scholarly journals Vertex Displacement-Based Discontinuous Deformation Analysis Using Virtual Element Method

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1252
Author(s):  
Hongming Luo ◽  
Guanhua Sun ◽  
Lipeng Liu ◽  
Wei Jiang
Keyword(s):  
Degrees Of Freedom ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Virtual Element Method ◽  
Time Step ◽  
Element Space ◽  
Displacement Mode ◽  
Discontinuous Deformation ◽  
Virtual Element ◽  
Element Method

To avoid disadvantages caused by rotational degrees of freedom in the original Discontinuous Deformation Analysis (DDA), a new block displacement mode is defined within a time step, where displacements of all the block vertices are taken as the degrees of freedom. An individual virtual element space V1(Ω) is defined for a block to illustrate displacement of the block using the Virtual Element Method (VEM). Based on VEM theory, the total potential energy of the block system in DDA is formulated and minimized to obtain the global equilibrium equations. At the end of a time step, the vertex coordinates are updated by adding their incremental displacement to their previous coordinates. In the new method, no explicit expression for the displacement u is required, and all numerical integrations can be easily computed. Four numerical examples originally designed by Shi are analyzed, verifying the effectiveness and precision of the proposed method.

scholarly journals Virtual Element Method for the Laplace-Beltrami equation on surfaces

2018 ◽  
Vol 52 (3) ◽  
pp. 965-993 ◽  
Author(s):  
Massimo Frittelli ◽  
Ivonne Sgura
Keyword(s):  
Numerical Experiments ◽  
Beltrami Equation ◽  
Convergence Result ◽  
Point Of View ◽  
Polygonal Approximation ◽  
Virtual Element Method ◽  
Element Space ◽  
First Order ◽  
Virtual Element ◽  
Element Method

We present and analyze a Virtual Element Method (VEM) for the Laplace-Beltrami equation on a surface in ℝ3, that we call Surface Virtual Element Method (SVEM). The method combines the Surface Finite Element Method (SFEM) (Dziuk, Eliott, G. Dziuk and C.M. Elliott., Acta Numer. 22 (2013) 289–396.) and the recent VEM (Beirão da Veiga et al., Math. Mod. Methods Appl. Sci. 23 (2013) 199–214.) in order to allow for a general polygonal approximation of the surface. We account for the error arising from the geometry approximation and in the case of polynomial order k = 1 we extend to surfaces the error estimates for the interpolation in the virtual element space. We prove existence, uniqueness and first order H1 convergence of the numerical solution.We highlight the differences between SVEM and VEM from the implementation point of view. Moreover, we show that the capability of SVEM of handling nonconforming and discontinuous meshes can be exploited in the case of surface pasting. We provide some numerical experiments to confirm the convergence result and to show an application of mesh pasting.

The DDA Method

2016 ◽  
pp. 90-102
Author(s):  
Katalin Bagi
Keyword(s):  
Numerical Integration ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Short Overview ◽  
Abrupt Changes ◽  
Discontinuous Deformation ◽  
Iteration Technique

“DDA” stands for “Discontinuous Deformation Analysis”, suggesting that the displacement field of the analyzed domain shows abrupt changes on the element boundaries in the model. This chapter introduces the theoretical fundaments of DDA: mechanical characteristics of the elements together with the basic degrees of freedom, contact behavior, the equations of motion and their numerical integration with the help of Newmark's beta-method taking into account contact creation, loss and sliding with the help of an open-close iteration technique. Finally, a short overview on practical and scientific applications for masonry structures is given.

Enhanced Discrete Element Method (EDEM) and its Application to Stability Analysis of the Slope with Non-Through Joints

2014 ◽  
Vol 644-650 ◽  
pp. 1539-1542 ◽  
Author(s):  
Yong Zheng Ma ◽  
Ke Jian Cai ◽  
Zhan Tao Li ◽  
Jun Li
Keyword(s):  
Discrete Element Method ◽  
Discrete Element ◽  
Discontinuous Deformation Analysis ◽  
Iteration Step ◽  
Deformation Analysis ◽  
Analysis Method ◽  
Meshfree Approximation ◽  
Discontinuous Deformation ◽  
Cracked Solids ◽  
Element Method

A new enhanced Discrete Element Method (EDEM) for modeling the system composed of cracked solids is developed by coupling the traditional Discontinuous Deformation Analysis method (DDA, a kind of implicit version of DEM) with Moving Least-Squares (MLS) meshfree approximation functions. Tracing crack growth inside fracturing blocks and other related capabilities are available in the postprocessing procedure at each iteration step. Some numerical examples are provided to verify this method, and it is prospective to solve stability problems of the slope with non-through joints and other fracture mechanics problems in a new way.

On Using Discrete Particle Approaches for Simulating the Perforation Process of Concrete Slab by Hard Projectile

2007 ◽  
Vol 353-358 ◽  
pp. 2973-2976 ◽  
Author(s):  
Yu Yong Jiao ◽  
Xiu Li Zhang ◽  
Shui Lin Wang ◽  
Huo Zhen Wu
Keyword(s):  
Discrete Element Method ◽  
Numerical Investigation ◽  
Concrete Slab ◽  
Discrete Element ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Discrete Particle ◽  
Discontinuous Deformation ◽  
Element Method

This study is to present a numerical investigation on fragmentation and perforation of concrete slab by hard projectile using discrete particle approaches. Discrete Element Method (DEM) and Discontinuous Deformation Analysis (DDA), the two representative discrete particle approaches, are employed to simulate a normal perforation of concrete slab by a hard ogival-nose shaped projectile, and the phenomena of spalling, plugging and scabbing are reproduced.

scholarly journals An H1-conforming virtual element for Darcy and Brinkman equations

2017 ◽  
Vol 28 (01) ◽  
pp. 159-194 ◽  
Author(s):  
Giuseppe Vacca
Keyword(s):  
Stokes Equations ◽  
Brinkman Equation ◽  
Optimal Order ◽  
Virtual Element Method ◽  
Element Space ◽  
Optimal Order Of Convergence ◽  
Brinkman Equations ◽  
Divergence Free ◽  
Virtual Element ◽  
Element Method

The focus of this paper is on developing a virtual element method (VEM) for Darcy and Brinkman equations. In [L. Beirão da Veiga, C. Lovadina and G. Vacca, ESAIM Math. Model. Numer. Anal. 51 (2017)], we presented a family of virtual elements for Stokes equations and we defined a new virtual element space of velocities such that the associated discrete kernel is pointwise divergence-free. We use a slightly different virtual element space having two fundamental properties: the [Formula: see text]-projection onto [Formula: see text] is exactly computable on the basis of the degrees of freedom, and the associated discrete kernel is still pointwise divergence-free. The resulting numerical scheme for the Darcy equation has optimal order of convergence and [Formula: see text]-conforming velocity solution. We can apply the same approach to develop a robust virtual element method for the Brinkman equation that is stable for both the Stokes and Darcy limit case. We provide a rigorous error analysis of the method and several numerical tests.

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