One of the first Meshfree methods is called the Smooth Particle Hydrodynamics (SPH) method and was developed by Lucy (L. B. Lucÿ, 1977) and Gingold and Monaghan (R. A. Gingold and J. J. Monaghan, 1977) in order to solve astrophysics problems and, later on, fluid dynamics problems (Bonet & Kulasegaram, (2000); Monaghan, (1988); Libersky, Randles, Carney, & Dickinson, (1997)). Libersky (L.D. Libersky, A.G. Petscheck, T.C. Carney, J.R. Hipp, 1993) were the first to employ SPH in solid mechanics (impact). Since its original version, SPH suffered from spurious instabilities and inconsistencies (Swegle, Hicks, & Attaway, (1995); Ted Belytschko, Guo, Liu, & Xiao, (2000); Xiao & Belytschko, (2005)), many improvements were proposed(T. Belytschko et al., (1996); Libersky et al., (1997); Bonet & Kulasegaram, (2000); Johnson & Beissel, (1996)). While SPH and their corrected version were based on a strong form, other methods were developed in the 90s, based on a weak form, most of them in solid mechanic applications. The element-free Galerkin (EFG) method (T. Belytschko et al., 1995) was developed in 1994 and was one of the first meshless method based on a weak global form. This method is one of the most popular meshlessmethods, and it was developed form the Diffuse Element Method (DEM) (Nayroles, Touzot, & Villon, 1992), which was the first method using the Moving Least Squares (MLS) (Lancaster & Salkauskas, 1981) approximants. One year later, the Reproducing Kernel Particle Method (RKPM) (W. K. Liu, Jun, & Zhang, 1995) was developed.
This work moves around the numerical solution of problems described either by differential or by integral equations. I deal chiefly with the implementation of the meshless techniques applied to such problems. This is not a work on numerical analysis, in which the application of tools from Functional Analysis is of utmost importance. I shall deal with such advanced subjects (rigorous analysis of convergence rates, derivation of upper and lower bounds for solutions, theorems, stability of solutions, normed spaces and so on) in a future work. The reason why I have somehow postponed that is simple. Many of the techniques described in this work are here applied to problems from Electrical Engineering for the first time. There was no book or paper I could resort to in order to find something dealing with meshlessmethods in Electromagnetism in a simple way. So I had to begin from the scratch. I compare it to the sowing of a field. In order for it to produce something, the herbs must be removed, the soil be revolved, the seeds must be watered. All of this has to be carried out before the plants begin to bear fruit; actually, even before they are born! So with this work, which aims at cleaning the terrain for the development of future sophisticated applications and more rigorous mathematical analyses. In
The first above mentioned technique has been used by Cavalcante et al. 2007 within the mesh-based FVM framework for functionally graded materials and also by Li et al. 2003 in the 3D formulation of the MLPG meth- od to problems with singularities and material discontinuities. In the latter, the heterogeneous medium is sepa- rated into isolated, homogeneous parts and then continuity constraints are enforced at the interface to ‘reconnect’ the pieces. To accomplish the ‘separation’, meshless approximation function applied separately within each ho- mogeneous part and therefore domains of influence are truncated at the material interfaces. Also, local sub- domains, which partially cut by the interface, are redefined to locate entirely inside the boundaries. In spite of the simple concept of this technique, the presence of truncated domains of influence could introduce some mesh de- pendency into the solution Cordes and Moran 1996, Li et al. 2000 ; Furthermore, re- definition of local sub- domains and domains of influence could be difficult and computationally expensive de Borst 2008 . The so- called enrichment technique has been applied both in the area of mesh-based and meshlessmethods. Melenk and Babuška 1996 enriched the standard finite element approximation, Belytschko and Black 1999 set up the frame of the extended FEM XFEM and Belytschko et al. 1996 implemented it within the EFG method for intro- ducing discontinuous derivatives into the solution. Batra et al. 2004 utilized this technique in the 1D meshless formulation of FVM to analyze heat conduction in a bimetallic circular disk. Recently, Yoon and Song 2014 and Hu et al. 2015 applied this technique in order to handle discontinuities in heterogeneous media. Using the en- richment technique is interesting since a fix and regular domain discretization can be applied and domain dis- cretization cost is reduced to a minimum An et al. 2011 . In this paper, based on the enrichment technique used already by Krongauz and Belytschko 1998 , a 2D formulation within the meshless FVM framework is proposed to handle material discontinuity.
