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: In this article, the performance of generalized elements that partially have a physical domain in the context of the finite cover method (FCM) was compared with the standard finite element model (FEM).
47 citations
TL;DR: In this article, an adaptive meshless approach for nonlinear solid mechanics is developed based on the element free Galerkin method, which is extended for linear elasto-static problems.
46 citations
23 May 2014
TL;DR: In this paper, stable and convergent nodal integration methods are presented and applied to transient and large deformation impact problems, and an eigenvalue analysis of the methods is also provided.
Abstract: Galerkin meshfree methods can suffer from instability and suboptimal convergence if the issue of quadrature is not properly addressed. The instability due to quadrature is further magnified in high strain rate events when nodal integration is used. In this paper, several stable and convergent nodal integration methods are presented and applied to transient and large deformation impact problems, and an eigenvalue analysis of the methods is also provided. Optimal convergence is attained using variationally consistent integration, and stability is achieved by employing strain smoothing and strain energy stabilization. The proposed integration methods show superior performance over standard nodal integration in the wave propagation and Taylor bar impact problems tested.
46 citations
TL;DR: A new discretization scheme for the Stokes equations using analytically divergence-free approximation spaces is developed based upon a meshfree method using matrix-valued kernels that can produce arbitrarily smooth and hence high order approximations.
Abstract: We develop a new discretization scheme for the Stokes equations using analytically divergence-free approximation spaces. Our scheme is based upon a meshfree method using matrix-valued kernels. The scheme works in arbitrary space dimension and can produce arbitrarily smooth and hence high order approximations. After deriving the scheme, we analyze the discretization error in Sobolev spaces and give a numerical example.
46 citations
TL;DR: In this article, a coupled mesh-free/finite element solver for automotive crashworthiness simulations is presented. But, it is not suitable for large-scale industrial applications.
46 citations