scholarly journals A SPH-GFDM Coupled Method for Elasticity Analysis

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1774
Author(s):  
Zheming Tong ◽  
Zezhao Peng ◽  
Yuqing Yue ◽  
Zhou Chen
Keyword(s):  
Boundary Conditions ◽  
Computational Domain ◽  
Numerical Accuracy ◽  
Coupled Method ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Explicit Formulae ◽  
Stress Boundary Conditions ◽  
Stress Boundary ◽  
Derivatives Of

SPH (smoothed particle hydrodynamics) is one of the oldest meshless methods used to simulate mechanics of continuum media. Despite its great advantage over the traditional grid-based method, implementing boundary conditions in SPH is not easy and the accuracy near the boundary is low. When SPH is applied to problems for elasticity, the displacement or stress boundary conditions should be suitably handled in order to achieve fast convergence and acceptable numerical accuracy. The GFDM (generalized finite difference method) can derive explicit formulae for required partial derivatives of field variables. Hence, a SPH–GFDM coupled method is developed to overcome the disadvantage in SPH. This coupled method is applied to 2-D elastic analysis in both symmetric and asymmetric computational domains. The accuracy of this method is demonstrated by the excellent agreement with the results obtained from FEM (finite element method) regardless of the symmetry of the computational domain. When the computational domain is multiply connected, this method needs to be further improved.

Development of stress boundary conditions in smoothed particle hydrodynamics (SPH) for the modeling of solids deformation

2016 ◽  
Vol 4 (4) ◽  
pp. 451-471 ◽  
Author(s):  
Thomas Douillet-Grellier ◽  
Ranjan Pramanik ◽  
Kai Pan ◽  
Abdulaziz Albaiz ◽  
Bruce D. Jones ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Smoothed Particle Hydrodynamics ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model

1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Energy Equation ◽  
Control Volume ◽  
Fluid Model ◽  
Complete Solution ◽  
Circular Model ◽  
Line Contacts ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.

Modeling Hypervelocity Impacts Using Smoothed Particle Hydrodynamics

2018 ◽  
Author(s):  
M. Ganser ◽  
B. van der Linden ◽  
C. G. Giannopapa
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Large Deformations ◽  
Hypervelocity Impact ◽  
Density Fluctuations ◽  
Computational Domain ◽  
Simulation Tool ◽  
Hypervelocity Impacts ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
The Impact

Hypervelocity impacts occur in outer space where debris and micrometeorites with a velocity of 2 km/s endanger spacecraft and satellites. A proper shield design, e.g. a laminated structure, is necessary to increase the protection capabilities. High velocities result in massive damages. The resulting large deformations can hardly be tackled with mesh based discretization methods. Smoothed Particle Hydrodynamics (SPH), a Lagrangian meshless scheme, can resolve large topological changes whereas it still follows the continuous formulation. Derived by variational principles, SPH is able to capture large density fluctuations associated with hypervelocity impacts correctly. Although the impact region is locally limited, a much bigger domain has to be discretized because of strong outgoing pressure waves. A truncation of the computational domain is preferable to save computational power, but this leads to artificial reflections which influence the real physics. In this paper, hypervelocity impact (HVI) is modelled by means of basic conservation assumptions leading to the Euler equations of fluid dynamics accompanied by the Mie-Grueneisen equation of state. The newly developed simulation tool SPHlab presented in this work utilizes the discretization method smoothed particle hydrodynamics (SPH) to capture large deformations. The model is validated through a number of test cases. Different approaches are presented for non-reflecting boundaries in order to tackle artificial reflections on a computational truncated domain. To simulate an HVI, the leading continuous equations are derived and the simulation tool SPHlab is developed. The method of characteristics allows to define proper boundary fluxes by removing the inwards travelling information. One- and two-dimensional model problems are examined which show excellent absorption behaviour. An hypervelocity impact into a laminated shield is simulated and analysed and a simple damage model is introduced to model a spallation failure mode.

Dynamic thermo-elastic response of a discrete multi-layered cylindrical shell subjected to transient thermal loading

2008 ◽  
Vol 222 (4) ◽  
pp. 549-561 ◽  
Author(s):  
J Y Zheng ◽  
X D Wu ◽  
Y J Chen ◽  
G D Deng ◽  
Q M Li ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Elastic Response ◽  
Elastic Part ◽  
Dynamic Part ◽  
Layered Cylindrical Shell ◽  
Stress Boundary Conditions ◽  
Transient Thermal ◽  
Stress Boundary

Explosion containment vessels (ECVs) are used to fully contain the effects of explosion events. A discrete multi-layered cylindrical shell (DMC) consisting of a thin inner cylindrical shell and helically cross-winding flat steel ribbons has been proposed, which has obvious advantages of fabrication convenience and low costs. The applications of ECVs are closely associated with blast and thermal loads, and thus, it is important to understand the response of a DMC under transient thermal load in order to develop a design code and operation procedures for the use of DMC as ECV. In this paper, a mathematical model for the elastic response of a DMC subjected to thermal loading due to rapid heating is proposed. Based on the axisymmetric plane strain assumption, the displacement solution of the dynamic equilibrium equations of both inner shell and outer ribbon layer are decomposed into two parts, i.e. a thermo-elastic part satisfying inhomogeneous stress boundary conditions and a dynamic part for homogeneous stress boundary conditions. The thermo-elastic part is solved by a linear method and the dynamic part is determined by means of finite Hankel transform and Laplace transform. The thermo-elastic solution of a DMC is compared with the solution of a monobloc cylindrical shell, and numerical results are presented and discussed in terms of winding angle and material parameters.

scholarly journals Consistent Thermo-Capillarity and Thermal Boundary Conditions for Single-Phase Smoothed Particle Hydrodynamics

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4530
Author(s):  
Claas Bierwisch
Keyword(s):  
Boundary Conditions ◽  
Smoothed Particle Hydrodynamics ◽  
Fluid Phase ◽  
Surface Force ◽  
Delta Function ◽  
Normal Vector ◽  
Large Set ◽  
Thermal Boundary Conditions ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

A model for capillary phenomena including temperature-dependency and thermal boundary conditions is presented in the numerical framework of smoothed particle hydrodynamics (SPH). The model requires only a single fluid phase and is therefore computationally more efficient than surface tension schemes which need an explicit fluid-fluid or fluid-gas interface. The model makes use of a surface identification mechanism based on the SPH renormalization tensor. All relevant properties of the continuum surface force (CSF) based approach, i.e., the delta function, normal vector and curvature, are calculated in a consistent manner. The model is parametrized by physical material properties and is successfully validated by means of a large set of analytical test cases. The applicability of the proposed model to more complex scenarios is demonstrated.

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