where c , b and p are positive constants and, the functions f and ψ are assumed to be sufficiently smooth. The main shortcoming of mesh-based methods such as the finite element method (FEM), the finite volume method (FVM) and the boundary element method (BEM) is that these numerical methods rely on meshes or elements. In the last two decades, in order to overcome the mentioned difficulties some techniques the so-called meshless meth- ods have been proposed . This method is used to establish system of algebraic equations for the whole domain of the problem without the use of predefined mesh for the domain discretization so that set of nodes scattered within the domain of the problem as well as sets of nodes on the boundaries of the domain to represent (but not to discretize) the domain of the problem and its boundaries is used. These sets of scattered nodes are usually called field nodes. There are three types of meshlessmethods: meshlessmethods basedon weakforms such as the ele- ment free Galerkin (EFG) method [38, 39], meshlessmethods based on collocation techniques (strong forms) such as the meshless collocation method based on radial basis functions (RBFs) [40–42] and meshlessmethods based on the combination of weak forms and collocation technique. Due to the ill-conditioning of the resultant linear systems in RBF-collocation method, various approaches are proposed to circumvent this problem, Refs. [43–46] being among them. The weak forms are used to derive a set of algebraic equations through a numerical integration process using a set of quadrature domain that may be constructed globally or locally in the domain of the problem. In the global weak form methods, global background cells are needed for numerical integration in computing the algebraic equations. To avoid the use of global background cells, a so-called local weak form is used to develop the meshless local Petrov-Galerkin (MLPG) method [47–52, 54]. When a local weak form is used for a field
The finite element method (FEM) has been the most frequently used numerical method in engineering during the three past decades. It has been used in most fields of applied sciences such as computational solid mechanics [1, 2, and 3] and so on. Mesh-based methods are not well suited to the problems associated with extremely large deformation and problems associated with frequently remeshing. To avoid these drawbacks of the FEM, a new class of numerical methods, meshlessmethods (also called mesh-free methods) have been developing [4, 5] in the recent decade. These methods have become an important tool in computational solid mechanics, owing to their advantages over the traditional finite element method (FEM), finite-volume method (FVM), and finite- difference method (FDM). Meshlessmethods rely only on a group of scatter points, which means not only that the burdensome work of mesh generation is avoided, but also more accurate description of irregular complex geometries can be achieved. Furthermore, the meshless approximation has higher smoothness, and no additional post-processing is needed.
Considering the issues mentioned before, and with the intention to create new solutions that would fulfil the existing problems, meshlessmethods were created. Moreover, the stress and displacement fields produced with meshlessmethods, relating the analysis of structural problems, are, usually, much more uniform and close to the analytical solution than those created by low order element meshes (three and four nodes). On the contrary of Finite Element Methods, which uses the element mesh to obtain the approximation, meshlessmethods build the approximation based on nothing but an arbitrary nodal set, without any knowledge of the relation between nodes, at first instance. 7
The mentioned meshlessmethods were the tool to analyse composite laminated plates using different High-Order Shear Deformation Theories that approximate the in-plane displacements across the plates thickness as nonlinear functions. The theories studied – three third-order shear deformation theories, two exponential theories, one trigonometric theory and one theory that is a combination of trigonometric and exponential functions – were implemented in the algorithms of the RPIM and the NNRPIM. Thus, a wide range of results were obtained. Ambartsumian’s theory is the older HSDT studied, proposed in 1960 as an extension of the Classical Plate Theory and applied initially to anisotropic plates and shallow shells. The solutions obtained from the theory of Ambartsumian were far from remarkable in comparison to the 3D Elasticity but the merit of Ambartsumian must be recognized since it was his work and the work developed by Reddy that led the investigation about HSDT. On the other side, Mantari theory showed the best agreement with the 3D Elasticity, in particular in the sensitive aspect of the transverse shear stresses (where the purpose of using HSDT is found). Karama and Aydogdu theories were those that allowed to obtained better results, immediately after Mantari theory, despite they did not work with antisymmetric laminates.
In meshlessmethods, the most used procedures for shape function generation are the Moving Least Squares (MLS) and the Point Interpolation Method (PIM) . The MLS approximation has a great feature that the approximated field function is continuous and smooth in the entire domain with the desired order of consistency, however it does not possess the Kronecker delta property. Unlike MLS, PIM produces approximations that have the Kronecker delta property, but that are nonconforming, i.e., they are discontinuous in some regions of the domain. The Kronecker delta property is interesting
Local sensitivity analysis (LSA) is mainly used to analyze local influence of parameters on model output. Gradients of parameters vs. model output can be achieved by using LSA. LSA is valuable to systems with simple mathematical representations, fewer undeterministic parameters and easily derived sensitivity equation. LSA methods include directed derivation, finite difference, and Green function.
