Curvilinear Coordinates

We consider a class of so-called quaternionic G-monogenic mappings associatedwith m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of allmappings from this class by using four analytic functions of complex variable. For G-monogenicmappings we generalize some analogues of classical integral theorems of the holomorphic functiontheory of the complex variable (the surface and the curvilinear Cauchy integral theorems,the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions.Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiablein the sense of Hausdorff) quaternionic mappings.

For G-monogenic mappings taking values in the algebra of complex quaternions, we generalize some analogues of classical integral theorems of the holomorphic function theory of complex variable (the surface and curvilinear Cauchy integral theorems).

In the paper [1] considered a new class of quaternionic mappings, so- called G-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, and the Cauchy integral formula for G-monogenic mappings.

ssCMap [1] computes the p-values of connectivity scores using a computationally intensive permutation test. It simulates many random scores and compares them with the observed score. However, we observe that the distribution of random scores converges to a normal distribution, which is consistent to the combinatorial central limit theorem [2]. On the basis of this observation and theorem, we deduce an analytical formulae for the p-values and validate them against the permutation-based results reported in ssCMap. We have observed a very good agreement and would therefore recommend using this much more computationally-efficient alternative to ssCMap, allowing real-time generation of results.

The subject of the paper is the construction of the solution of the linear polyparabolic problem for the curvilinear time spatial trapezium with initial conditions of Cauchy type and boundary conditions of Lauricella type. To construct the solution we shall apply the convenient heat polyparabolic potentials with unknown densities and polyparabolic potential of the source function. To determine these densities we shall apply the system of Volterra integral equations of the first and second kind. The solution is a sum of the boundary polyparabolic potentials and the polyparabolic potential of the source function.

Tree growth, especially diameter growth of tree stems, is an important issue for understanding the productivity and dynamics of forest stands. Metabolic scaling theory predicted that the 2/3 power of stem diameter at a certain time is a linear function of the 2/3 power of the initial diameter and that the diameter growth rate scales to the 1/3 power of the initial diameter. We tested these predictions of the metabolic scaling theory for 11 Japanese secondary forests at various growth stages. The predictions were not supported by the data, especially in younger stands. Alternatively, we proposed a new theoretical model for stem diameter growth on the basis of six assumptions. All these assumptions were supported by the data. The model produced a nearly linear to curvilinear relationship between the 2/3 power of stem diameters at two different times. It also fitted well to the curvilinear relationship between diameter growth rate and the initial diameter. Our model fitted better than the metabolic scaling theory, suggesting the importance of asymmetric competition among trees, which has not been incorporated in the metabolic scaling theory.

The word radome is a contraction of radar and dome. The function of radomes is to protect antennas from atmospheric agents. Radomes are closed structures that protect the antennas from environmental factors such as wind, rain, ice, sand, and ultraviolet rays, among others. The radomes are passive structures that introduce return losses, and whose proper design would relax the requirement of complex front-end elements such as amplifiers. The radome consists mostly in a thin dielectric curved shape cover and sometimes needs to be tuned using metal inserts to cancel the capacitive performance of the dielectric. Radomes are in the near field region of the antennas and a full wave analysis of the antenna with the radome is the best approach to analyze its performance. A major numerical problem is the full wave modeling of a large radome-antenna-array system, as optimization of the radome parameters minimize return losses. In the present work, the finite difference time domain (FDTD) comb...

This paper describes a method for the enhancement of curvilinear structures such as vessels and bronchi in three-dimensional (3-D) medical images. A 3-D line enhancement filter is developed with the aim of discriminating line structures from other structures and recovering line structures of various widths. The 3-D line filter is based on a combination of the eigenvalues of the 3-D Hessian matrix. Multi-scale integration is formulated by taking the maximum among singlescale filter responses, and its characteristics are examined to derive criteria for the selection of parameters in the formulation. The resultant multi-scale line-filtered images provide significantly improved segmentation and visualization of curvilinear structures. The usefulness of the method is demonstrated by the segmentation and visualization of brain vessels from magnetic resonance imaging (MRI) and magnetic resonance angiography (MRA), bronchi from a chest CT, and liver vessels (portal veins) from an abdominal CT.

