THE TIME-STEP BOUNDARY-ELEMENT SCHEME ON THE NODES OF THE LOBATTO METHOD IN PROBLEMS OF 3-D DYNAMIC POROELASTICITY

被引：1

作者：

Igumnov, L. A. ^{[1
]}

Petrov, A. N. ^{[2
]}

Vorobtsov, I. V. ^{[1
]}

机构：

[1] Natl Res Lobachevski State Univ Nizhniy Novgorod, Res Inst Mech, 23 Gagarin Ave,Bld 6, Nizhnii Novgorod 603950, Russia

[2] Don State Tech Univ, Res & Educ Ctr Mat, 1 Gagarin Sq, Rostov Na Donu 344010, Russia

来源：

MATERIALS PHYSICS AND MECHANICS | 2019年 / 42卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

boundary element method; Runge-Kutta method; poroelasticity; transient dynamic analysis; wave propagation; KUTTA CONVOLUTION QUADRATURE; FORMULATION; EQUATIONS; BEM;

D O I：

10.18720/MPM.4212019_9

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

A boundary-element scheme for analyzing initial boundary-value problems of 3-D porelasticity is considered. The scheme is based on a time-step method of numerically inverting Laplace transform. According to the method, a solution in time is calculated using quadrature formulas, based on complex values of the function in specific points. The choice of the points is determined by Lobatto method being one of Runge-Kutta methods. A possibility of using two- and three-stage Lobatto methods is considered. Using as an example the problem about a force, acting upon end of a prismatic poroelastic body, the effect of time-step on the dynamic responses of the forces is studied. The present results are compared with the results obtained on the nodes of Radau method.

引用

页码：103 / 111

页数：9

共 25 条

[1] Scalar wave propagation in 2D: a BEM formulation based on the operational quadrature method [J].

Abreu, AI ;

Carrer, JAM ;

Mansur, WJ .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2003, 27 (02) :101-105

[2]

Aliabadi Mohammad H, 2002, applications in solids and structures, V2

[3]

Amenitsky A.V., 2009, PROBLEMS STRENGTH PL, V71, P164

[4] RAPID SOLUTION OF THE WAVE EQUATION IN UNBOUNDED DOMAINS [J].

Banjai, L. ;

Sauter, S. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 47 (01) :227-249

[5] Runge-Kutta convolution quadrature for the Boundary Element Method [J].

Banjai, Lehel ;

Messner, Matthias ;

Schanz, Martin .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 245 :90-101

[6] Runge-Kutta convolution quadrature for operators arising in wave propagation [J].

Banjai, Lehel ;

Lubich, Christian ;

Melenk, Jens Markus .

NUMERISCHE MATHEMATIK, 2011, 119 (01) :1-20

[7] An error analysis of Runge-Kutta convolution quadrature [J].

Banjai, Lehel ;

Lubich, Christian .

BIT NUMERICAL MATHEMATICS, 2011, 51 (03) :483-496

[8]

Bazhenov VG, 2008, BOUNDARY INTEGRAL EQ

[9]

Bishop A.W., 1950, GEOTECHNIQUE, V2, P13, DOI DOI 10.1680/GEOT.1950.2.1.13

[10]

Bishop A.W., 1959, TEKNISK UKEBLAD, V106, P859

← 1 2 3 →