Numerical Solution of the Problem of Deformation of Elastic Solids under Pulsed Loading

2020 ◽  
Keyword(s):  
Numerical Solution ◽  
Elastic Solids ◽  
Pulsed Loading

Numerical Solution by the CESE Method of a First-Order Hyperbolic Form of the Equations of Dynamic Nonlinear Elasticity

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Lixiang Yang ◽  
Robert L. Lowe ◽  
Sheng-Tao John Yu ◽  
Stephen E. Bechtel
Keyword(s):  
Numerical Solution ◽  
Numerical Approach ◽  
The Other ◽  
Hyperbolic Partial Differential Equations ◽  
Elastic Solids ◽  
First Order ◽  
Diagonal Forms ◽  
Hyperbolic Form ◽  
Spurious Oscillations ◽  
Wave Problems

This paper reports the application of the space-time conservation element and solution element (CESE) method to the numerical solution of nonlinear waves in elastic solids. The governing equations consist of a pair of coupled first-order nonlinear hyperbolic partial differential equations, formulated in the Eulerian frame. We report their derivations and present conservative, nonconservative, and diagonal forms. The conservative form is solved numerically by the CESE method; the other forms are used to study the eigenstructure of the hyperbolic system (which reveals the underlying wave physics) and deduce the Riemann invariants. The proposed theoretical/numerical approach is demonstrated by directly solving two benchmark elastic wave problems: one involving linear propagating extensional waves, the other involving nonlinear resonant standing waves. For the extensional wave problem, the CESE method accurately captures the sharp propagating wavefront without excessive numerical diffusion or spurious oscillations, and predicts correct reflection characteristics at the boundaries. For the resonant vibrations problem, the CESE method captures the linear-to-nonlinear evolution of the resonant waves and the distribution of wave energy among multiple modes in the nonlinear regime.

Numerical Solution of Frictional Contact Problems for Viscoelastic Solids by SGBEM and Quadratic Programming

2016 ◽  
Vol 681 ◽  
pp. 175-184
Author(s):  
Roman Vodička ◽  
Vladislav Mantič
Keyword(s):  
Quadratic Programming ◽  
Numerical Solution ◽  
Coulomb Friction ◽  
Frictional Contact ◽  
Viscoelastic Model ◽  
Time Discretization ◽  
Contact Problems ◽  
Elastic Solids ◽  
Numerical Examples ◽  
Galerkin Boundary Element Method

The contact problem with Coulomb friction together with a simple Kelvin-Voigt viscoelastic model is studied. The numerical solution is obtained using a time discretization by a semi-implicit formula, the visco-elastic solids in contact being discretized by Symmetric Galerkin Boundary Element Method (SGBEM). The resulting minimization problem with a nonsmooth cost functional is suitably transformed in several ways. Firstly, a transformation is performed to apply SGBEM without any viscoelastic fundamental solution. Secondly, a transformation of contact quantities leads to a minimimization with a quadratic programming structure. Numerical examples show the applicability of the proposed approach to solve rather intricate frictional contact problems.

Backscattering Analysis of Cylinder Shaped Scatterer in Vegetation Medium: Comparison Between Theories

2020 ◽  
Vol 2 (1) ◽  
pp. 15-18
Author(s):  
Syabeela Syahali ◽  
Ewe Hong Tat ◽  
Gobi Vetharatnam ◽  
Li-Jun Jiang ◽  
Hamsalekha A Kumaresan
Keyword(s):  
Numerical Solution ◽  
Cross Section ◽  
Traditional Method ◽  
Microwave Remote Sensing ◽  
Solution Model ◽  
Complex Nature ◽  
Good Match ◽  
Equivalent Source ◽  
Backscattering Cross Section ◽  
Method Model

This paper analyses the backscattering cross section of a cylinder both using traditional method model and a new numerical solution model, namely Relaxed Hierarchical Equivalent Source Algorithm (RHESA). The purpose of this study is to investigate the prospect of incorporating numerical solution model into volume scattering calculation, to be applied into microwave remote sensing in vegetation area. Results show a good match, suggesting that RHESA may be suitable to be used to model the more complex nature of vegetation medium.

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