Topic
Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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TL;DR: A boundary-type meshfree algorithm is proposed to accurately and stably deal with the two-dimensional inverse Stokes problems, which are highly ill-conditioned and dependent on the Laplacian decomposition.
11 citations
TL;DR: In this paper, the authors developed a computational technique to couple finite element and mesh free methods for locking-free analysis of shear deformable beams and plates, and to impose the boundary conditions directly when the matching field approach is adopted in the mesh free region.
Abstract: Purpose – The purpose of this paper is to develop a computational technique to couple finite element and meshfree methods for locking‐free analysis of shear deformable beams and plates, and to impose the boundary conditions directly when the matching field approach is adopted in the meshfree region.Design/methodology/approach – Matching field approach eliminates shear‐locking which may occur due to inconsistencies in the approximations of the transverse displacement and rotation fields in shear‐deformable beams and plates. Continuous blending method is modified in order to be able to satisfy the constraint conditions of the matching field strategy.Findings – For both transverse displacement and rotation fields, the developed technique produces approximation functions that satisfy the Kronecker delta property at the required nodes of the meshfree region when the matching field approach is adopted.Originality/value – This approach allows for direct assembly of the stiffness matrices that are built for separ...
11 citations
TL;DR: In this paper, the effect of microstructure on quasi-brittle properties within the finite element simulation is modeled explicitly by subdividing a finite element into small elements called cells.
11 citations
TL;DR: In this paper, the virtual boundary mesh-free Galerkin method (VBMGM) is presented to calculate the single-domain heat conduction with heat source problem. And the numerical meanings of the weighted values in VBMGM, such as the partial derivative the temperature, the heat flux and the heat source expression, are definite.
11 citations
Dissertation•
01 Jan 2010
TL;DR: In this paper, an innovative numerical framework for 3D fracture modeling using the element-free Galerkin method and the level set method is presented. But the method is not suitable for the case of 3D cracks.
Abstract: Accurate analysis of fracture is of vital importance yet methods for effetive 3D calculations are currently unsatisfactory. In this thesis, novel numerical techniques are developed which solve many of these problems. This thesis consists two major parts: firstly an investigation into the theory of meshless methods and secondly an innovative numerical framework for 3D fracture modelling using the element-free Galerkin method and the level set method. The former contributes to some fundamental issues related to accuracy and error control in meshless methods needing to be addressed for fracture modelling developed later namely, the modified weak form for imposition of essential boundary conditions, the use of orthogonal basis functions to obtain shape functions and error control in adaptive analysis. In the latter part, a simple and efficient numerical framework is developed to overcome the difficulties in current 3D fracture modelling. Modelling cracks in 3D remains a challenging topic in computational solid mechanics since the geometry of the crack surfaces can be difficult to describe unlike the case in 2D where cracks can be represented as combinations of lines or curves. Secondly, crack evolution requires numerical methods that can accommodate the moving geometry and a geometry description that maintains accuracy in successive computational steps. To overcome these problems, the level set method, a powerful numerical method for describing and tracking arbitrary motion of interfaces, is used to describe and capture the crack geometry and forms a local curvilinear coordinate system around the crack front. The geometry information is used in the stress analysis taken by the element-Free Galerkin method as well as in the computation of fracture parameters needed for crack propagation. Examples are tested and studied throughout the thesis addressing each of the above described issues.
11 citations