Application of Finite Volume Method for Solid Mechanics

2003 ◽  
Author(s):  
Bryce L. Fowler ◽  
Raymond K. Yee
Keyword(s):  
Finite Element ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Solid Mechanics ◽  
Preliminary Test ◽  
Test Case ◽  
Element Analysis ◽  
Vibration Isolators ◽  
Incompressible Materials ◽  
Volume Method

Polymers constitute a large class of nearly incompressible solid materials (i.e., Poisson’s Ratio near 0.5). These materials are often used as passive vibration isolators. Accurately modeling vibration isolators made of nearly incompressible materials has been extremely difficult with standard finite element analysis. This paper provides an alternative to the specialized finite element formulations currently used to model incompressible materials. The finite volume methodology of computational fluid dynamics is employed in this paper to solve the Hooke’s Law equations in solid mechanics. Test cases have been performed to evaluate the performance of finite volume method applied to solid mechanics problems. The formulation has been coded in Matlab for practical use. Based on the preliminary test case results, the finite volume formulation compares favorably to finite element method.

scholarly journals Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow

2020 ◽  
Vol 24 (4) ◽  
pp. 1605-1624
Author(s):  
Philipp Selzer ◽  
Olaf A. Cirpka
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Particle Tracking ◽  
Mass Conservation ◽  
Velocity Fields ◽  
Test Case ◽  
Hydraulic Gradients ◽  
Volume Method

Abstract Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity field, computed on triangles and tetrahedra, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec ($\mathcal {RTN}_{0}$ R T N 0 ) space, which meets the requirements of accurate particle tracking. The projection is based on minimizing the difference in the hydraulic gradients at the element centroids between the standard FEM solution and the hydraulic gradients consistent with the $\mathcal {RTN}_{0}$ R T N 0 velocity field imposing element-wise mass conservation. Using the conforming velocity field in $\mathcal {RTN}_{0}$ R T N 0 space on triangles and tetrahedra, we present semi-analytical particle tracking methods for divergent and non-divergent flow. We compare the results with those obtained by a cell-centered finite volume method defined for the same elements, and a test case considering hydraulic anisotropy to an analytical solution. The velocity fields and associated particle trajectories based on the projection of the standard FEM solution are comparable to those resulting from the finite volume method, but the projected fields are smoother within zones of piecewise uniform hydraulic conductivity. While the $\mathcal {RTN}_{0}$ R T N 0 -projected standard FEM solution is thus more accurate, the computational costs of the cell-centered finite volume approach are considerably smaller.

scholarly journals Finite element method to solve engineering problems using ansys

2021 ◽  
Vol 342 ◽  
pp. 01015
Author(s):  
Adrian Bogdan Şimon-Marinică ◽  
Nicolae-Ioan Vlasin ◽  
Florin Manea ◽  
Gheorghe-Daniel Florea
Keyword(s):  
Finite Element ◽  
Finite Number ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Physical Phenomenon ◽  
Approximate Solutions ◽  
Computational Technique ◽  
Element Analysis ◽  
Engineering Problems ◽  
Volume Method

The Finite Element Analysis method, is a powerful computational technique for approximate solutions to a variety of real – world engineering problems having complex domains subjected to general boundary conditions. The method itself has become an essential step in the design or modelling of a physical phenomenon in various engineering disciplines. A physical phenomenon usually occurs in a continuum of matter (solid, liquid or gas) involving several field variables. The field variables vary from point to point, thus possessing an infinite number of solutions in the domain. The basis of finite volume method relies on the decomposition of the domain into a finite number of subdomains (elements) for which the systematic approximate solution is constructed by applying the variational or weighted residual methods. In effect, finite volume method reduces the problem to that of a finite number of unknowns by dividing the domain into elements and by expressing the unknown field variable in term of the assumed approximating functions within each element.

scholarly journals Pixels and their neighbors: Finite volume

2016 ◽  
Vol 35 (8) ◽  
pp. 703-706 ◽  
Author(s):  
Rowan Cockett ◽  
Lindsey J. Heagy ◽  
Douglas W. Oldenburg
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Direct Current ◽  
Numerical Results ◽  
Dc Resistivity ◽  
Matrix Representations ◽  
Volume Method

We take you on the journey from continuous equations to their discrete matrix representations using the finite-volume method for the direct current (DC) resistivity problem. These techniques are widely applicable across geophysical simulation types and have their parallels in finite element and finite difference. We show derivations visually, as you would on a whiteboard, and have provided an accompanying notebook at http://github.com/seg to explore the numerical results using SimPEG ( Cockett et al., 2015 ).