We use the notation C from to to denote a coordinate transformation matrix from one coordinate frame (designated by ``from'') to another coordinated frame (designated by ``to''). For example, ENU denotes the coordinate transformation matrix from earth-centered inertial (ECI) coordinates to earth-®xed east±north±up (ENU) local coordinates and C RPY NED denotes the coordinate transformation matrix from vehicle body-®xed roll± pitch±yaw (RPY) coordinates to earth-®xed north±east±down (NED) coordinates. Coordinate transformation matrices satisfy the composition rule where A, B, and C represent different coordinate frames. What we mean by a coordinate transformation matrix is that if a vector v has the representation v v x v y v z P R Q S C:1

The formulation of the constrained elastica problem proposed in this paper is predicated on two key concepts: first, the deformed elastica is described by means of the distance from the conduit axis; second, the problem is formulated in terms of the Eulerian curvilinear coordinate of the conduit rather than the natural curvilinear coordinate of the elastica. This approach is further implemented within a segmentation algorithm, which transforms the global constrained elastica problem into a sequence of analogous auxiliary problems that result from dividing the conduit and the elastica into segments limited by contacts. Each auxiliary segment entails solving a segment of elastica subject to isoperimetric constraints corresponding to the assumed positions of the segment ends along the conduit. This new formulation resolves in one stroke a series of issues that afflict the classical Lagrangian approach: (i) the contact detection is reduced to checking whether a threshold on the distance function is violated, (ii) the isoperimetric conditions are transformed into regular boundary conditions, instead of being treated as external integral constraints, (iii) the method yields a well-conditioned set of equations that does not degenerate with decreasing flexural rigidity of the elastica and/or decreasing clearance between the conduit and the elastica.

The characteristic of magnetohydrodynamic flow of viscous fluids is explained here. The energy equation behavior is studied in the presence of heat, viscous dissipation, and joule heating. The major emphasis of this study is the physical behavior of the entropy optimization rate. Based on the implementation of curvilinear coordinates, the basic flow equations are established. Nonlinear partial differential expressions are reduced by appropriate transformation to the ordinary differential system. In the engineering and industrial processes, nanoparticles and their shape have practical consequences. For this reason, we give a detailed investigation of the shape impacts on the flow through the curved stretching surface of nanoparticles. The flow equations are reduced into a number of nonlinear differential equations which are solved numerically using a useful numerical approach called Runge-Kutta-4 (RK-4). The shooting method is first used to reduce the equations to a number of problems of first order, and then the RK-4 approach is used for solution. Impacts for entropy optimization, Bejan number, velocity, concentration, and temperature of several physical parameters are graphically studied.

The characteristic of magnetohydrodynamic flow of viscous fluids is explained here. The energy equation behavior is studied in the presence of heat, viscous dissipation, and joule heating. The major emphasis of this study is the physical behavior of the entropy optimization rate. Based on the implementation of curvilinear coordinates, the basic flow equations are established. Nonlinear partial differential expressions are reduced by appropriate transformation to the ordinary differential system. In the engineering and industrial processes, nanoparticles and their shape have practical consequences. For this reason, we give a detailed investigation of the shape impacts on the flow through the curved stretching surface of nanoparticles. The flow equations are reduced into a number of nonlinear differential equations which are solved numerically using a useful numerical approach called Runge‐Kutta‐4 (RK‐4). The shooting method is first used to reduce the equations to a number of problem...

The shift towards designing more dense urban social housing neighbourhoods has started with the embracing of urban sustainability principles by the UAE government since the beginning of the 21st century. The assessment of the recent neighbourhoods designs still lacks concrete evidence about their expected performance especially for pedestrian mobility networks. This concern is gaining further significance with the noticeable tendency of most of the recent urban designs towards developing organic and curvilinear networks instead of the conventional orthogonal grids of the mobility networks that distinguished the traditionally designed neighbourhoods in the country. To bridge this gap, the research comparatively and quantitively analysed the accessibility performance indicators of both of the traditional and the modern urban network designs. The research adopted the Case Study method with quantitative investigation tools that are fundamental to Urban Network Analysis, especially in relation to Accessibility. The simulation of the urban networks of two selected urban social housing neighbourhood forms, representing the networks of both the traditional urban orthogonal sprawl and the recent curvilinear dense one, were utilized employing the UNA toolbox. Three complementary Accessibility Indices were analysed including: Reach, Gravity and Straightness. Through this analysis, the aspects that affected the accessibility performance of the two urban form paradigms and the problems that have been associated with the designs of the urban networks of the new social housing projects, have been revealed. It became evident that the denser urban form was not sufficient in enabling more accessible facilities in the recent neighbourhoods designs. The orthogonal grid, even with its very low Floor Area Ratio showed better performance of in the three accessibility indices especially the Straightness index, if compared with the much denser curvilinear grid with it ‘naturally longer’ pattern. The inefficient number and the inappropriate distribution locally provided facilities in relation to the pedestrian mobility networks have contributed to these disappointing results. So, it is essential to include this and/or similar urban network quantitative simulation tools to help develop genuinely sustainable urban forms for this significant type of urban development in the UAE cities.