Objective: To evaluate the operation and surgical time of autotransplanted parathyroid in a single site comparing it to the implant performed in five and twenty locations. MethodsMethodsMethodsMethodsMethods: Patients who underwent total parotidectomy with auto implant (Ptx-AI) for secondary and tertiary hyperparathyroidism were evaluated in groups of 20 implant sites (A), 5 sites (B) and single site (C), compared as for Functional Status (FE) of the implant and the surgical time of the procedure. Four functional states were determined according to the systemic level of PTH: 1-below normal, 2-normal, 3-high, no more than three times and 4 - more than three times higher. Results Results Results Results: There were 349 patients subjected to Ptx-AI for renal hyperparathyroidism from Results 1994 to 2009. For the functional study, 101 patients were eligible for the following observations: group A (n = 30) - 16.6% EF1, 50% EF2, 23.3% EF3 and 10%EF4; group B (n = 41) - 14.6% EF1, 58.5% EF2, 22% EF3 and 4.9% EF4; Group C (n = 30) - 17% EF1, 57% EF2, 20%EF3 and 6% EF4 (p = 0.9, x 2 ). But in group C the mean operative time of implant was statistically lower (7.9
Objective: To investigate whether the abbreviation of preoperative fasting with a drink containing glutamine and maltodextrin improves organic response to surgical trauma. MethodsMethodsMethodsMethodsMethods: Thirty-six female patients adult (18-62 years) candidates for elective laparoscopic cholecystectomy were randomly divided into three groups: conventional fasting (fasting group), and two groups receiving two different diets, eight hours (400ml) and two hours before induction of anesthesia (200ml): carbohydrate (CHO) group (12.5% maltodextrin) and the glutamine (GLN) group (12.5% maltodextrin and 40 and 10g of glutamine, respectively). Blood samples were collected pre and postoperatively. Results Results Results Results Results: Twenty-eight patients completed the study. No pulmonary complication occurred. Gastric residual volume was similar between groups (p = 0.95). Postoperatively, all patients from the fasting group had abnormal glucose (> 110mg/dl), this abnormality being of 50% when compared to the CHO group (p = 0.14), and of 22.2% when compared to the GLN group (p = 0.01). All patients who had the fasting period shortened (CHO + GLN) had normal postoperative insulin, contrasting with 66.7% in the fasted group (p = 0.02). The abnormal sensitivity to insulin postoperatively rose from 32.1% to 46.4% of cases (p = 0.24), and it occurred in only 11.1% of patients in GLN group when compared to 55.5% in the fasting group (p = 0.02). Conclusion Conclusion Conclusion Conclusion: the abbreviation of preoperative fasting for two hours with maltodextrin and glutamine improves insulin Conclusion sensitivity in patients undergoing elective laparoscopic cholecystectomy.
Objective: To analyze the videos on the You Tube video sharing site, noting which points addressed in the videos related to CPR and BLS, based on the 2010 Guidelines for the American Heart Association (AHA). Methods: Methods: Methods: Methods: Methods: This was an exploratory, quantitative and qualitative research performed in the Youtube sharing site, using as keywords the expressions in Portuguese equivalent to the Medical Subject Headings (MeSH) “Cardiopulmonary Resuscitation” and “Basic Life Support” for videos that focused on the basic life support. Results: Results: Results: Results: Results: The research totaled 260 videos over the two searches. Following the exclusion criteria, 61 videos remained. These mostly are posted by individuals and belong to the category Education. Moreover, most of the videos, despite being added to the site after the publication of the 2010 AHA Guidelines, were under the older 2005 guidelines. Conclusion: Conclusion: Conclusion: Conclusion: Conclusion: Although the video- sharing site Youtube is widely used today, it lacks videos about CPR and BLS that comply to the most recent AHA recommendations, which may negatively influence the population that uses it.
Objective: To evaluate the acceptability of an educational project using A porcine model of airway for teaching surgical cricothyroidotomy to medical students and medical residents at a university hospital in southern Brazil. MethodsMethodsMethodsMethodsMethods: we developed a teaching project using a porcine model for training in surgical cricothyroidotomy. Medical students and residents received lectures about this surgical technique and then held practical training with the model. After the procedure, all participants filled out a form about the importance of training in airway handling and the model used. Results Results Results Results Results: There were 63 participants. The overall quality of the porcine model was estimated at 8.8, while the anatomical correlation between the model and the human anatomy received a mean score of 8.5. The model was unanimously approved and considered useful in teaching the procedure. Conclusion Conclusion Conclusion Conclusion Conclusion: the training of surgical cricothyroidotomy with a porcine model showed good acceptance among medical students and residents of this institution.
