Discrete Singular Convolution Approach Research Articles

Application of the optimized deep networks in the prediction of the coupled thermoelasticity response of the axially graded composite system subjected to thermal shock loading

This research is done to examine the coupled thermoelastic response of composite axially graded beams. Thermal shock is applied axially to the beam. Three-dimensional elasticity theory is used to generate the governing equations of motion. While the Fourier heat conduction relationship and the Lord–Shulman heat transfer theorem are used to construct the time-varying heat conduction connection. Using the discrete singular convolution approach and the Laplace transform, the time-varying equations of motion are solved at design locations. A modified version of the Dubner and Abate method is used to translate the system response from the Laplace domain to the time domain. The Whale Optimization Algorithm and the optimized deep neural network are employed as a prediction mechanism to estimate the system reaction under various scenarios in the final stage. By comparing the outcomes of the procedures utilized with those found in published resources, the correctness of the approaches was confirmed. Results on the doubly thermoelastic response of axially graded composite beams exposed to thermal shock loading are important and are presented in this work. As applicable results for related industries can be observed that by changing the boundary conditions from SS to CC, the location of maximum normal strain tends to be at the center of the axially graded beam

Discrete Singular Convolution Method for Acoustic Transmission Lines

Discrete singular convolution (DSC) algorithm is an accurate dynamic analysis method for single structures. However, vibration analysis of connected structures via the DSC method is limited to step beams and plates. This paper extends the applicability of the DSC method in handling acoustic transmission lines composed of several duct elements with different diameter ratios. Connections of elements are handled by setting up continuity equations at geometric discontinuities. Conformity of DSC equations at these connections is carried out using Taylor series expansion. In this study, natural frequencies, mode shapes and power transmission coefficients of acoustic transmission lines are performed to test the proposed DSC implementation. Power transmission coefficients are obtained through the two-load method using the data provided by the DSC approach. The results are compared with finite element method and analytical solutions (if applicable), and the analytical transfer matrix method is also used for validating the power transmission coefficients. This paper shows that the DSC method is accurate and reliable, and so applicable for acoustic transmission line analysis.

Erratum for “Numerical Analysis of Free Longitudinal Vibration of Nonuniform Rods: Discrete Singular Convolution Approach” by Mohammad Shokrollahi and Amir Zayeri Baghlani Nejad

C-F −2.5 4.884 2.96 × 10−02 3.455 8.28 × 10−02 2.904 1.17 × 10−01 1.674 2.59 × 10−01 −0.5 3.233 −4.78 × 10−03 2.109 3.06 × 10−02 1.684 4.98 × 10−02 0.812 −5.66 × 10−03 0.5 2.350 −1.65 × 10−02 1.432 −5.79 × 10−02 1.100 1.42 × 10−02 0.470 1.39 × 10−03 2.5 0.864 2.99 × 10−03 0.424 2.87 × 10−02 0.295 5.03 × 10−03 0.101 4.05 × 10−02 C-C −2.5 5.286 5.77 × 10−02 4.486 9.52 × 10−02 4.316 1.02 × 10−01 4.353 8.18 × 10−02 −0.5 3.622 5.47 × 10−03 3.309 4.21 × 10−02 3.384 3.95 × 10−02 4.015 1.88 × 10−03 0.5 2.817 −3.78 × 10−03 2.906 −2.94 × 10−03 3.154 2.59 × 10−03 4.115 −2.03 × 10−03 2.5 2.030 3.89 × 10−02 3.074 5.56 × 10−02 3.598 3.99 × 10−02 5.012 2.38 × 10−03

Discrete Singular Convolution Method for Numerical Solutions of Fifth Order Korteweg-De Vries Equations

A new computational method for solving the fifth order Korteweg-de Vries (fKdV) equation is proposed. The nonlinear partial differential equation is discretized in space using the discrete singular convolution (DSC) scheme and an exponential time integration scheme combined with the best rational approximations based on the Carathéodory-Fejér procedure for time discretization. We check several numerical results of our approach against available analytical solutions. In addition, we computed the conservation laws of the fKdV equation. We find that the DSC approach is a very accurate, efficient and reliable method for solving nonlinear partial differential equations.

