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On semi-analytical stochastic boundary element method and its application to Eigen problem of thin elastic plate immersed into a fluid

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ENGINEERING ANALYSIS WITH boundary elementS 2022年 134卷 219-230页

作者： Guminiak, Micha s Kaminski, Marcin Pozna n Univ Technol Inst Struct Anal Dept Struct Mech PL-60965 Poznan Poland Lodz Univ Technol Fac Civil Engn Architecture & Environm Engn Dept Struct Mech Al Politech 6 PL-90924 Lodz Poland

The main objective in this work is to study an application of the B-spline approximations in the Least Squares method recovery of the structural response for boundary value problems in some linear elastic systems. These responses were approximated before using polynomial bases in the stochastic perturbation-based boundary element method and now are replaced with second or third order B-spline functions. A majority of such an approach is that the resulting expected values and standard deviations of structural response are obtained using analytical calculus of probability integrals, so that neither statistical nor expansion methods are necessary. Numerical illustration delivered in this paper includes fundamental eigenfrequencies of elastic thin homogeneous and isotropic plate immersed into Newtonian fluid subjected to various boundary conditions at its external edges.

关键词： stochastic boundary element method B-spline approximation Semi-analytical probabilistic technique

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A stochastic boundary element method for piezoelectric problems

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ENGINEERING ANALYSIS WITH boundary elementS 2018年 95卷 248-254页

作者： Wang, Guoqing Guo, Fenglin Shanghai Jiao Tong Univ Sch Naval Architecture Ocean & Civil Engn Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ State Key Lab Ocean Engn Shanghai 200240 Peoples R China

In this paper, the stochastic boundary element method of piezoelectric problems with randomness of material parameters and randomness of applied loads is proposed. By using the method of first-order Taylor expansion, each random quantity is written into the sum of the mean and deviation. The boundary integral equations corresponding to the means and deviations of the displacements and electric potential are derived, respectively. It is demonstrated that the randomness of material parameters can be transformed into the equivalent random body forces and equivalent random charge density, so that the fundamental solutions of deterministic piezoelectric problems can be used in boundary integral equations of the means or deviations due to the similarity between the governing equations with randomness and those of deterministic piezoelectric problems. Finally, several numerical examples are performed to verify the validity of the proposed stochastic boundary element method.

关键词： Piezoelectric problems stochastic boundary element method Mean Deviation

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Stability of rectangular Kirchhoff plates using the stochastic boundary element methods

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ENGINEERING ANALYSIS WITH boundary elementS 2022年 144卷 441-455页

作者： Guminiak, Michas Kaminski, Marcin Poznan Univ Tech Inst Struct Anal Dept Struct Mech PL-60965 Poznan Poland Lodz Univ Technol Fac Civil Engn Dept Struct Mech Architecture & Environm Engn Al Politech 6 PL-90924 Lodz Poland

The main objective in this work is to study an application of the stochastic boundary element methods implemented due to three different probabilistic approaches to analyze stability of the rectangular thin elastic and isotropic plates. This is completed with the use of polynomial approximations applied for the Least Squares method recovery of critical forces resulting from some material and geometrical random imperfections in the plate, e.g. Young's modulus, Poisson's ratio, thickness. A deterministic core for solving the plate stability problem is the boundary element method in direct approach and modified formulation of the boundary and domain integral equations. Probabilistic approaches employed here include traditional Monte-Carlo simulation, the semi-analytical approach as well as the iterative generalized stochastic perturbation method. stochastic response in the form of up to the fourth order characteristics are studied numerically in addition to the input uncertainty level.

