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, a meshless collocation (MC) and an element-free Galerkin (EFG) method, using the differential reproducing kernel (DRK) interpolation, are developed for the quasi-three-dimensional (3D) analysis of simply supported, multilayered composite and functionally graded material (FGM) plates.
70 citations
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TL;DR: In this paper, the authors analyse the convenience and possible advantages of using meshless methods in numerical simulations in biomechanics and discuss the use of one of them, the natural element method.
69 citations
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TL;DR: In this paper, the boundary conditions necessary to match the exact solution are not followed, and the effectivity of adaptive procedures is compromised as a test problem for adaptive procedures as the perfect refined mesh is uniform.
69 citations
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TL;DR: In this paper, a mesh-less approach based on the smoothed particle hydrodynamics (SPH) method is proposed for the simulation of shell fracture under impact, which relies on an entirely meshless approach.
Abstract: This paper introduces a new modeling method suitable for the simulation of shell fracture under impact. This method relies on an entirely meshless approach based on the smoothed particle hydrodynamics (SPH) method. The paper also presents the SPH shell formulation being used as well as the different test cases used for its validation. A plasticity model of the global type throughout the thickness is also proposed and validated. Finally, in order to illustrate the capabilities of the method, fracture simulations using a simplified fracture criterion are presented.
69 citations
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TL;DR: In this paper, the effect of numerical integration on meshless methods with shape functions that reproduce polynomials of degree k ⩾ 1 was analyzed and an estimate for the energy norm of the error between the exact solution and the approximate solution from the meshless method was derived under the assumption that the numerical integration scheme satisfied a form of Green's formula.
68 citations