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Presents a new B‐spline finite element for the dynamic analysis of unsymmetrical sandwich shells of revolution. The formulation takes account of the membrane and bending effects in isotropic or orthotropic elastic facings, and membrane, bending and transverse shearing effects in an isotropic or othotropic elastic core. Both geometry and local displacements are interpolated by a set of B‐spline functions. The main aspects added by the sandwich structure of the element are the transverse shearing and membrane‐bending coupling effects in the core. These are well represented by a set of new variables which are the mean end relative in‐plane displacements of the facing middle surfaces. Together with the transverse displacement, these variables constitute the degrees of freedom (dofs) of this new B‐spline sandwich element. The finite elements are grouped into super‐elements with C¹ continuity to obtain the whole finite element model. For each super‐element a total of five dofs per node is then obtained except for its end nodes where the derivatives of these dofs with respect to the meridional co‐ordinate are added. This choice reduces to a minimum the total number of dofs in comparison to existing sandwich elements. Evaluates the efficiency and accuracy of the proposed element through several benchmark examples. Compares the results with the analytical and numerical solutions found in the literature. A very satisfactory behaviour of the element was observed in all test cases.

The purpose of this paper is to present some of the key achievements. At DLR, a sophisticated interdisciplinary aircraft design process is being developed, using the CPACS data format (Nagel et al., 2012; Scherer and Kohlgrüber, 2016) as a means of exchanging results. Within this process, TRAFUMO (Scherer et al., 2013) (transport aircraft fuselage model), built on ANSYS and the Python programming language, is the current tool for automatic generation and subsequent sizing of global finite element fuselage models. Recently, much effort has gone into improving the tool performance and opening up the modeling chain to further finite element solvers.

Much functionality has been shifted from specific routines in ANSYS to Python, including the automatic creation of global finite element models based on geometric and structural data from CPACS and the conversion of models between different finite element codes. Furthermore, a new method for modeling and interrogating geometries from CPACS using B-spline surfaces has been introduced.

Several new modules have been implemented independently with a well-defined central data format in place for storing and exchanging information, resulting in a highly extensible framework for working with finite element data. The new geometry description proves to be highly efficient while also improving the geometric accuracy.

The newly implemented modules provide the groundwork for a new all-Python model generation chain, which is more flexible at significantly improved runtimes. With the analysis being part of a larger multidisciplinary design optimization process, this enables exploration of much larger design spaces within a given timeframe.

In the presented paper, key features of the newly developed model generation chain are introduced. They enable the quick generation of global finite element models from CPACS for arbitrary solvers for the first time.

The purpose of this paper is to illustrate how the numerical solution of the Burgers' equation is obtained using the methods of cubic B‐spline collocation and quadratic B‐spline Galerkin over the geometrically graded mesh.

The spatial domain is partitioned into geometrically graded mesh. The finite element methods are constructed within the Galerkin and collocation methods using an expansion of the quadratic and cubic B‐splines as an approximate function, respectively, over this mesh.

When the higher errors are observed at near boundaries for shock‐like and travelling wave solutions of the Burgers' equation, accuracy of the defined methods increase by using finer mesh at near this boundary.

Over the geometrically graded mesh definitions of the quadratic B‐spline Galerkin and cubic B‐spline collocation are given.

This study aims to design the rotor geometry of switched reluctance motor (SRM) in a completely flexible way. In the proposed method, there is no default geometry for the rotor. The initial geometry of the rotor can start from a circle or any other shape and depending on the required performance takes the final shape during the optimal design. In this way, the best performance, possible with geometric design, can be achieved.

The rotor boundary of a 4/2 SRM is defined by a few B-splines. Some control points are located around the rotor and changing their locations causes customized changes in the rotor boundary. Locations of these points are defined as design variables. A 2-D finite element analysis using MATLAB/PDE is applied to the SRM model and sensitivity analysis is used to optimization design by means of minimizing of objective function.

The proposed method has many more capabilities for matching different objective functions. For the suggested objective function, while the conventional rotor torque profile difference with the desired torque profile reaches 40%, this difference for B-spline rotor is about 17%. Experimental results from a prototype motor have a close agreement with analysis results.

The B-splines have been used to design machines and electromagnetic devices. However, this method is used for the first time in design of the whole rotor of a SRM.

The purpose of this paper is to provide numerical solutions of the time‐dependent advection‐diffusion problem by using B‐spline finite element methods in which Taylor series expansion is used for the related time discretization.

The solution domain is partitioned into uniform mesh. The collocation and the Galerkin methods where B‐spline functions are used as base functions are applied to advection‐diffusion equation.