The anisotropic advantageous properties of fiber reinforced composites may not be fully exploited unless the fibers are properly placed in their optimal spatial orientations. This paper investigates application of Cellular Automata (CA) for curvilinear fiber design of composite laminae for in-plane responses. CA use local rules to update both field and design variables in an iterative scheme till convergence. In the present study, displacement update rules are derived using a finite element model governing the equilibrium of the cell neighborhood and fiber angles are locally optimized based on a minimum strain energy criterion. A manufacturing improvement is applied on top of the local optimum orientation wherever this angle is not consistent with the cell neighborhood orientation trend. Numerical studies showed convergency of the local update rules and considerable improvements in the stiffness properties for a cantilever bending test and a square plate with a cutout.

With high-order methods becoming increasingly popular in both academia and industry, generating curvilinear meshes that align with the boundaries of complex geometries continues to present a significant challenge. Whereas traditional low-order methods use planar-faced elements, high-order methods introduce curvature into elements that may, if added naively, cause the element to self-intersect. Over the last few years, several curvilinear mesh generation techniques have been designed to tackle this issue, utilizing mesh deformation to move the interior nodes of the mesh in order to accommodate curvature at the boundary. Many of these are based on elastic models, where the mesh is treated as a solid body and deformed according to a linear or non-linear stress tensor. However, such methods typically have no explicit control over the validity of the elements in the resulting mesh. In this article, we present an extension of this elastic formulation, whereby a thermal stress term is introduced to 'heat' or 'cool' elements as they deform. We outline a proof-of-concept implementation and show that the adoption of a thermo-elastic analogy leads to an additional degree of robustness, by considering examples in both two and three dimensions.

The goal of this paper is to construct discretizations for the equations of Lagrangian gas dynamics that preserve plane, cylindrical, and spherical symmetry in the solution of the original differential equations. The new method uses a curvilinear grid that is reconstructed from a given logically rectangular distribution of nodes. The sides of the cells of the reconstructed grid can be segments of straight lines or arcs of local circles. Our procedure is exact for straight lines and circles; that is, it reproduces rectangular and polar grids exactly. We use the method of support operators to construct a conservative finite-difference method that we demonstrate will preserve spatial symmetries for certain choices of the initial grid. We also introduce a "curvilinear" version of artificial edge viscosity that also preserves symmetry. We present numerical examples to demonstrate our theoretical considerations and the robustness of the new method.

A major problem of the existing curvilinear grid Line Integral Convolution (LIC) algorithm is that the resulting LIC textures may be distorted after being mapped onto the parametric surfaces, since a curvilinear grid usually consists of cells of different sizes. This paper proposes a way for solving the problem through using multi-granularity noise as the input image for LIC. A stochastic sampling technique called Poisson ellipse sampling is employed to resample the computational space of a curvilinear grid into a set of randomly distributed points. From this set of points, we are able to reconstruct a noise image with its local noise granularity being adapted to the physical space cell size of the grid.

The success of using streamline technique for visualizing a vector field usually depends largely on the choice of adequate seed points. Turk and Banks developed an elegant technique for automatically placing seed points to achieve a uniform distribution of streamlines on a 2D vector field. Their method uses an energy function calculated from the low-pass filtered streamline image to guide the optimization process of the streamline distribution. This paper proposes a new technique for creating evenly distributed streamlines on 3D parametric surfaces found in curvilinear grids. We make use of Turk and Banks's 2D algorithm by first mapping the vectors on a 3D surface into the computational space of the curvilinear grid. To take into the consideration the mapping distortion caused by the uneven grid density in a curvilinear grid, a new energy function is designed and used for guiding the placement of streamlines in the computational space with desired local densities.

