEM to hydraulic engineering, granular flows, manufacturing and landslides problems. For all the mentioned fields, the potential of the PFEM has been demonstrated and the main works have been referenced.
The nodes insertion can be done inside the element (for example, in its center of mass, Fig. 7b) or along an edge (for example, in the middle of its largest edge, Fig. 7c).
For continuum mechanics problems, in a Eulerian approach, the finite element mesh is fixed and the material moves across the grid, being the mesh nodes dissociated from physical particles. Due to the relative motion between the material and the grid, convective terms appear in the definition of the time derivatives. Eulerian meshes are particularly suited for large deformation problems in enclosed domains, as those generally considered in standard Computational Fluid Dynamics (CFD). On the other hand, they do not provide a natural definition of evolving interfaces (like a free surface in fluid flows), calling for ad-hoc techniques such as level set [97] or volume of fluid [42] approaches.
It is also important to remark that equations of motions solved in step 4, can be non-linear and so they may require an iterative solution scheme. For those formulations using historical variables, e.g. in non-linear solid mechanics (Sect. 5), a remap of the historical variables stored at the Gauss points on the new mesh is needed before step 4.
O PFMEA (ou FMEA de processo) é uma metodologia analítica, utilizada para garantir que problemas potenciais tenham sido percebidos durante todo o processo para desenvolvimento do produto.
The first PFEM-solid formulation [95] was applied to complex industrial processes, such as metal forging, machining, or powder filling, and showed the capability of the method to track accurately the deforming shape of the material and to deal with the complex interactions between the different solid bodies. This first work opened up the way to many other PFEM-solid formulations. References [84, 104, 106, 107] applied their PFEM-solid methods to different types of manufacturing processes, [4, 11, 12] analyzed tunneling and excavation applications, while bed erosion in river dynamics was tackled in [81, 82, 86]. Several PFEM-solid formulations have been proposed in the field of soil mechanics and geotechnal engineering, especially for the modelling of frictional materials and granular flows [10, 24, 56, 66, 127, 128] and for different types of geomechanics problems [75,76,77,78]
Excluding the FEM solution of the differential equations, which differ for each specific problem, the PFEM solution algorithm is independent on the physics of the problem. A general solution scheme of the PFEM can be summarized as follows.
The main reason that explains the success of PFEM in the framework of fluid–structure interaction (FSI) analysis, lays undoubtedly in its accurate tracking of moving interfaces. This feature is extremely useful for the solution of a wide range of engineering and industrial problems with fluid–solid interfaces undergoing large motions.
The PFEM remeshing procedure consists of erasing all the elements of the distorted mesh and creating the new tessellation over the cloud of points composed by the mesh nodes (Sect. 2). For PFEM-solid formulations using Gaussian integration, this remeshing strategy implies that all elemental information must be transferred from the elements of the old mesh to the nodes, and then, from these to the new mesh elements.
Adding and removing nodes can also be done without altering the total number of nodes. In this case, a new node is added only if a node can be removed from another position. Doing so, the mesh size tends to remain constant during the analysis. Moreover, this is also useful from the implementation point of view, as it enables the use of simplified data structure with dimensions fixed in time.
Another important implication of remeshing on the FEM solution is related to the continuous elimination of the elements. In standard methods using Gaussian integration, this makes necessary the implementation of specific techniques for the recovery of historical variables [96]. Nevertheless, remapping can be avoided in case of using a nodal integration scheme, as the historical variables are stored at the nodes [126]. More details can be found in Sect. 5.1.
Em novembro de 1991, pela primeira vez uma policial feminina assumiu o comando da Cia P Fem: a Capitão Rita Aparecida de Oliveira, policial militar formada em Engenharia Química, pela Universidade Federal do Paraná, e em Direito, pela Faculdade de Direito de Curitiba.
Another possibility is to modify the alpha-shape criterion according to error estimation considerations. For example, in manufacturing processes to simulate complex large deformation, the insertion of particles is based on the equidistribution of the plastic power and the removal were driven by a Zienkiewicz-Zhu error estimator [104, 106].
are removed from the mesh. Figure 4 shows the Delaunay triangulation coupled with the alpha-shape scheme for the example introduced previously.
The PFEM combines the accuracy and robustness of mesh-based techniques with the advantages of particle-based methods. The PFEM discretizes the physical domain with a mesh on which the differential governing equations are solved with a standard finite element approach. Following a Lagrangian description, the mesh nodes move according to the equations of motion, behaving like particles and transporting their momentum together with all their physical properties. In the PFEM, the mesh distortion issue, typical of Lagrangian mesh-based solvers, is overcome by generating a new mesh when the current one gets too distorted. However, unlike the previously mentioned methods, to avoid remapping from mesh to mesh, the PFEM keeps the nodes of the previous mesh fixed. The new connectivity is built using the Delaunay Tessellation and a specific technique is used to identify internal and external boundaries. The obtained mesh is then used as the support over which the differential equations are solved in a standard FEM fashion.
The second possibility to avoid mesh distortion is a remeshing technique. Here, when the Lagrangian mesh becomes too distorted, a new mesh is created with an ad-hoc procedure. An example of the application of this technique to fluid flow problems can be found in [36], where the authors reconstruct locally triangular meshes to solve fluid dynamics problems with a finite difference approach. Alternatively, in [3] a new finite element mesh is built from scratch whenever the elements become too distorted. Muttin et al. [80] uses a Lagrangian finite element method to simulate metal casting problems with an automatic remeshing technique to avoid mesh distortion. Radovitzky and Ortiz [100] and Malcevic and Ghattas [68] propose a continuous and adaptive remeshing at each time step. All these Lagrangian approaches are based on some form of remeshing techniques. In all cases, when a new mesh is generated, the results need to be remapped from the old to the new mesh. Unavoidably, these operations introduce unwanted numerical diffusion into the numerical solution [36].
An interesting feature of PFEM-2 is the possibility to use an explicit time integration independently on the Courant number. The method remains explicit and stable independently on the mesh size. The time step is established following only accuracy considerations, besides the limits given by the Fourier number.