Numerically Analytical Modeling the Dynamics of a Prismatic Body of Two- and Three-Component Materials

Abstract. The problem of loading on a one-dimensional partially saturated poroelastic rod is considered. A mathematical model of a partially saturated porous medium based on the Bio model was used. Solid skeleton displacements and pore pressures of fillers are chosen as basic functions defining wave process. A mathematical model of the boundary-value problem of the dynamic theory of poroelasticity is considrered in Laplace domain. The solution in time domain is obtained using the stepping method of numerical inversion of the Laplace transform. Dynamic displacement responses and pore pressures are presented for different values of the parameters of the poroelastic material model.

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“…The method, based on the operational calculus theorem, allows to calculate the required original function using quadrature formula [19]:…”

Section: Methods For Numerically Inverting Laplace Transformmentioning

confidence: 99%

Numerical-analytical study on effect of three-phase poroelastic medium model parameters on dynamic displacements and porous pressures response

et al. 2017

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“…It helps to get rid of fundamental solutions in time requirement and shows a better stability [4]. A similar boundary element scheme based on the stepping method for Laplace transform numerical inversion is considered in [5]. To solve a 3d poroelastodynamic problem in the scope of the boundary element method, the modification of the scheme with a varied integration step relying on highly oscillatory quadrature principles and symmetry of the integrand function is employed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Analysis of 3D poroelastodynamics using BEM based on modified time-step scheme

Игумнов

Petrov

Vorobtsov

2017

IOP Conf. Ser.: Earth Environ. Sci.

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Abstract. The development of 3d boundary elements modeling of dynamic partially saturated poroelastic media using a stepping scheme is presented in this paper. Boundary Element Method (BEM) in Laplace domain and the time-stepping scheme for numerical inversion of the Laplace transform are used to solve the boundary value problem. The modified stepping scheme with a varied integration step for quadrature coefficients calculation using the symmetry of the integrand function and integral formulas of Strongly Oscillating Functions was applied. The problem with force acting on a poroelastic prismatic console end was solved using the developed method. A comparison of the results obtained by the traditional stepping scheme with the solutions obtained by this modified scheme shows that the computational efficiency is better with usage of combined formulas. IntroductionThere are two major approaches to dynamic processes modeling by means of BEM: solving directly in time domain using stepping scheme and in Laplace or Fourier domain followed by the respective transform inversion [1]. The first approach with traditional stepping schemes has some disadvantages, e.g. requires fundamental solutions in time, significant computing costs and a low stability rate. The New Convolution Quadrature Method (CQM), which is widely applied in construction of time-step boundary element schemes on the basis of fundamental solutions in Laplace domain, was introduced in [2,3]. It helps to get rid of fundamental solutions in time requirement and shows a better stability [4]. A similar boundary element scheme based on the stepping method for Laplace transform numerical inversion is considered in [5]. To solve a 3d poroelastodynamic problem in the scope of the boundary element method, the modification of the scheme with a varied integration step relying on highly oscillatory quadrature principles and symmetry of the integrand function is employed in this paper.

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Three-Dimensional Dynamic Response of a Cylindrical Cavity in a Half-Space of Partially Saturated Soil Under Internal Step-Loading

Petrov

Grigoryev

Игумнов

2021

Advanced Materials Modelling for Mechanical, Medical and Biological Applications

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Numerically Analytical Modeling the Dynamics of a Prismatic Body of Two- and Three-Component Materials

Cited by 5 publications

References 14 publications

Numerical-analytical study on effect of three-phase poroelastic medium model parameters on dynamic displacements and porous pressures response

Numerical-analytical study on effect of three-phase poroelastic medium model parameters on dynamic displacements and porous pressures response

Analysis of 3D poroelastodynamics using BEM based on modified time-step scheme

Three-Dimensional Dynamic Response of a Cylindrical Cavity in a Half-Space of Partially Saturated Soil Under Internal Step-Loading

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