Application of the Sinc method to a dynamic elasto-plastic problem

Abstract

This paper presents the application of Sinc bases to simulate numerically the dynamic behavior of a one-dimensional elastoplastic problem. The numerical methods that are traditionally employed to solve elastoplastic problems include finite difference, finite element and spectral methods. However, more recently, biorthogonal wavelet bases have been used to study the dynamic response of a uniaxial elasto-plastic rod [Giovanni F. Naldi, Karsten Urban, Paolo Venini, A wavelet-Galerkin method for elastoplasticity problems, Report 181, RWTH Aachen IGPM, and Math. Modelling and Scient. Computing, vol. 10, 2000]. In this paper the Sinc-Galerkin method is used to solve the straight elasto-plastic rod problem. Due to their exponential convergence rates and their need for a relatively fewer nodal points, Sinc based methods can significantly outperform traditional numerical methods [J. Lund, K.L. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, 1992]. However, the potential of Sinc-based methods for solving elastoplasticity problems has not yet been explored. The aim of this paper is to demonstrate the possible application of Sinc methods through the numerical investigation of the unsteady one dimensional elastic-plastic rod problem.

Solving Multi-Point Boundary Value Problems Using Sinc-Derivative Interpolation

“…It is assumed that the function g has the properties which guarantee the existence and uniqueness of the solution of the problem. Sinc numerical methods have been used to solve a wide range of applications involving boundary value problems [27][28][29][30][31][32][33][34]. In addition to their high efficiency in handling boundary value problems involving singularities, Sinc numerical methods are highly accurate since approximate solutions based on Sinc bases are characterized by exponentially decaying errors [35][36][37][38].…”

Solving Integro-Differential Boundary Value Problems Using Sinc-Derivative Collocation

“…We note that the method described in this paper can easily be extended to higher order IDBVPs. Sinc numerical methods have become more prevalent in recent years as a method of solving a wide range of applications involving boundary value problems [25][26][27][28][29][30][31][32]. Partly this is due to their high efficiency in handling singular boundary value problems but also due to their ability to provide highly accurate solutions with exponentially decaying errors [33][34][35][36].…”

Error analysis of sinc-Galerkin method for time-dependent partial differential equations

“…Particular examples include Euler-Bernoulli beam problems [3], elliptic problems [2], Poisson-like problems [28], inverse problem [22], dynamic elasto-plastic problem [1], the generalized regularized long wave(GRLW) equation [19], integral equation [17,18], system of second-order differential equation [7], Sturm-Liouville problems [4], higher-order differential equation [5,21], multiple space dimensions [16], Troesch's problem [6], clamped plate eigenvalue problem [10], biharmonic problems [11], and fourth-order parabolic equation [12].…”