Abstract
A meshless approach, collocation discrete least square (CDLS) method, is extended in this paper, for solving elasticity problems and grid irregularity effect is assessed. In the present CDLS method, the problem domain is discretized by distributed field nodes. The field nodes are used to construct the trial functions. The moving least-squares interpolant is employed to construct the trial functions. Some collocation points that can be independent of the field nodes are used to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of the residuals for the collocation points. The final stiffness matrix is symmetric and therefore can be solved directly via efficient solvers. The boundary conditions are easily enforced by the penalty method. The present method does not require any mesh so it is a truly meshless method. Numerical examples are studied in detail, which show that the present method is stable and possesses good accuracy, high convergence rate and high efficiency for both regular and irregular point distribution.
Highlights
The finite element method (FEM) has been the most frequently used numerical method in engineering during the three past decades
Mesh-based methods are not well suited to the problems associated with extremely large deformation and problems associated with frequently remeshing. To avoid these drawbacks of the FEM, a new class of numerical methods, meshless methods have been developing [4, 5] in the recent decade. These methods have become an important tool in computational solid mechanics, owing to their advantages over the traditional finite element method (FEM), finite-volume method (FVM), and finitedifference method (FDM)
A truly meshless method based on the least-squares approach, the collocation discrete least-squares (CDLS) method, was proposed to solve Poisson’s equation [19] and free surface seepage problem [20] and was presented for error estimation and adaptive refinement in one dimensional fluid mechanics [21]
Summary
The finite element method (FEM) has been the most frequently used numerical method in engineering during the three past decades It has been used in most fields of applied sciences such as computational solid mechanics [1, 2, and 3] and so on. Mesh-based methods are not well suited to the problems associated with extremely large deformation and problems associated with frequently remeshing To avoid these drawbacks of the FEM, a new class of numerical methods, meshless methods ( called mesh-free methods) have been developing [4, 5] in the recent decade. A truly meshless method based on the least-squares approach, the collocation discrete least-squares (CDLS) method, was proposed to solve Poisson’s equation [19] and free surface seepage problem [20] and was presented for error estimation and adaptive refinement in one dimensional fluid mechanics [21]. In this research the CDLS method is extended for elasticity problems and effect of grid irregularity is assessed
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