Dynamic Response of Underwater Structures Subject to Impact Loads

2011 ◽  
Author(s):  
Lingyu Sun ◽  
Weiwei Chen ◽  
Xiaojie Wang ◽  
Ning Kang ◽  
Bin Xu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Response ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Impact Loads ◽  
Main Body ◽  
Energy Absorber ◽  
Volume Method ◽  
Element Method

The present paper studied the dynamic response of an underwater system with its navigation plate rotated relative to the main body until it was blocked by an energy absorber. In this process, the relation between fluid-driving moment and speed of main body, as well as the relation between rotation angle of the plate and design parameters of absorber, was investigated through combined finite element method and finite volume method. Before the plate contacted with the energy absorber, it was modeled by linear elastic material, the movement process was solved by finite volume method with dynamic boundary. When the plate started to contact and crash with the absorber, it was modeled by elastic-plastic material, and the interaction of fluid-structure coupling was simulated by explicit finite element method in LSDYNA and finite volume method in FLUENT. The two-way data exchange on the interface between fluid and structure was carried out through equivalent force and moment on each patch of the interface. In addition, the simulation accuracy on large plastic deformation of absorber was verified through a group of drop hammer experiments. After the energy absorber was crushed to ultimate shape, the open angle of plate reached the maximum value and the plate kept relative static to the rigid body. The maximum structural stress and deformation, the opening time and angle of the plate were evaluated by numerical method. It is demonstrated that the proposed method can effectively predict the dynamic response of underwater system under impact loads, and both the absorption capability of the block and the speed of moving body affect the dynamic response history and structural safety.

Numerical Solution of Multidimensional Compressible Flow by High Order Nodal Discontinuous Galerkin Method

2013 ◽  
Vol 392 ◽  
pp. 100-104 ◽  
Author(s):  
Fareed Ahmed ◽  
Faheem Ahmed ◽  
Yong Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Finite Volume Method ◽  
Discontinuous Galerkin ◽  
Finite Volume ◽  
High Order ◽  
Numerical Predictions ◽  
Volume Method ◽  
Element Method

In this paper we present a robust, high order method for numerical solution of multidimensional compressible inviscid flow equations. Our scheme is based on Nodal Discontinuous Galerkin Finite Element Method (NDG-FEM). This method utilizes the favorable features of Finite Volume Method (FVM) and Finite Element Method (FEM). In this method, space discretization is carried out by finite element discontinuous approximations. The resulting semi discrete differential equations were solved using explicit Runge-Kutta (ERK) method. In order to compute fluxes at element interfaces, we have used Roe Approximate scheme. In this article, we demonstrate the use of exponential filter to remove Gibbs oscillations near the shock waves. Numerical predictions for two dimensional compressible fluid flows are presented here. The solution was obtained with overall order of accuracy of 3. The numerical results obtained are compared with experimental and finite volume method results.

2D Unstructured Mesh Finite Volume Method for Simulating Structural Dynamics

2013 ◽  
Vol 376 ◽  
pp. 345-348
Author(s):  
Miao Yu Hai ◽  
Xiao Hui Su ◽  
Yao Cao ◽  
Yong Zhao ◽  
Jian Tao Zhang
Keyword(s):  
Finite Volume ◽  
Unstructured Mesh ◽  
Solid Mechanics ◽  
Elastic Solid ◽  
Test Case ◽  
Time Step ◽  
Step Algorithm ◽  
Volume Method ◽  
Matrix Free ◽  
Fluidstructure Interaction

A novel procedure for calculating the dynamic response of elastic solid structures is presented. The ultimate aim of this study is to develop a consistent set of finite volume (FV) methods on unstructured meshes for the analysis of dynamic fluidstructure interaction (FSI). This paper describes a two-dimensional (2D) FV cell-vertex based method for dynamic solid mechanics. A novel matrix-free implicit scheme was developed using the Newmark method and dual time step algorithm and the model is validated with a 2D cantilever test case as well as a 2D plate one.

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