An extended isogeometric analysis approach via symplectic system for interface V-notched magneto-electro-elastic bimaterial

Fracture analysis of magnetoelectroelastic solid weakened by periodic cracks and line inclusions

Full analytical sensitivities in NURBS based isogeometric shape optimization

A method on how to generate traditional quadrilateral NURBS surfaces, non-quadrilateral NURBS surfaces, such as triangle NURBS (Non-uniform Rational B-spline) surfaces and pentagon NURBS surfaces and their equidistant surfaces is presented. A NURBS surface is a bi-parameter surface, and the surface can be generated in accordance with its parameters. With the method given by this paper, if a series of values of the two parameters can be obtained in sequence, Surface Points and the Equidistant Surfaces Points based on these values of the two parameters can be obtained. These points can comprise a NURBS surface and its equidistant surface. Traditionally a NURBS surface is a quadrilateral surface. It is difficult to obtain a non-quadrilateral NURBS surface. A strategy is to generate non-quadrilateral surfaces by adjusting the NURBS surfaces' control points. The results show that the NURBS surface generation method is effective and the strategy to generate non-quadrilateral surfaces by adjusting the control points is feasible in some areas. What discussed in the paper can be used at computer graphics and numerical control areas.

This research deals with dimensionality reduction technique which is based on radial basis function (RBF) theory. The technique uses RBF for mapping multidimensional data points into a low-dimensional space by interpolating the previously calculated position of so-called control points. This paper analyses various ways of selection of control points ( regularized orthogonal least squares method, random and stratified selections). The experiments have been carried out with 8 real and artificial data sets. Positions of the control points in a low-dimensional space are found by principal component analysis. We demonstrate that random and stratified selections of control points are efficient and acceptable in terms of balance between projection error ( stress ) and time-consumption. DOI: 10.15181/csat.v4i1.1095

A safe and smooth operating path is a prerequisite for mobile robots to accomplish tasks. Although the existing path optimization methods improve the smoothness of the planned path by introducing Bezier curve to locally optimize the path with regard to turning points, most of these methods manually select the position of control points and subjectively analyze the feasibility of the optimized path. It is argued unfavorably that it exhibits strong subjectivity and cumbersome selection process. To fill this gap, an adaptive path-smoothening optimization method is proposed in this study, which combines neural network, genetic algorithm, and Bezier curve to transform the path smoothing problem into an optimization problem. It rapidly determines the position of the optimal control point based on comprehension of constraints, e.g., path safety, curvature and kinematic restrains of the robot. The currently proposed method resolves the long-standing problems of strong subjectivity, cumbersome steps, and thus low efficiency in the selection process of control points, and lays the theoretical groundwork for smoothening the locus and path. To start with, according to the actual working conditions, the dataset corresponding to the position of the control point and the path deviation is constructed, and the neural network algorithm is used to solve the prediction model of the path deviation, so as to obtain the mapping relationship between the length and included angle of the control edge in the second-order Bezier curve and the path deviation. Subsequently, with reference to the prediction model of path deviation, a reliability evaluation function is formulated by comprehending multiple influential factors of mobile robot motion safety and path smoothness. The genetic algorithm is then introduced to detect the satisfactory control points in different environments. The currently proposed method is verified by experiments in different operating environments. The study results show that the currently proposed adaptive path-smoothening optimization method exhibits remarkably superior applicability and effectiveness compared to the currently prevailing methods. It demonstrates advantages of fast path planning, reduced path turning points, and desirable path smoothness. In addition, it can also ensure the safety of mobile robot along the planned path as availed by a pre-set criterion.

A novel method of designing array-fed reflector antenna for spatial power combining is proposed. The reflector is modeled using NURBS surface. Genetic algorithm is used to optimize the shape of surface and get the maximum power combining efficiency by adjusting the positions of NURBS surface's control points properly. The optimal positions of the control points can be attained. Besides, we also study the influence of NURBS surface's degree on shape modification. Numerical results are presented showing the validity of the method and the antenna designed with this method can combine the microwave power in the desired direction efficiently.

A new coupled method for high-accuracy determination of fracture parameters of an interface V-notch in magneto-electro-elastic bimaterial

An accurate technique to perform NURBS surface fitting via genetic algorithms is presented. In this technique, the initial NURBS surface is generated by using object points as control points. Then, the genetic algorithm computes the weights and control points to obtain the NURBS surface fitting. The genetic algorithm is implemented through an objective function, which is deduced from NURBS surface and object points. The objective function is minimised by means of simulated binary crossover. This procedure is carried out based on the initial NURBS surface and NURBS surface constructed by employing the object height average as control point. Thus, the genetic algorithm provides the weights and control points of the NURBS surface that represent the object shape. The proposed algorithm improves the accuracy and speed of the NURBS fitting, which is created via genetic algorithms and gradient methods. It is because the proposed algorithm calculates the weights and control points from a known search space, which is produced by NURBS surfaces. Thus, the genetic algorithm minimises the objective function in fast form with high accuracy. The contribution of the proposed method is corroborated by an evaluation based on accuracy and speed of the traditional genetic algorithms and gradient methods.

A novel finite element discretized symplectic method is developed for analyzing interface fracture of magneto-electro-elastic (MEE) materials under anti-plane loads. The overall cracked body is meshed by conventional finite elements and divided into a finite size singular region near the crack tip (near field) and a regular region far away from the crack tip (far field). In the near field, a based-Hamiltonian model is introduced to find the analytical series expressions, and the large number nodal unknowns are condensed into a small set of the undetermined coefficients of the symplectic series by a transformation. The nodal unknowns in the far field remain unchanged. The stress, electric and magnetic intensity factors, energy release rates (ERRs) and explicit expressions of singular field variables in the near field are simultaneously obtained without any processing.