Being able to interactively detect and recognize 3D actions based on skeleton data, in unsegmented streams, has become an important computer vision topic. It raises three scientific problems in relation with variability. The first one is the temporal variability that occurs when subjects perform gestures with different speeds. The second one is the inter-class spatial variability, which refers to disparities between the displacement amounts induced by different classes (i.e. long vs. short movements). The last one is the intra-class spatial variability caused by differences in style and gesture amplitude. In this paper, we design an original approach that better considers these three issues. To address temporal variability we introduce the notion of curvilinear segmentation. It consists in extracting features, not on temporally-based sliding windows, but on trajectory segments for which the cumulated displacement equals a class-based amount. Second, to tackle inter-class spatial variability, we define several competing classifiers with their dedicated curvilinear windows. Last, we address intra-class spatial variability by designing a fusion system that takes the decisions and confidence scores of every competing classifier into account. Extensive experiments on four challenging skeleton-based datasets demonstrate the relevance of the proposed approach for action recognition and online action detection.

PurposeDrawing from resource-based theory, the authors aim to study how and under what conditions small- and medium-sized enterprises (SMEs) capitalise on their proactive entrepreneurial behaviour (PEB) to achieve new product development (NPD) performance.Design/methodology/approachThe authors’ data were drawn from a cross-sectional questionnaire survey of 401 UK-based SMEs in the manufacturing sector.FindingsThe authors identify an upward curvilinear relationship between PEB and NPD performance. Taking a step further, the authors propose and confirm that this curvilinear association arises from, in part, SMEs’ innovation capability, which in turn translates into NPD performance. The authors also find that this upward curvilinear relationship between PEB and innovation capability flips to a downward curvilinear relationship when firms pursue a customer and competitor orientation.Originality/valueThis paper looks beyond the linear relationship that exists among entrepreneurial behavi...

In this paper as a result of the analytical solution of the Navier-Stokes equations for gas flow in the plane semicircular annular channel the radial and circumference velocity components were determined taking into account boundary conditions, limitations and hypotheses. Equation for gas leakages determination and expression for pressure distribution were received.

This paper presents a strain localization analysis in nonlinear models detached from constitutive models. The proposed implementation was performed on the INteractive Structural ANalysis Environment (INSANE) platform, an open source project developed by the Structural Engineering Department of the Federal University of Minas Gerais. Strain localization is associated with weak discontinuities and materials instabilities that occur during physically nonlinear structural analysis. Singularity of the acoustic tensor is considered the classical condition for strain localization and it can be calculated regardless of constitutive model selection. Localization analysis consists in searching for a unit vector which defines the direction at which the acoustic tensor becomes singular. This unit vector points towards the normal direction of the discontinuity surface in the body, which is created by the localization phenomenon. Localization analysis can be approached as a minimization problem o...

The transfer equation for photons is obtained from the Lindquist formalism in curvilinear coordinates (no symmetry assumed), in an arbitrary frame and in any basis (natural or physical), to first order in O(v/c). Acceleration terms in the fluid are introduced via a modification of the metric tensor. The local tetrad attached to the accelerated fluid element follows a Fermi-Walker transport. Lorentz transformations are used to transform locally the equation from Lagrangian to Eulerian space-time coordinates. The resulting equation agrees in the case of a local Minkowskian space with the equation obtained directly using special-relativistic considerations.

The geometric complexity of mechanical components of mechatronic systems is a challenge to apply Additive Manufacturing. The focus of this study is to evaluate the potential of AM processes for the fabrication of different types of multistage spur gears, bevel gears, worm gears, Harmonic drive gears, cycloidal drives and pumps. The precision of different AM technologies is compared. Material behavior is investigated on a gear test rig. The opportunities and limitations of processes using plastics for the fabrication of gears are discussed in this paper.

A numerical simulation of steady and unsteady two-dimensional flows past cylinder with dimples based on highly accurate pseudospectral method is the subject of the present paper. The vorticity and streamfunction formulation of two-dimensional incompressible Navier- Stokes equations with no-slip boundary conditions is used. The system is formulated on a unit disk using curvilinear body fitted coordinate system. Key issues of the curvilinear coordinate transformation are discussed, to show its importance in properly defined node distribution. For the space discretization of the governing system the Fourier-Chebyshev pseudospectral approximation on a unit disk is implemented. For steady flow simulations the non-linear time-independent Navier-Stokes problem is solved using the Newton’s method. For the time-dependent problem the semi-implicit third order Adams-Bashforth backward differentiation scheme is used. Finally numerical result for both steady and unsteady problems are presented. ...

