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The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves.

The proposed algorithm computes the parametric increments of all segments to obtain the parametric coordinates of all discrete nodes. This process is recursively applied until the optimal discretization of curves is obtained. The parametric increment of a segment is inversely proportional to the number of sub-segments, which can be subdivided, and the sum of parametric increments of all segments is constant. Thus, a new expression for parametric increment of a segment can be obtained. In addition, the number of sub-segments, which a segment can be subdivided is calculated approximately, thus avoiding Gaussian integration.

The proposed method can use less CPU time to perform the optimal discretization of three-dimensional curves. The results of curves discretization can also meet requirements for mesh generation used in the preprocessing of numerical simulation.

Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the algorithm saves in the process of curve discretization.

To provide an advanced cutting trajectory algorithm for the profiled edge laminae (PEL) rapid tooling (RT) process, which is ideally suited for large‐scale dies and molds. The process involves assembling an array of laminae whose top edges are simultaneously profiled and beveled using a line‐of‐sight cutting method based on a CAD model of the intended tool surface.

The cutting profiles for an individual tool lamina are based on intersection curves obtained directly from the CAD model, and generated with exact geometrical accuracy. Two adjacent slice profiles, which define a lamination's top edge and are represented as polylines, are stitched together using an adaptive surface reconstruction algorithm. A cutting trajectory algorithm then develops a series of suitable cutting vectors (i.e. position and cutting direction) that minimize abrasive waterjet (AWJ) cutting errors due to non‐uniform motion and variations in kerf geometry resulting from process parameter variations. The proposed cutting trajectory generation process is demonstrated virtually for an actual production tool.

The proposed algorithm yields well‐behaved AWJ cutting trajectories for individual lamina used in a PEL tool that are better than those obtained using any other algorithm found in the literature.

The algorithm is intended for use with AWJ cutting of PEL tool surfaces. Suggested future research includes assessment of the algorithm for other lamina cutting methods including laser cutting and wire‐type electro‐discharge machining, extending the algorithm to handle conformal cooling/heating channels and internal cavities, and application of the algorithm to several industrial tool case studies.

The algorithm generates cutting trajectories directly from CAD geometry that are ideal for AWJ cutting of profiled edge lamina. It will simply make industrial implementation of the PEL RT process easier.

This paper provides a new cutting trajectory algorithm for the PEL RT process that is a significant improvement over comparable algorithms proposed in the literature.

A scheme is presented for the automatic generation of triangular meshes over general analytical curved surfaces with explicit control on the discretization error over the interior of the domain. The element size on the curved surface is estimated based on the given allowable discretization error and the surface curvature. The mesh generation starts with the subdivision of the curved boundary of the domain into straight line segments in compliance with the given discretization error constraint. Elements are generated directly over the surface in such a way that the discretization error is kept within the required geometrical tolerance. Those elements violating the given constraint are noted and post‐processed by either element subdivision or node repositioning. Various schemes as to how improvement should be made are proposed, which reduce the discretization error by different strategies depending on the position of the point where the maximum discretization error occurs.

The purpose of this paper is to present an algorithm for determining the inner and outer loops of arbitrary parametric surfaces.

The algorithm considers two sub-algorithms: one for non-closed surfaces and another one for closed surfaces. The first sub-algorithm named by area positive and negative method (APNM), combines a curve discretization algorithm with the polygon direction judgment algorithm to judge the inner and outer loops of non-closed surfaces. The second sub-algorithm, called by cross-period number method (CPNM), combines a curve discretization algorithm with the periodicity of closed surfaces to judge the type of boundary loops.

The APNM can use less CPU time to determining the inner and outer loops of the non-closed parametric surfaces. The CPNM can also determine the inner and outer loops of closed parametric surfaces effectively. The judgment results of loops can ensure that the direction of meshes generated on these surfaces is right. And finally ensure the correctness of the numerical simulation results.

Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the APNM saves in the process of determining the inner and outer loops for non-closed surfaces. The CPNM is also a new method to determining the inner and outer loops for closed parametric surfaces. The single run-time of CPNM is very small and can reach the level of microseconds.

This paper presents finite volume computations of turbulent flow through a square cross‐sectioned U‐bend of curvature strong enough (Rc/D =0.65) to cause separation. A zonal turbulence modelling approach is adopted, in which the high‐Re k‐ε model is used over most of the flow domain with the low‐Re, I‐equation model of k‐transport employed within the near‐wall regions. Computations with grids of different sizes and also with different discretization schemes, demonstrate that for this flow the solution of the k and ε equations is more sensitive to the scheme employed in their convective discretization than the solution of the mean flow equations. To avoid the use of extremely fine 3‐Dimensional grids, bounded high order schemes need to be used in the discretization of the turbulence transport equations. The predictions, while encouraging, displayed some deficiencies in the downstream region due to deficiencies in the turbulence model. Evidently, further refinements in the turbulence model are necessary. Initial computations of flow and heat transfer through a rotating U‐bend, indicate that at rotational numbers (Ro = ΩD/W_b) relevant to blade cooling passages, the Coriolis force can substantially modify the hydrodynamic and thermal behaviour.

This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional time‐harmonic electromagnetic wave propagation problems.

