Using the finite element method and radial point interpolation method to analyze the jaw bone*

Cellular solid materials are progressively becoming more predominant in lightweight structural applications as more technologies realize these materials can be improved in terms of performance, quality control, repeatability and production costs, when allied with fast developing manufacturing technologies such as Additive Manufacturing. In parallel, the rapid advances in computational power and the use of new numerical methods, such as Meshless Methods, in addition to the Finite Element Method (FEM) are highly beneficial and allow for more accurate studies of a wide range of topologies associated with the architecture of cellular solid materials. Since these materials are commonly used as the cores of sandwich panels, in this work, two different topologies were designed — conventional honeycombs and re-entrant honeycombs — for 7 different values of relative density, and tested on the linear-elastic domain, in both in-plane directions, using the Natural Neighbor Radial Point Interpolation Method (NNRPIM), a newly developed meshless method, and the Finite Element Method (FEM) for comparison purposes.

Download Full-text

Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x20935572 ◽

2020 ◽

Vol 31 (20) ◽

pp. 2342-2361

Author(s):

Liming Zhou ◽

Bin Nie ◽

Chuanxin Ren ◽

Shuhui Ren ◽

Guangwei Meng

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Interpolation Method ◽

Homogenization Method ◽

Asymptotic Homogenization ◽

Radial Point Interpolation Method ◽

Radial Point Interpolation ◽

Asymptotic Homogenization Method ◽

Point Interpolation Method ◽

Point Interpolation

The node-based smoothed radial point interpolation method combined with the asymptotic homogenization method was proposed, as an addition to the finite element method, to address the static and dynamic reactions of magneto-electro-elastic coupling micromechanical problems. First, several basic equations for relevant problems were derived. Second, asymptotic homogenization method was utilized to determine the material properties of magneto-electro-elastic nanomaterials. Third, node-based smoothed radial point interpolation method was applied to obtain the discrete equations of magneto-electro-elastic nanostructures. Then, the Newmark method was introduced to solve the response of microcosmic problems. Finally, several numerical examples were calculated to prove the accuracy, convergence, and reliability of node-based smoothed radial point interpolation method by comparing the results of node-based smoothed radial point interpolation method with those of finite element method.

Download Full-text

Using a radial point interpolation meshless method and the finite element method for application of a bio-inspired remodelling algorithm in the design of optimized bone scaffold

Journal of the Brazilian Society of Mechanical Sciences and Engineering ◽

10.1007/s40430-021-03280-2 ◽

2021 ◽

Vol 43 (12) ◽

Author(s):

A. I. Pais ◽

J. L. Alves ◽

J. Belinha

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Meshless Method ◽

Bone Scaffold ◽

The Finite Element Method ◽

Radial Point Interpolation ◽

Point Interpolation ◽

Element Method

Download Full-text

A Combination of Singular Cell-Based Smoothed Radial Point Interpolation Method and FEM in Solving Fracture Problem

International Journal of Computational Methods ◽

10.1142/s0219876218500792 ◽

2018 ◽

Vol 15 (08) ◽

pp. 1850079 ◽

Cited By ~ 5

Author(s):

Guiyong Zhang ◽

Yaomei Wang ◽

Yong Jiang ◽

Yichen Jiang ◽

Zhi Zong

Keyword(s):

Strain Energy ◽

Interpolation Method ◽

The Finite Element Method ◽

Radial Point Interpolation Method ◽

Bound Solution ◽

Numerical Studies ◽

Radial Point Interpolation ◽

Point Interpolation Method ◽

Point Interpolation ◽

Lower Bound Solution

The singular cell-based smoothed radial point interpolation method (CS-RPIM) has been previously proposed and shown good performance in solving fracture problems. Motivated from the fact that CS-RPIM performs over softly by providing an upper bound solution and the finite element method (FEM) is overly stiff by providing a lower bound solution, this work proposes a combination of singular CS-RPIM and FEM with a correlation coefficient [Formula: see text], and [Formula: see text] has been recommended through intensive numerical studies. Several numerical examples have been studied and the proposed method has been found perform quite well from both stress intensity factors and strain energy.

Download Full-text