Use of the Global Positioning System (GPS) for quantifying athletic performance is common in many team sports. The effect of running velocity on measurement validity is well established, but the influence of rapid directional change is not well understood in team sport applications. This effect was systematically evaluated using multidirectional and curvilinear adaptations of a validated soccer simulation protocol that maintained identical velocity profiles. Team sport athletes completed 90 min trials of the Loughborough Intermittent Shuttle-running Test movement pattern on curvilinear, and multidirectional shuttle running tracks while wearing a 5 Hz (with interpolated 15 Hz output) GPS device. Reference total distance (13 200 m) was systematically over-and underestimated during curvilinear (2.6160.80%) and shuttle (23.1762.46%) trials, respectively. Within-epoch measurement uncertainty dispersion was widest during the shuttle trial, particularly during the jog and run phases. Relative measurement reliability was excellent during both trials (Curvilinear r = 1.00, slope = 1.03, ICC = 1.00; Shuttle r = 0.99, slope = 0.97, ICC = 0.99). Absolute measurement reliability was superior during the curvilinear trial (Curvilinear SEM = 0 m, CV = 2.16%, LOA 6 223 m; Shuttle SEM = 119 m, CV = 2.44%, LOA 6 453 m). Rapid directional change degrades the accuracy and absolute reliability of GPS distance measurement, and caution is recommended when using GPS to quantify rapid multidirectional movement patterns.

To achieve the full potential of high-order numerical methods for solving partial differential equations, the generation of a high-order mesh is required. One particular challenge in the generation of high-order meshes is avoiding invalid (tangled) elements that can occur as a result of moving the nodes from the loworder mesh that lie along the boundary to conform to the true curved boundary. In this paper, we propose a heuristic for correcting tangled second-and third-order meshes. For each interior edge, our method minimizes an objective function based on the unsigned angles of the pair of triangles that share the edge. We present several numerical examples in two dimensions with second-and third-order elements that demonstrate the capabilities of our method for untangling invalid meshes.

In this paper we study the two-dimensional compaction of integrated circuit layouts. A curvilinear representation for circuit elements, specifically chosen to make the compaction efficient, is developed. A Monte Carlo algorithm with heuristic termination criteria was applied to a variety of designs. These experiments give running times for compaction th at are consistent with a conjectured average complexity of O(N 3 1 2 log 2 (N)) where N is the number of non-wire primitives in the cell. These experiments also produced favorable comparisons with hand-designs and with designs using iterated applications of one dimensional compactors. Several cells also were fabricated and tested to demonstrate the practicality of the representation and the compaction technique.

This research presents the application of a beam finite element, specifically derived for simulating bending–torsion coupling in equivalent box-beam structures with curvilinear stiffeners. The stiffener path was simulated and optimized to obtain an expected coupling effect with respect to four typical static load cases, including geometric constraints related to the additive manufacturing production method. The selected load condition was applied to the centroid of the beam section, and the structure performance was consequently determined. A variation in load position up to one-fourth of the beam width was considered for investigating the stiffener path variation corresponding to a minimum bending–torsion coupling effect. The results demonstrated the capability of such a beam finite element to correctly represent the static behavior of beam structures with curvilinear stiffeners and show the possibility to uncouple its bending–torsion behavior using a specific stiffener orientation...

An Algorithm for Solving Nonlinear Least-Squares Problems with a New Curvilinear Search. We propose a modification of an algorithm introduced by Martiuez (1987) for solving nonlinear least-squares problems. Like in the previous algorithm, after the calculation of an approximated Gauss-Newton direction d, we obtain the next iterate on a two-dimensional subspace which includes d. However, we simplify the process of searching the new point, and we define the plane using a scaled gradient direction, instead of the original gradient. We prove that the new algorithm has global convergence properties. We present some numerical experiments.

