An Explicit Finite Element Integration Scheme for Linear Eight Node Convex Quadrilaterals Using Automatic Mesh Generation Technique over Plane Regions

This paper presents an explicit integration scheme to compute the stiffness matrix of an eight node linear convex quadrilateral element for plane problems using symbolic mathematics and an automatic generation of all quadrilateral mesh technique , In finite element analysis, the boundary problems governed by second order linear partial differential equations,the element stiffness matrices are expressed as integrals of the product of global derivatives over the linear convex quadrilateral region. These matrices can be shown to depend on the material properties and the matrix of integrals with integrands as rational functions with polynomial numerator and the linear denominator (4+ ) in bivariates over an eight node 2-square (-1 ).In this paper,we have computed these integrals in exact and digital forms using the symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme is illustrated by computing the Prandtl stress function values and the torisonal constant for the square cross section by using the eight node linear convex quadrilateral finite elements.An automatic all quadrilateral mesh generation techniques for the eight node linear convex quadrilaterals is also developed for this purpose.We have presented a complete program which automatically discritises the arbitrary triangular domain into all eight node linear convex quadrilaterals and applies the so generated nodal coordinate and element connection data to the above mentioned torsion problem. Key words: Explicit Integration, Gauss Legendre Quadrature, Quadrilateral Element, Prandtl’s Stress Function for torsion, Symbolic mathematics,all quadrilateral mesh generation technique

Numerical Integration over Curved Domains Using Convex Quadrangulations And Gauss Legendre Quadrature Rules

This paper presents a numerical integration formula for the evaluation of where and is any curved domain in . That is a closed domain with boundary composed of N oriented piecewise curved segments with end points , and . We Join each of these curved segments to a reference point interior to the domain . This creates N triangles ) in and each of these triangles have one curved side and two straight sides. We transform each into a standard triangle T which also transforms the integrand to = . We then divide T into right isosceles triangles of side lengths 1/m units. These triangles will be finally divided into three special quadrilaterals . This process can be expressed as where represent the transformed forms of the integrand over the domains T, and . We approximate the curved segments by a parabolic arc which passes through the four points of the curved segment, the two end points , and the two intermediate points of . Proposed numerical integration formula is applied to integrate over a curved domain in the shape of lunar model for complicated integrands

Evaluation of a quality improvement intervention to reduce anastomotic leak following right colectomy (EAGLE): pragmatic, batched stepped-wedge, cluster-randomized trial in 64 countries

Background Anastomotic leak affects 8 per cent of patients after right colectomy with a 10-fold increased risk of postoperative death. The EAGLE study aimed to develop and test whether an international, standardized quality improvement intervention could reduce anastomotic leaks. Methods The internationally intended protocol, iteratively co-developed by a multistage Delphi process, comprised an online educational module introducing risk stratification, an intraoperative checklist, and harmonized surgical techniques. Clusters (hospital teams) were randomized to one of three arms with varied sequences of intervention/data collection by a derived stepped-wedge batch design (at least 18 hospital teams per batch). Patients were blinded to the study allocation. Low- and middle-income country enrolment was encouraged. The primary outcome (assessed by intention to treat) was anastomotic leak rate, and subgroup analyses by module completion (at least 80 per cent of surgeons, high engagement; less than 50 per cent, low engagement) were preplanned. Results A total 355 hospital teams registered, with 332 from 64 countries (39.2 per cent low and middle income) included in the final analysis. The online modules were completed by half of the surgeons (2143 of 4411). The primary analysis included 3039 of the 3268 patients recruited (206 patients had no anastomosis and 23 were lost to follow-up), with anastomotic leaks arising before and after the intervention in 10.1 and 9.6 per cent respectively (adjusted OR 0.87, 95 per cent c.i. 0.59 to 1.30; P = 0.498). The proportion of surgeons completing the educational modules was an influence: the leak rate decreased from 12.2 per cent (61 of 500) before intervention to 5.1 per cent (24 of 473) after intervention in high-engagement centres (adjusted OR 0.36, 0.20 to 0.64; P < 0.001), but this was not observed in low-engagement hospitals (8.3 per cent (59 of 714) and 13.8 per cent (61 of 443) respectively; adjusted OR 2.09, 1.31 to 3.31). Conclusion Completion of globally available digital training by engaged teams can alter anastomotic leak rates. Registration number: NCT04270721 (http://www.clinicaltrials.gov)