Unilaterally Supported Plates on Elastic Foundations by the Boundary Element Method

1992 ◽  
Vol 59 (3) ◽  
pp. 580-586 ◽  
Author(s):  
E. J. Sapountzakis ◽  
J. T. Katsikadelis
Keyword(s):  
Boundary Element Method ◽  
Integral Representation ◽  
Contact Problem ◽  
Boundary Element ◽  
Biharmonic Equation ◽  
Solution Procedure ◽  
Unilateral Contact ◽  
Thin Elastic Plate ◽  
Element Solution ◽  
Subgrade Reaction

A boundary element solution is developed for the unilateral contact problem of a thin elastic plate resting on elastic homogeneous or nonhomogeneous subgrade. The reaction of the subgrade may depend linearly, or nonlinearly, on the deflection of the plate. The contact between the plate and the subgrade is unbonded. The subgrade surface is not necessarily plane, and miscontact between plate and subgrade due to initial gaps is also encountered. The solution procedure is based on the integral representation of the deflection for the biharmonic equation in which the unknown subgrade reaction is treated as loading term. The effectiveness of the proposed method is illustrated by several examples.

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.

Anisotropic Contact and Wear Simulation Using Boundary Elements

2014 ◽  
Vol 618 ◽  
pp. 73-98 ◽  
Author(s):  
Luis Rodríguez-Tembleque ◽  
M.H. Aliabadi ◽  
R. Abascal
Keyword(s):  
Boundary Element Method ◽  
Contact Problem ◽  
Boundary Element ◽  
Tribological Properties ◽  
Augmented Lagrangian ◽  
Rolling Contact ◽  
Lagrangian Formulation ◽  
Wear Simulation ◽  
Contact Pressures ◽  
Augmented Lagrangian Formulation

Wear is present in all mechanical interface interaction problems –contact, fretting, orrolling-contact–, and it is one of the main reasons for inoperability in mechanical components. Thepresented work is a review of recent research carried out by the authors [1, 2, 3]. A boundary-element-based methodology to compute anisotropic wear on 3D contact, fretting, or rolling-contact conditionsis presented. Damage on the geometries of the solids and the contact pressures evolution under or-thotropic tribological properties can be predicted using this contact framework, where the formulationuses the Boundary Element Method to compute the elastic inuence coefcients. Contact problem isbased on an Augmented Lagrangian formulation, and restrictions fullment is established by a set ofprojection functions. The boundary element anisotropic wear formulation presented is illustrated withsome examples, in which some studies about the inuence of anisotropic wear on contact variablesevolution are shown.

On the Solution of the 3D Crack Surface Contact Problem Using the Boundary Element Method

2010 ◽  
Vol 454 ◽  
pp. 11-29 ◽  
Author(s):  
Wilhelm Weber ◽  
Karsten Kolk ◽  
Kai Willner ◽  
Günther Kuhn
Keyword(s):  
Boundary Element Method ◽  
Contact Problem ◽  
Boundary Element ◽  
Crack Surface ◽  
Load Cycle ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Non Linear ◽  
Surface Contact ◽  
Element Method

The efficient solution of the 3D crack surface contact problem utilizing the boundary element method (BEM) is presented. The dual discontinuity method (DDM), a special formulation of the BEM, is applied. This method deals directly with the relative displacements and the discontinuities of the tractions at the crack. For the normal behavior a unilateral contact is assumed and for the description of the tangential behavior Coulomb’s frictional law is utilized. The hard contact formulation is regularized by the application of the penalty method. An incremental iterative procedure based on a radial return mapping algorithm is applied for the solution of this non-linear problem. Based on the stress field the fracture mechanical parameters are determined by an extrapolation method for all increments of a characteristic load cycle. By the analysis of this load cycle the cyclic fracture mechanics values are obtained. Due to the non-linear nature of crack growth the simulation is implemented in the framework of a predictor-corrector scheme. For the investigation of the influence of the crack surface roughness on the behavior of cracks two numerical examples are presented.

Clamped Plates on Pasternak-Type Elastic Foundation by the Boundary Element Method

1986 ◽  
Vol 53 (4) ◽  
pp. 909-917 ◽  
Author(s):  
J. T. Katsikadelis ◽  
L. F. Kallivokas
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Elastic Foundation ◽  
Analytical Solutions ◽  
Element Solution ◽  
Concentrated Loads ◽  
Numerical Examples ◽  
Line Loads ◽  
Element Method

A boundary element solution is developed for the analysis of thin elastic clamped plates of any shape resting on a Pasternak-type elastic foundation. The plate may have holes and it is subjected to concentrated loads, line loads, and distributed loads. The analysis is complete, i.e., deflections, stress resultants, subgrade reactions, and reactions on the boundary are evaluated. Several numerical examples are worked out and the results are compared with those available from analytical solutions. The efficiency of the BEM is demonstrated and discussed.

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