The current research study presents a numerical approach in modelling the conjugate heat transfer system of the gas-turbine rotating discs-cavities. The work was undertaken to understand such phenomena and, more specifically, to numerically investigate the thermal interactions in rotating discs-cavities. The developed solver is capable of dealing with complex heat transfer problems, such as unsteady three-dimensional compressible rotating-flows. The development was based on integrating an inhouse computational fluid dynamics code (SURF) with a heat conduction solver internally. Method of interpolation using mapped area was also introduced for treating non-matching meshes at interface, which plays an effective role in exchanging boundary data. This thesis also documents the development of a numerical finite volume cell-vertex hybrid edgebased heat conduction code by the author using FORTRAN. The heat conduction solver was developed and validated to deal with three dimensional solid-domains using unstructured elements. The validation process was carried out on several test cases for investigating the temperature distribution. The test results were presented to show good agreement with the analytical, experimental and other commercial numerical solutions where they exist.

Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy-density plasma physics, the examples ranging from plasma flows in x-ray-generating Z pinches [Maron et al., Phys. Rev. Lett. 111, 035001 (2013)] to the experiments in support of the recently suggested concept of impact ignition in ICF [Azechi et al., Phys. Rev. Lett. 102, 235002 (2009); Murakami et al., Nucl. Fusion 54, 054007 (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never been studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case, the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a power-law, oscil...

A major drawback in the operation of mechanical heart valve prostheses is thrombus formation in the near valve region potentially due to the high shear stresses present in the leakage jet flows through small gaps between leaflets and the valve housing. Detailed flow analysis in this region during the valve closure phase is of interest in understanding the relationship between shear stress and platelet activation. An efficient Cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three-dimensional immersed solid bodies as well as fluid-fluid interfaces. The embedded boundaries are represented using Levelsets and treated in a sharp manner without the use of source terms to represent boundary effects. The resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second-order accuracy. When dealing with problems of disparate length scales encountered in many applications, it is necessary to resolve the physically important length scales adequately to ensure accuracy of the solution. Fixed grid methods often have the disadvantage of heavy mesh requirement for well resolved calculations. A quadtree based adaptive local mesh refinement scheme is developed to complement the sharp interface Cartesian grid method scheme for efficient and optimized calculations. Detailed timing and accuracy data is presented for a variety of benchmark problems involving moving boundaries. The above method is then applied to modeling heart valve closure and predicting thrombus formation. Leaflet motion is calculated dynamically based on the fluid forces acting on it employing a fluid-structure interaction algorithm. Platelets are modeled and tracked as point particles by a Lagrangian particle tracking method which incorporates ABSTRACT A major drawback in the operation of mechanical heart valve prostheses is thrombus formation in the near valve region potentially due to the high shear stresses present in the leakage jet flows through small gaps between leaflets and the valve housing. Detailed flow analysis in this region during the valve closure phase is of interest in understanding the relationship between shear stress and platelet activation. An efficient Cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three-dimensional immersed solid bodies as well as fluid-fluid interfaces. The embedded boundaries are represented using Levelsets and treated in a sharp manner without the use of source terms to represent boundary effects. The resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second-order accuracy. When dealing with problems

The asymptotic accuracies of structural shell theories are reviewed. Several finite element models to solve arch problems are formulated by utilizing the shell theories. The asymptotic rate of energy convergence is determined by the ability of the approximate strains to assume arbitray polynomial states. The optimal choice of interpolation functions for tangential and normal displacement is treated. Stress resultants and stress couples are evaluated by using nodal forces (strain integration method) or internal strain patterns (strain method). The accuracy of these methods are investigated. In particular the distribution of errors in the strains calculated by the strain method is determined and utilized for accuracte stress evaluation. The theoreticat considerations are supported by a vaste number of numerical experiments, which confirm the theoretical results. * dw/ds is utilized for the w-field. Instead of using the parameter du/ds for the u-field, an additional transformation is performed to have es (cfr. Table la) as parameter.

The asymptotic accuracies of structural shell theories are reviewed. Several finite element models to solve arch problems are formulated by utilizing the shell theories. The asymptotic rate of energy convergence is determined by the ability of the approximate strains to assume arbitray polynomial states. The optimal choice of interpolation functions for tangential and normal displacement is treated. Stress resultants and stress couples are evaluated by using nodal forces (strain integration method) or internal strain patterns (strain method). The accuracy of these methods are investigated. In particular the distribution of errors in the strains calculated by the strain method is determined and utilized for accuracte stress evaluation. The theoreticat considerations are supported by a vaste number of numerical experiments, which confirm the theoretical results. * dw/ds is utilized for the w-field. Instead of using the parameter du/ds for the u-field, an additional transformation is performed to have es (cfr. Table la) as parameter.