Objective: To evaluate the influence of end-stage liver disease and orthotopic liver transplantation in the pituitary function and hormone metabolism before and after liver transplantation. Methods: Methods: Methods: Methods: Methods: In a prospective study, serum levels of follicle stimulating hormone (FSH), luteinizing hormone (LH), estradiol (E2) and prolactin (PRL) of 30 male patients with cirrhosis were determined two to four hours before and six months after liver transplantation. The results were compared according to the Model for End-stage Liver Disease (MELD). Results Results Results Results Results: male patients with liver cirrhosis have hypogonadism. FSH was normal, but inappropriately low due to androgen failure; E2 and PRL, on their turn, were high. After liver transplantation, FSH and LH levels increased (p < 0.05), whereas E2 and PRL normalized (p < 0.05). The MELD score did not influence changes in FSH, PRL and LH, however, the more severe the cirrhosis was, the more significant was the normalization of E2 (p = 0.01). Conclusion Conclusion Conclusion Conclusion Conclusion: Patients with cirrhosis and male hypogonadism have inappropriately normal levels of FSH and LH, associated with an increase in E2 and LRP. After liver transplantation, FSH and LH increased, while E2 and PRL returned to normal. Changes in E2 levels were most pronounced in patients with MELD > 18. The severity of cirrhosis had no influence on FSH, PRL and LH.
Objective: To conduct a critical analysis of thoracotomies performed in the emergency rooms. MethodsMethodsMethodsMethodsMethods: We analyzed mortality rates and survival as outcome variables, mechanism of injury, site of injury and anatomic injury as clinical variables, and gender and age as demographic variables of patients undergoing thoracotomy in the emergency room after traumatic injury. Results Results Results Results: Of the Results 105 patients, 89.5% were male. The average age was 29.2 years. Penetrating trauma accounted for 81% of cases. The most common mechanism of trauma was wound by a firearm projectile (gunshot), in 64.7% of cases. Patients with stab wounds (SW) accounted for 16.2% of cases. Overall survival was 4.7%. Survival by gunshot was 1.4%, and by SW, 23.5%. The ERT following blunt trauma showed a 100%mortality. Conclusion Conclusion Conclusion Conclusion Conclusion: The results obtained in the Emergency Hospital of Porto Alegre POA-HPS are similar to those reported in the world literature.
Objective: To evaluate the protective effect of remote ischemic per-conditioning in ischemia and reperfusion-induced renal injuiry. MethodsMethodsMethodsMethodsMethods: Fifteen rats (Rattus norvegicus) were randomized into three groups (n = 5): Group Normality (GN), Control – Ischemia and Reperfusion (GIR) and Group remote ischemic per-conditioning (GPER). With the exception of the GN group, all others underwent renal ischemia for 30 minutes. In group GPER we performed the ischemic remote per-conditioning, consisting of three cycles of ischemia and reperfusion applied every five minutes during the ischemic period, to the left hindlimb of the rats by means of a tourniquet. To quantify the lesions we measured serum levels of creatinine and urea, as well as analyzed renal histopathology. Results Results Results Results Results: The GPER group presented with better levels of urea (83.74 ± 14.58%) and creatinine (0.72 ± 26.14%) when compared to GIR group, approaching the GN group. Histopathologically, the lower levels of medullary congestion and hydropic degeneration were found in group GPER. Conclusion Conclusion Conclusion Conclusion Conclusion: The remote ischemic per-conditioning had a significant protective effect on renal ischemia and reperfusion.
Objective: To evaluate the results of subcostal incisional hernia repair using polypropylene mesh, the technical aspects of musculo- aponeurotic reconstruction, routine fixation of supra-aponeurotic mesh and follow-up for five years. MethodsMethodsMethodsMethodsMethods: We conducted a retrospective study that assessed 24 patients undergoing subcostal incisional hernia repair with use of polypropylene mesh; 15 patients (62.5%) were female; ages ranged from 33 to 82, and 79.1% had comorbidities. Results Results Results Results Results: Early complications: three cases (12.5%) of wound infection, three cases (12.5%) of seroma, one case (4.1%) of hematoma; and one case (4.1%) of wound dehiscence. Late complications occurred in one case (4.1%) of hernia recurrence attributed to technical failure in the fixation of the mesh and in one case (4.1%) of chronic pain. There were no cases of exposure or rejection of the mesh. Conclusion Conclusion Conclusion Conclusion Conclusion: The subcostal incisional hernia, though not very relevant, requires adequate surgical treatment. Its surgical correction involves rebuilding the muscle-aponeurotic defect, supra-aponeurotic fixation of polypropylene mesh, with less complexity and lower rates of complications and recurrences.
Although abdominal CT was performed in five patients, only in two the diagnosis was established. The low sensitivity is probably due to the low resolution of the images obtained in the first two patients, in the 80s, one with suspected choledocholithiasis and another with suspected cyst of head of pancreas. They were submitted to percutaneous cholangiography and venous cholangiography, respectively. These diagnostic modalities are no longer used, since they could be replaced by less invasive and more sensitive radiological methods 1 . On the