A Meshfree Minimum Length Method
Author(s)
G. R. Liu, K. Y. Dai & X. Han
Abstract
A meshfree minimum length method (MLM) has been proposed for solids
mechanics and heat conduction problems. In this method, both polynomial terms
as well as modified radial basis functions (RBFs) are used to construct shape
functions using arbitrarily distributed nodes based on the minimum length
procedure. The shape functions constructed possess delta function property. The
numerical examples show that the method achieves better accuracy than the
finite element method especially for problems with steep gradients. Some
numerical implementation issues for MLM are also discussed in detail.
Keywords: meshfree method, meshless method, minimum length method, radial
basis function (RBF), interpolation function.
1 Introduction
Meshfree method has achieved remarkable progress in recent year to avoid the
problems related to the creation and application of predefined meshes in the
traditional numerical methods, such as the finite element method (FEM), the
finite difference method (FDM). In general meshfree methods developed so far
can be categorized into three main groups, i.e., meshfree methods based on
strong-form formulation [1, 2], on weak-form formulation [3-6] and on the
combination of the above two [7, 8]. Meshfree weak-form methods can usually
achieve higher accuracy than strong-form methods especially in dealing with
problems in solids and structures. In addition, they can treat Neumann boundary
condition more easily and the results are more stable. Hence weak-form
formulation will be used in this work. One of the most important issues in
meshfree method is the construction of shape functions. There are two widely
Keywords
meshfree method, meshless method, minimum length method, radial
basis function (RBF), interpolation function.
Related Book
Other papers in this volume
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