A new approach to generate structured grids for two-dimensional multiply connected regions with several holes is proposed. The bounding curves may include corners or cusps. The new algorithm constitutes an extension of the Branch Cut Grid Line Control (BCGC) technique introduced byVillamizar et al. [V. Villamizar, O. Rojas, J. Mabey, Generation of curvilinear coordinates on multiply connected regions with boundary-singularities, J. Comput. Phys. 223 (2007) 571-588] to domains with a finite number of holes. Regions with multiple holes are reduced to several contiguous single hole subregions. Then, the BCGC algorithm is applied to each single hole subregion producing a smooth grid with line control. Finally, the subregions with their respective grids are joined and their interfaces are smoothed resulting a globally smooth grid. The advantages of the novel grids are revealed by employing them to numerically solve acoustic scattering problems in the presence of multiple complexly shaped obstacles.

The applicability of the Dirichlet-to-Neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape. The original boundary value problem (BVP) for the multiple scattering problem is reformulated as an interface BVP. A heterogenous medium with variable physical properties in the vicinity of the obstacles is considered. A rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given. The problem is written in terms of generalized curvilinear coordinates inside the computational region. Then, novel elliptic grids conforming to complex geometrical configurations of several two-dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained. The numerical method developed is validated by comparing the approximate and exact far-field patterns for the scattering from two circular obstacles. In this case, for a second order finite difference scheme, a second order convergence of the numerical solution to the exact solution is easily verified.

Despite research related to flexible or continuum curvilinear robots, there lacks a common simulation tool for continuum robots, which are unlike rigid robots. Thus, in this paper, a robotics toolbox is utilized to model a wire-driven flexible manipulator as one of the continuum robots. Constant curvature property can enable the robotics toolbox to represent the flexible manipulator and validate its kinematics. Moreover, because the closed-form inverse kinematics methods developed previously for real-time control conceded limitations in modeling some continuum robots, we hereby develop an inverse kinematics method for the wire-driven flexible manipulator which can provide fast and reliable inverse results. Experimental results showed that geometrical information offered a stable starting point for the proposed inverse kinematics algorithm. Moreover, the first and second derivatives of a fitness function further contributed to a fast-converging solution within a few microseconds. Las...

This work aims to calculate interlaminar stress distribution through the thickness of multilayered composite shell structures by employing a novel nonlinear layer-wise shell finite element formulation. Adapting the Mindlin-Reissner theory in each layer, the shear-deformable layer-wise shell element presents the interlaminar shear stress distributions by increasing the number of layers. The interlaminar normal stress distribution is then determined by the finite difference solution of the general form of equilibrium equation in the non-orthogonal curvilinear grid along the Gaussian points. Two boundary conditions at the bottom and the top surfaces are satisfied by adopting the linear Lagrange interpolation function. The developed formulation is assessed through some illustrative problems solved using a proprietary finite element computer program. The results compare very well with those available in the literature and those obtained by simulations with the commercial finite element software Ansys.

In the problem of cracking of composite structures of several sorts, the pullout problem has frequently been solved. In some previous papers by the authors, curvilinear fibers reinforcing concrete mainly during its curing process have been studied. It was shown that the fibers of Dramix type proved to have a higher local bearing capacity than the straight fibers. The problem was solved in 3D on a unit cell assuming a periodicity of fiber placing. The linear behavior of concrete was taken into account and the pullout test was simulated by the finite element method. In this paper the optimal slope of fibers is sought. Using similar computations as those which were carried out in the above-mentioned papers, the optimum conditions have been added. They obey the typical Mohr-Coulomb law along the fiber-concrete interfacial zones and the compressive strength in the concrete cannot be exceeded at any point. The study is carried out on different unit cells, i.e. different positioning of fibers is considered. A different fiber ratio is also considered to show the mechanical behavior and to limit analysis of the composite aggregate.

Due to significant advancements being made in the field of drug design, the use of topological descriptors remains the primary approach. When combined with QSPR models, descriptors illustrate a molecule’s chemical properties numerically. Numbers relating to chemical composition topological indices are structures that link chemical composition to physical characteristics. This research concentrates on the analysis of curvilinear regression models and degree-based topological descriptors for thirteen skin cancer drugs. The physicochemical characteristics of the skin cancer drugs are examined while regression models are built for computed index values. An analysis is performed for several significant results based on the acquired data.