Buckling and Vibration of Elastically Restrained Standing Vertical Plates

This paper investigates the buckling and vibration of heavy standing plates with rotational elastic edge constraints. The discrete singular convolution (DSC) method as a powerful numerical technique is applied to derive the governing eigenvalue equation. Convergence and comparison studies are conducted to authenticate the correctness and accuracy of the DSC approach. Accurate first-known vibration solutions for elastically restrained vertical plates subjecting to body forces/self-weight are presented. Some contour mode shapes for the vibration of elastically restrained vertical plates are also depicted for illustration.

Three-dimensional Elasticity Analysis of Rectangular Composite Plates

An analysis of laminated composite plates is performed using the three-dimensional equations of linear elasticity. The methodology of the solution is based on the discrete singular convolution (DSC) method. The governing equations for bending and vibration and related boundary conditions are normalized and discretized via DSC approach. The results are carried out and effects of some parameters on static deformation and free vibration are discussed. The method of DSC provides results that show good agreement with available benchmark problems having different material compositions, thickness, and boundary conditions. It is found that the method of DSC yields accurate and efficient results for the composite laminated plate problems under investigation.

Discrete singular convolution method for buckling analysis of rectangular Mindlin plates

The discrete singular convolution (DSC) method is proposed for solving the elastic buckling problem of thick rectangular plates under a uniaxial compressive loading. To allow for the effect of transverse shear deformation in thick plates, the Mindlin plate theory has been adopted. The numerical results are checked against available analytical and other numerical solutions. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers.

Free vibration and buckling analyses of composite plates with straight-sided quadrilateral domain based on DSC approach

Discrete singular convolution (DSC) method has been proposed to obtain the frequencies and buckling loads of composite plates. By using geometric transformation, the straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. Plates having different geometries such as rectangular, skew, trapezoidal and rhombic plates are presented. The obtained results are compared with those of other numerical methods. Numerical results indicate that the DSC is a simple, accurate and reliable algorithm for vibration and buckling analyses of composite plates.

Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method

The main objective of this study is to give a numerical solution of three-dimensional analysis of thick rectangular plates. The analysis uses discrete singular convolution (DSC) method. Free vibration, bending and buckling of rectangular plates have been studied in this paper. Regularized Shannon's delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The obtanied results are compared with those of other numerical methods. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers.

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm

AbstractThis paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that different methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of different plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in the following paper to plates with complex support conditions, which have not been fully addressed in the literature yet. Copyright © 2002 John Wiley & Sons, Ltd.

DSC ANALYSIS OF RECTANGULAR PLATES WITH NON-UNIFORM BOUNDARY CONDITIONS

This paper introduces the discrete singular convolution (DSC) for the vibration analysis of rectangular plates with non-uniform and combined boundary conditions. A systematic scheme is proposed for the treatment of boundary conditions required in the proposed approach. The validity of the DSC approach for plate vibration is tested by using a large number of numerical examples that have a combination of simply supported, clamped and transversely supported (with non-uniform elastic rotational restraint) edges. The present results are in excellent agreement with those in the literature.

A NEW BENCHMARK QUALITY SOLUTION FOR THE BUOYANCY-DRIVEN CAVITY BY DISCRETE SINGULAR CONVOLUTION

This article introduces a high-accuracy discrete singular convolution (DSC) for the numerical simulation of coupled convective heat transfer problems. The problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures. One is a quasi-wavelet-based DSC approach, which uses the regularized Shannon's kernel, while the other is a standard form of the Galerkin finite-element method. The integration of the Navier-Stokes and energy equations is performed by employing velocity correction-based schemes. The entire laminar natural convection range of 10 3 h Ra h 10 8 is numerically simulated by both schemes. The reliability and robustness of the present DSC approach is extensively tested and validated by means of grid sensitivity and convergence studies. As a result, a set of new benchmark quality data is presented. The study emphasizes quantitative, rather than qualitative comparisons.