The Construction of Plate Finite Elements Usingwavelet Basis Functions
نویسنده
چکیده
In the last years, applying wavelets analysis has called the attention in a wide variety of practical problems, in particular for the numerical solutions of partial differential equations using different methods, as finite differences, semi-discrete techniques or the finite element method. In the construction of wavelet-based elements, instead of traditional polynomial interpolation, scaling and wavelet functions have been adopted to form the shape function to construct elements. Due to their properties, wavelets are very useful when it is necessary to approximate efficiently the solution on non-regular zones. Furthermore, in some cases it is convenient to use the Daubechies wavelet, which has properties of orthogonality and minimum compact support, and provides guaranty of convergence and accuracy of the approximation in a wide variety of situations. The aim of this research is to explore the Galerkin method using wavelets to solve plate bending problems. Some numerical examples, with B-splines and Daubechies, are presented and show the feasibility of our proposal.
منابع مشابه
New DKFT Elements for the Finite Element Analysis of Thin Viscoelastic Plates
In this paper, finite element analysis of thin viscoelastic plates is performed by proposing new plate elements using complex Fourier shape functions. New discrete Kirchhoff Fourier Theory (DKFT) plate elements are constructed by the enrichment of quadratic function fields in a six-noded triangular plate element with complex Fourier radial basis functions. In order to illustrate the validity...
متن کاملSolution of Harmonic Problems with Weak Singularities Using Equilibrated Basis Functions in Finite Element Method
In this paper, Equilibrated Singular Basis Functions (EqSBFs) are implemented in the framework of the Finite Element Method (FEM), which can approximately satisfy the harmonic PDE in homogeneous and heterogeneous media. EqSBFs are able to automatically reproduce the terms consistent with the singularity order in the vicinity of the singular point. The newly made bases are used as the compliment...
متن کاملFinite Plate with Circular and Square Hole under Partial Loading
In this paper a general analytical solution is obtained to find stress distribution in a finite elastic plate with a circular or square hole subjected to arbitrary biaxial partial loading using modified boundary condition by assuming plane stress conditions. The method employed is based on solution of circular hole in finite rectangular plate. This plate is mapped to circular ones and the parti...
متن کاملNon Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations
Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...
متن کاملSolution representations for Trefftz-type finite elements
Solution representations are available for severeal differential equations. For elasticity problems some of the solution representations are considered in this paper. The solution representations can be used for a systematic construction of Trefftz functions for the derivation of Trefftz-type finite elements. For the example of a thick plate a set of Trefftz functions is presented.
متن کامل