A NURBS-based interface-enriched generalized finite element method for problems with complex discontinuous gradient fields
نویسندگان
چکیده
A non-uniform rational B-splines (NURBS)-based interface-enriched generalized finite element method is introduced to solve problems with complex discontinuous gradient fields observed in the structural and thermal analysis of the heterogeneous materials. The presented method utilizes generalized degrees of freedom and enrichment functions based on NURBS to capture the solution with non-conforming meshes. A consistent method for the generation and application of the NURBS-based enrichment functions is introduced. These enrichment functions offer various advantages including simplicity of the integration, possibility of different modes of local solution refinement, and ease of implementation. In addition, we show that these functions well capture weak discontinuities associated with highly curved material interfaces. The convergence, accuracy, and stability of the method in the solution of two-dimensional elasto-static problems are compared with the standard finite element scheme, showing improved accuracy. Finally, the performance of the method for solving problems with complex internal geometry is highlighted through a numerical example. Copyright © 201 John Wiley & Sons, Ltd.
منابع مشابه
A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries
An interface-enriched generalized finite element method (GFEM) is introduced for 3D problems with discontinuous gradient fields. The proposed method differs from conventional GFEM by assigning the generalized degrees of freedom to the interface nodes, i.e., nodes generated along the interface when creating integration subdomains, instead of the nodes of the original mesh. A linear combination o...
متن کاملTime-Discontinuous Finite Element Analysis of Two-Dimensional Elastodynamic Problems using Complex Fourier Shape Functions
This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in comple...
متن کاملA NURBS-enhanced Discontinuity-Enriched Finite Element Method
Generalized finite element methods have proved a great potential in the mesh-independent modeling of both weak and strong discontinuities, such as the ones encountered when treating materials with inclusions or cracks. By removing the constraint of a conforming mesh, more freedom is offered to modeling exact geometries by means of splines. However, very few studies have been published which com...
متن کاملAn interface-enriched generalized FEM for problems with discontinuous gradient fields
A new generalized FEM is introduced for solving problems with discontinuous gradient fields. The method relies on enrichment functions associated with generalized degrees of freedom at the nodes generated from the intersection of the phase interface with element edges. The proposed approach has several advantages over conventional generalized FEM formulations, such as a lower computational cost...
متن کاملElasto-plastic analysis of discontinuous medium using linearly conforming radial point interpolation method
In this paper, the linearly conforming enriched radial basis point interpolation method is implemented for the elasto-plastic analysis of discontinuous medium. The linear conformability of the method is satisfied by the application of stabilized nodal integration and the enrichment of radial basis functions is achieved by the addition of linear polynomial terms. To implement the method for the ...
متن کامل