Given methods are unconditionally stable and the obtained results are comparable with some earlier studies in terms of accuracy.

Quadratic and cubic B‐spline base functions are used with Taylor series expansion for the discretization of the equation.

The purpose of this paper is to develop an efficient numerical scheme for non-linear two-dimensional (2D) parabolic partial differential equations using modified bi-cubic B-spline functions. As a test case, method has been applied successfully to 2D Burgers equations.

The scheme is based on collocation of modified bi-cubic B-Spline functions. The authors used these functions for space variable and for its derivatives. Collocation form of the partial differential equation results into system of first-order ordinary differential equations (ODEs). The obtained system of ODEs has been solved by strong stability preserving Runge-Kutta method. The computational complexity of the method is O(p log(p)), where p denotes total number of mesh points.

Obtained numerical solutions are better than those available in literature. Ease of implementation and very small size of computational work are two major advantages of the present method. Moreover, this method provides approximate solutions not only at the grid points but also at any point in the solution domain.

First time, modified bi-cubic B-spline functions have been applied to non-linear 2D parabolic partial differential equations. Efficiency of the proposed method has been confirmed with numerical experiments. The authors conclude that the method provides convergent approximations and handles the equations very well in different cases.

The purpose of this study is to construct quartic trigonometric tension (QTT) B-spline collocation algorithms for the numerical solutions of the Coupled Burgers’ equation.

The finite elements method (FEM) is a numerical method for obtaining an approximate solution of partial differential equations (PDEs). The development of high-speed computers enables to development FEM to solve PDEs on both complex domain and complicated boundary conditions. It also provides higher-order approximation which consists of a vector of coefficients multiplied by a set of basis functions. FEM with the B-splines is efficient due both to giving a smaller system of algebraic equations that has lower computational complexity and providing higher-order continuous approximation depending on using the B-splines of high degree.

The result of the test problems indicates the reliability of the method to get solutions to the CBE. QTT B-spline collocation approach has convergence order 3 in space and order 1 in time. So that nonpolynomial splines provide smooth solutions during the run of the program.

There are few numerical methods build-up using the trigonometric tension spline for solving differential equations. The tension B-spline collocation method is used for finding the solution of Coupled Burgers’ equation.

The purpose of this paper is to demonstrate how numerical solutions of the nonlinear Huxley equation are obtained by collocation‐based method using cubic B‐spline over finite elements.

For the numerical procedure, time derivative is discretized using usual finite difference scheme. Solution and its principal derivatives over the subintervals are approximated by the combination of the cubic B‐spline and unknown element parameters.

The numerical results are found to be in good agreement with the exact solution. Also the method is very accurate and conditionally stable; the results are very accurate at a small h (discretization) of x so this method can be applied for any nonlinear partial differential equations.

The paper demonstrates how numerical solutions of the nonlinear Huxley equation are obtained by collocation‐based method using cubic B‐spline over finite elements.

This paper aims to develop a novel numerical method based on bi-cubic B-spline functions and alternating direction (ADI) scheme to study numerical solutions of advection diffusion equation. The method captures important properties in the advection of fluids very efficiently. C.P.U. time has been shown to be very less as compared with other numerical schemes. Problems of great practical importance have been simulated through the proposed numerical scheme to test the efficiency and applicability of method.

A bi-cubic B-spline ADI method has been proposed to capture many complex properties in the advection of fluids.

Bi-cubic B-spline ADI technique to investigate numerical solutions of partial differential equations has been studied. Presented numerical procedure has been applied to important two-dimensional advection diffusion equations. Computed results are efficient and reliable, have been depicted by graphs and several contour forms and confirm the accuracy of the applied technique. Stability analysis has been performed by von Neumann method and the proposed method is shown to satisfy stability criteria unconditionally. In future, the authors aim to extend this study by applying more complex partial differential equations. Though the structure of the method seems to be little complex, the method has the advantage of using small processing time. Consequently, the method may be used to find solutions at higher time levels also.

ADI technique has never been applied with bi-cubic B-spline functions for numerical solutions of partial differential equations.

The purpose of this paper is to investigate the numerical solutions of the Burgers' and modified Burgers' equation using sextic B‐spline collocation method.

Crank‐Nicolson central differencing scheme has been used for the time integration and sextic B‐spline functions have been used for the space integration to the modified and time splitted modified Burgers' equation.

It has been found that the proposed method is unconditionally stable and obtained results are consistent with some earlier published studies.

Sextic B‐spline collocation method for the Burgers' and modified Burgers' equation is given.