Relevance. Rational Bezier curves and NURBS curves are widely used in modeling curvilinear objects due to the great flexibility and efficiency of the method. Therefore, it is relevant to develop an interpolation method and approximation by these curves of a discrete series of points both in the plane and in three-dimensional space. Method. The work is devoted to the development of a new approach to interpolation and approximations curve fitting, represented by a set of discrete points. The analytical description of the desired curve is implemented using a rational Bezier curve and a NURBS-curve. To solve this problem, two approaches are proposed. The first approach is that the weights of the points are set in advance and then the coordinates of the points of the interpolating or approximating rational Bezier curve as well as the NURBS-curve are calculated. The second approach is that the coordinates of the points are set in advance and then the weights of the control points of the Bezier curve as well as the NURBS-curve are calculated. At the beginning of the process, are set not only coordinates, but also parameters are set to a discrete row of points, that is, each point has the following definition: T (x, y, u) on the plane or T (x, y, z, u) in the three-dimensional space, where u - parameter. To solve the interpolation problem, a system of linear equations is created in which each equation reflects the equality between the analytical formula for a curve and a given point. Moreover, the number of interpolated points cannot be more than the order of the interpolating curve. Thus, we have a system of N linear equations, where N is the number of points equal to the number of points of the curve. Unknown are N control points of the desired curve. Moreover, in the first approach, the unknowns are coordinates of control points, and in the second weights of points.To solve the approximation problem, the Least Squares method is used. In the beginning, a sum of squared functional of the terms of the differences between the analytic formula of the curve and the coordinate of the given point is created. The optimization problem of minimizing this functional is solved. For this, a system of linear equations is created., each equation of which is a derivative of the functional with respect to a given parameter and equated to zero. In the first approach, the desired parameters are the coordinates of points, and in the second weights of points. Results.Two methods of interpolation and approximation of a point series by rational Bezier curves and NURBS-curves were developed. Conclusions. The test cases carried out using computer programs and visualization of results confirm the validity of the proposed methods.

This study deals with the free vibration of the sandwich microplate with the core made of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) and magneto-electro-elastic (MEE) face sheets. The governing equation of the microplates is derived by using the refined plate theory (RPT) with two variables and the modified strain gradient theory (MSGT). The Non-Uniform Rational B-Splines (NURBS) basis function of the isogeometric approach (IGA) is used for the approximation of the displacement and electric and magnetic fields of the microplates. The paper studies the effect of the length scale parameters (LSPs), CNTs distributions, CNTs volume fraction, magnetic and electric loads and geometry on the vibrational frequency of the MEE sandwich microplate.

The ability to predict, and ultimately optimise, aerodynamic forces when the design variable is the geometric definition of the domain is of great importance in many areas of computational fluid dynamics. This problem is known to be extremely computationally intensive due to the vast number of configurations that must be tested and the high computational cost of each one of the simulations involved in the optimisation process. In this talk a novel approach for computing an off-line solution for a set of geometric parameters that define the computational domain will be presented. The proposed approach is based on the proper generalised decomposition and, contrary to similar approaches, the geometric parameters are the position of the control points that define the NURBS boundary representation. Examples involving the solution of Stokes flow problems in two and three dimensions will be used to demonstrate the potential of the proposed approach.

Isogeometric shape optimization for widening band gaps of periodic composite plates

The head shape of high-speed trains has become a critical factor in boosting the speed further. Aerodynamic simulation-based optimization is a dominant method to obtain the optimal head shape which relies on detailed train head models defined by a lot of design variables. Since aerodynamic simulation-based optimization involves heavy calculations, too many design variables not only causes high computational costs, but also makes the optimal solution difficult to obtain. Therefore, how to use few design variables to define detailed train head model is the key to success. Partial differential equation (PDE)-based geometric modelling which creates a complicated PDE patch with few design variables provides an effective solution to this problem. In addition, it also has the advantage of naturally maintaining any high-order continuities between two adjacent surfaces which is very important in designing highly smooth train heads to achieve excellent aerodynamic performance. At the present time, PDE-based geometric modelling cannot be directly applied in computer-aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) since it has not become an industrial standard. In contrast, non-uniform rational B-splines (NURBS) are commonly used in CAD, CAM, CAE, and many other engineering fields. They have already become part of industry wide standards. In order to apply PDE-based geometric modelling in shape design of high-speed train heads for CAD etc., how to optimally convert PDE surfaces into NURBS surfaces must be addressed. In this paper, a new method of achieving optimal conversion of PDE surfaces representing high-speed train heads into NURBS surfaces is developed. It takes control points and weight deformations of NURBS surfaces to be design variables, and the error between NURBS surfaces and PDE surfaces as the objective function. The least squares fitting and the genetic algorithm are combined to obtain the optimal conversion between PDE surfaces and NURBS surfaces. The application examples demonstrate the effectiveness of the developed method.

In cam design process, synthesizing the motion curves is very important because of the effect of motion curves to cam size, force, and vibration. Thus, improving the kinematics of cam curves is significant. This paper presents a general synthesis of motion curves of cam mechanisms. A Non Uniform Rational B-Spline (NURBS) is used to improve the kinematics. The linear system of equations is established to determine motion curves for arbitrary boundary conditions of displacement, velocity, acceleration, and jerk. By controlling the weight parameters of NURBS, the peak values of acceleration and jerk can decrease. Several examples are presented to demonstrate this research. The results are also compared with traditional motion curves.