Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded Materials

In this paper, an easy-to-implement domain-type meshless method—the generalized finite difference method (GFDM)—is applied to simulate the bending behavior of functionally graded (FG) plates. Based on the first-order shear deformation theory (FSDT) and Hamilton’s principle, the governing equations and constrained boundary conditions of functionally graded plates are derived. Based on the multivariate Taylor series and the weighted moving least-squares technique, the partial derivative of the underdetermined displacement at a certain node can be represented by a linear combination of the displacements at its adjacent nodes in the GFDM implementation. A certain node of the local support domain is formed according to the rule of “the shortest distance”. The proposed GFDM provides the sparse resultant matrix, which overcomes the highly ill-conditioned resultant matrix issue encountered in most of the meshless collocation methods. In addition, the studies show that irregular distribution of structural nodes has hardly any impact on the numerical performance of the generalized finite difference method for FG plate bending behavior. The method is a truly meshless approach. The numerical accuracy and efficiency of the GFDM are firstly verified through some benchmark examples, with different shapes and constrained boundary conditions. Then, the effects of material parameters and thickness on FG plate bending behavior are numerically investigated.

Improved LZW Compression Technique using Difference Method

This work attempts to give a best approach for selecting one of the popular image compression algorithm. The proposed method is designed to find the best performance approach amongst the several compression algorithms. In this work existing lossless compression technique LZW (Lempel-Ziv-Welch) is redesigned to achieve better compression ratio. LZW compression technique works on the basis of repetition of data. In a situation where all the values are distinct or repetition of data does not present the LZW can’t work properly. To avoid this problem, difference method called difference matrix method which is actually calculate the difference between two consequence data and store it in a resultant matrix is used. In this case the matrix contains repetitive data which is more effective compared to LZW technique. Another problem of LZW is dictionary overflow, because of LZW works on ASCII character there is a limit of 256 dictionary length initially. In this work dynamic dictionary method is used without using the ASCII rather than this static method. As a result, this dictionary can contain the initial value anything in a range of -256 to 255. Here ASCII values are not used because the proposed method is applicable grayscale image, where the pixel values are between in range 0 to 255. Using these two changes the proposed improved LZW method becomes more powerful that can compress a non-repetitive set of data significantly. The proposed method is applied on many standard gray images found in the literature achieved 7% to 18% more compression the normal LZW keeping quality of the image same as existing.

Decision Trees in the Tests of Artillery Igniters

The article addressed the method for building decision trees paying attention to the binary character of the tree structure. The methodology for building our decision tree for KW-4 igniters was presented. It involves determining features of tested igniters and applied predictors, which are necessary to create the correct model of the tree. The classification tree was built based on the possessed test results, determining the adopted post-diagnostic decision as the qualitative independent variable. The schema of the resultant classification tree and the full structure of this tree together with the results in end nodes were shown. The obtained graphic and tabular sequence of the designed tree was characterized, and the prediction accuracy was evaluated on the basis of the resultant matrix of incorrect classifications. The quality of the resultant predictive model was assessed on the basis of the chosen examples by means of the ‘ROC’ curve and the graph of the cumulative value of increase coefficient.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms

A geometric modeling and solution procedure for direct kinematic analysis of 6-4 Stewart platforms with any link parameters is proposed based on conformal geometric algebra (CGA). Firstly, the positions of the two single spherical joints on the moving platform are formulated by the intersection, dissection, and dual of the basic entities under the frame of CGA. Secondly, a coordinate-invariant equation is derived via CGA operation in the positions of the other two pairwise spherical joints. Thirdly, the other five equations are formulated in terms of geometric constraints. Fourthly, a 32-degree univariate polynomial equation is reduced from a constructed 7 by 7 matrix which is relatively small in size by using a Gröbner-Sylvester hybrid method. Finally, a numerical example is employed to verify the solution procedure. The novelty of the paper lies in that (1) the formulation is concise and coordinate-invariant and has intrinsic geometric intuition due to the use of CGA and (2) the size of the resultant matrix is smaller than those existed.