An Energetic Approach to Rate Independent Delamination with Cohesive Contact - An SGBEM Implementation

2014 ◽  
Vol 969 ◽  
pp. 24-27 ◽  
Author(s):  
Jozef Kšiňan ◽  
Roman Vodička
Keyword(s):  
Mathematical Model ◽  
Boundary Element Method ◽  
Numerical Algorithm ◽  
Time Discretization ◽  
Local Solution ◽  
Interface Damage ◽  
Energetic Approach ◽  
Energetic Formulation ◽  
Galerkin Boundary Element Method ◽  
Independent Model

A mathematical model for analysis of contact delamination problems has been developed and implemented into the program Matlab by means of the Symmetric Galerkin Boundary Element Method (SGBEM). The SGBEM numerical algorithm enables to exploit an energetic formulation which governs interface rupture. A rate-independent model of the delamination process is obtained, considering an interface damage variable. A numerical algorithm has been proposed to provide maximallydissipative local solution which yields numerically stable time-discretization. The developed 2-dimensional sample example of mathematical model demonstrates the model behaviour and its suitability in many aspects of engineering practise.

scholarly journals An Energetic Approach for Numerical Analysis of an Interface crack in Shearing Mode

2012 ◽  
Vol 7 (2) ◽  
pp. 87-98
Author(s):  
Roman Vodička
Keyword(s):  
Mathematical Model ◽  
Fracture Toughness ◽  
Numerical Analysis ◽  
Interface Crack ◽  
Layered Structure ◽  
Numerical Approach ◽  
Physical Situation ◽  
Interface Cracks ◽  
Energetic Approach ◽  
Energetic Formulation

Abstract A mathematical model of a layered structure and initiation and growth of interface cracks are presented. A numerical approach for solving this problem is described, with the emphasis to the analysis of a shearing-mode crack. The model defines a scalar damage variable in the interface and also plastic tangential slip, which increases the fracture toughness in the shearing crack mode. An energetic formulation governing the adhesive damage until it breaks is proposed. The approach is also tested numerically to demonstrate the behaviour of the model and to assess its suitability in a particular physical situation.

scholarly journals GEODYNAMICS

GEODYNAMICS ◽  
2011 ◽  
Vol 2(11)2011 (2(11)) ◽  
pp. 84-85
Author(s):  
L. M. Zhuravchak ◽  
◽  
Yu. O. Fedoryshyn ◽  
Keyword(s):  
Mathematical Model ◽  
Electromagnetic Field ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Algorithm ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Steady Oscillations ◽  
Dimensional Object ◽  
The Mathematical Model

The mathematical model for steady oscillations of electromagnetic field in the three-dimensional object is built. For calculating of the distribution of the electromagnetic field the numerical algorithm based on the boundary element method is developed. Numerical experiments are performed.

Swimming speed estimation of extinct marine reptiles: energetic approach revisited

Paleobiology ◽  
2002 ◽  
Vol 28 (2) ◽  
pp. 251-262 ◽  
Author(s):  
Ryosuke Motani
Keyword(s):  
Mathematical Model ◽  
Metabolic Rate ◽  
Swimming Speed ◽  
Body Shape ◽  
Speed Estimation ◽  
The Past ◽  
Marine Reptiles ◽  
Energetic Approach ◽  
Shape Models ◽  
Significant Tendency

Cruising speeds of Mesozoic marine reptiles have been estimated in the past by using a mathematical model of energetic equilibrium during steady swimming. This method suffered from a significant tendency to overestimate speeds of extant cetaceans for no clear reason, which raised questions about the validity of the approach itself. The present study identifies the factors that caused this shortcoming and proposes corrections and some additional modifications. These include the use of more accurate body shape models, updated metabolic rate models, and optimal rather than critical swimming speeds. The amended method successfully approximates published optimal speeds of several extant marine vertebrates, including cetaceans, showing that the basic framework of the energetic approach is valid. With this confirmation, the method was applied to Mesozoic marine reptiles, by assuming three different metabolic rate categories known in extant swimming vertebrates (i.e., average ectothermic, raised ectothermic, and marine endothermic levels). The results support previous inferences about the relative cruising capabilities of Mesozoic marine reptiles (i.e., ichthyosaurs > plesiosaurs > mosasaurs). Stenopterygius, a thunniform ichthyosaur, was probably capable of cruising at a speed at least comparable to those reported for some extant thunniform teleosts with similar diets (~1 m/second).

Dynamic Analysis of a Three-Dimensional Poroelastic Beam Using the Boundary-Element Method

2018 ◽  
Vol 769 ◽  
pp. 329-335
Author(s):  
Andrey Petrov ◽  
Leonid A. Igumnov
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Element Solution ◽  
Harmonic Force ◽  
Porosity And Permeability ◽  
Beam Thickness ◽  
Element Method

The problem of the effect of a normal harmonic force on a porous beam in a 3D formulation is solved using the boundary-element method. A homogeneous fully saturated elastic porous medium is described using Biot’s mathematical model. The effect of the porosity and permeability parameters on the deflection of the beam and the distribution of pore pressure over the beam thickness is investigated. The comparison of the boundary-element solution with a 2D numerical-analytical one is given.

Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems

2020 ◽  
Vol 36 (6) ◽  
pp. 749-761
Author(s):  
Y. -Y. Ko
Keyword(s):  
Boundary Element Method ◽  
Rigid Body ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Neumann Problems ◽  
Galerkin Boundary Element Method ◽  
Element Method

ABSTRACTWhen the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

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