The proposed HDG method for the discretization of the two‐dimensional transverse magnetic Maxwell equations relies on an arbitrary high order nodal interpolation of the electromagnetic field components and is formulated on triangular meshes. In the HDG method, an additional hybrid variable is introduced on the faces of the elements, with which the element‐wise (local) solutions can be defined. A so‐called conservativity condition is imposed on the numerical flux, which can be defined in terms of the hybrid variable, at the interface between neighbouring elements. The linear system of equations for the unknowns associated with the hybrid variable is solved here using a multifrontal sparse LU method. The formulation is given, and the relationship between the considered HDG method and a standard upwind flux‐based DG method is also examined.

The approximate solutions for both electric and magnetic fields converge with the optimal order of p+1 in L₂ norm, when the interpolation order on every element and every interface is p and the sought solution is sufficiently regular. The presented numerical results show the effectiveness of the proposed HDG method, especially when compared with a classical upwind flux‐based DG method.

The work described here is a demonstration of the viability of a HDG formulation for solving the time‐harmonic Maxwell equations through a detailed numerical assessment of accuracy properties and computational performances.

The purpose of this paper is to present a simplified hybrid modeling (HYMOD) approach which overcomes limitations regarding computational cost and permits the simulation and prediction of the nonlinear inelastic behavior of full-scale RC structures.

The proposed HYMOD formulation was integrated in a research software ReConAn FEA and was numerically studied through the use of different numerical implementations. Then the method was used to model a full-scale two-storey RC building, in an attempt to demonstrate its numerical robustness and efficiency.

The numerical results performed demonstrate the advantages of the proposed hybrid numerical simulation for the prediction of the nonlinear ultimate limit state response of RC structures.

A new numerical modeling method based on finite element method is proposed for simulating accurately and with computational efficiency, the mechanical behavior of RC structures. Currently 3D detailed methods are used to model single structural members or small parts of RC structures. The proposed method overcomes the above constraints.

The purpose of this study is to determine the impact of two-phase power law nanofluid on a curved arterial blood flow under the presence of ovelapped stenosis. Over the past couple of decades, the percentage of deaths associated with blood vessel diseases has risen sharply to nearly one third of all fatalities. For vascular disease to be stopped in its tracks, it is essential to understand the vascular geometry and blood flow within the artery. In recent scenarios, because of higher thermal properties and the ability to move across stenosis and tumor cells, nanoparticles are becoming a more common and effective approach in treating cardiovascular diseases and cancer cells.

The present mathematical study investigates the blood flow behavior in the overlapped stenosed curved artery with cylinder shape catheter. The induced magnetic field and entropy generation for blood flow in the presence of a heat source, magnetic field and nanoparticle (Fe₃O₄) have been analyzed numerically. Blood is considered in artery as two-phases: core and plasma region. Power-law fluid has been considered for core region fluid, whereas Newtonian fluid is considered in the plasma region. Strongly implicit Stone’s method has been considered to solve the system of nonlinear partial differential equations (PDE’s) with 10–6 tolerance error.

The influence of various parameters has been discussed graphically. This study concludes that arterial curvature increases the probability of atherosclerosis deposition, while using an external heating source flow temperature and entropy production. In addition, if the thermal treatment procedure is carried out inside a magnetic field, it will aid in controlling blood flow velocity.

The findings of this computational analysis hold great significance for clinical researchers and biologists, as they offer the ability to anticipate the occurrence of endothelial cell injury and plaque accumulation in curved arteries with specific wall shear stress patterns. Consequently, these insights may contribute to the potential alleviation of the severity of these illnesses. Furthermore, the application of nanoparticles and external heat sources in the discipline of blood circulation has potential in the medically healing of illness conditions such as stenosis, cancer cells and muscular discomfort through the usage of beneficial effects.

To research the feasibility in using artificial neural networks (ANN) and response surfaces (RS) techniques for reliability analysis of concrete structures.

The evaluation of the failure probability and safety levels of structural systems is of extreme importance in structural design, mainly when the variables are eminently random. It is necessary to quantify and compare the importance of each one of these variables in the structural safety. RS and the ANN techniques have emerged attempting to solve complex and more elaborated problems. In this work, these two techniques are presented, and comparisons are carried out using the well‐known first‐order reliability method (FORM), with non‐linear limit state functions. The reliability analysis of reinforced concrete structure problems is specially considered taking into account the spatial variability of the material properties using random fields and the inherent non‐linearity.

It was observed that direct Monte Carlo simulation technique has a low performance in complex problems. FORM, RS and neural networks techniques are suitable alternatives, despite the loss of accuracy due to approximations characterizing these methods.

The examples tested are limited to moderated large non‐linear reinforced concrete finite element models. Conclusions are drawn based on the examples.

Some remarks are outlined regarding the fact that RS and ANN techniques have presented equivalent precision levels. It is observed that in problems where the computational cost of structural evaluations (computing failure probability and safety levels) is high, these two techniques could improve the performance of the structural reliability analysis through simulation techniques.

This paper is important in the field of reliability analysis of concrete structures specially when neural networks or RS techniques are used.

A boundary element method in terms of the field variables is applied to three‐dimensional electromagnetic scattering problems. Especially, the influence of a dipole excited field on low conducting materials situated very close to the antenna will be discussed. We use higher order edge elements of quadilateral shape for the field approximation on curved surfaces. The tangential components of the unknown field variables are interpolated by vector element functions. The Galerkin method is implemented to obtain a set of linear equations. The applicability of the proposed edge element is investigated by the comparison of different BEM‐formulations and FEM‐results.