关键词： stochastic boundary element method Polynomial response function Semi -analytical approach Generalized stochastic perturbation technique Elastic plate stability Monte -Carlo simulation

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stochastic boundary element method analysis of the interface defects in composite materials

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COMPOSITE STRUCTURES 2012年第2期94卷 394-402页

作者： Kaminski, Marcin Tech Univ Lodz Fac Civil Engn Architecture & Environm Engn Dept Struct Mech PL-90924 Lodz Poland Polymer Res Inst D-01069 Dresden Germany

The main aim of this paper is to present a mathematical model and its numerical realization of the composite materials with stochastic interface defects. Those defects are modeled as the semicircular "bubbles" lying with their diameters on the reinforcement-matrix interface and inside the weaker material region. Both total number of the defects as well as their radii are treated as the Gaussian random variables with the given first two probabilistic moments. According to those parameters the microgeometry is simulated and the entire composite in both scales is discretized using the boundary element method. Its probabilistic version is provided thanks to the Response Function method, where several numerical tests with varying values of the random parameters enable to determine the structural response and, thanks to the Least Squares method, its final probabilistic moments. The proposed technique has been validated on the example of the carbon-epoxy composite with the few interface defects having Gaussian random radii subjected to the shear test. The presented approach may be extended towards a full 3D BEM model of the composites with stochastic interface defects as well as to provide the homogenization method for such composites using the elastostatics BEM programs. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Composite materials Interface defects stochastic boundary element method Least squares technique

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Iterative scheme in determination of the probabilistic moments of the structural response in the stochastic perturbation-based boundary element method

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COMPUTERS & STRUCTURES 2015年 151卷 86-95页

作者： Kaminski, Marcin Tech Univ Lodz Fac Civil Engn Architecture & Environm Engn Dept Struct Mech PL-90924 Lodz Poland

The main aim of this work is to present mathematical apparatus, numerical algorithm and computational illustrations of the improved version of the stochastic perturbation-based boundary element method. It is based on the general order Taylor expansion of all input random parameters and on an iterative algebraic determination of higher order probabilistic moments and characteristics of the structural response. The expected values of both random input parameters and the state functions are analytically expanded first and then they are inserted into all the formulas for higher order statistics, so that linearization procedure inherent for the previous approaches is replaced with the theoretically exact expansion terms. This approach is used in conjunction with the Weighted Least Squares method applied to determine local polynomial representations of the structural response with respect to the input uncertainty. This new approach is compared with the previous version of the SBEM on the example of both isotropic and composite plane cantilever panels modeled with an uncertainty in their material parameters and parabolic boundary elements and also with the Monte-Carlo simulation scheme. Apparently higher precision in determination of third and fourth probabilistic characteristics is obtained, while the computational effort and time consumption remains the same as for linearized perturbation scheme. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： stochastic boundary element method Iterative stochastic perturbation technique Least Squares method

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Application of the generalized perturbation-based stochastic boundary element method to the elastostatics

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ENGINEERING ANALYSIS WITH boundary elementS 2007年第6期31卷 514-527页

作者： Kaminski, Marcin Tech Univ Lodz PL-93590 Lodz Poland

This paper is entirely devoted to the demonstration of a solution for some boundary value problems of isotropic linear elastostatics with random parameters using the boundary element method. The stochastic perturbation technique in its general nth-order Taylor series expansion version is used to express all the random parameters and the state functions of the problem. These expansions inserted in the classical deterministic equilibrium statement return up to the nth-order (both PDEs and matrix) equations. Contrary to the previous implementations of the stochastic perturbation technique, any order partial derivatives with respect to the random input are derived from the deterministic structural response function (SRF) at a given point. This function is approximated using polynomials by the leasts-quares method from the multiple solution of the initial deterministic problem solved for the expectations of random structural parameters. First two probabilistic moments have been computed symbolically here using the computational MAPLE environment, also as the polynomial expressions including perturbation parameter epsilon. It should be mentioned that such a generalized perturbation approach makes it possible to analyze all types of random variables (not only Gaussian) and to compute even higher probabilistic moments with a priori given accuracy. The entire methodology can be implemented after minor modifications to analyze nonlinear phenomena for both statics and dynamics of even heterogeneous domains. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： boundary element method stochastic perturbation method probabilistic mechanics stochastic boundary element method

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Chance-constrained optimization of pumping in coastal aquifers by stochastic boundary element method and genetic algorithm

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CMC-COMPUTERS MATERIALS & CONTINUA 2005年第2期2卷 85-96页

作者： Amaziane, B Naji, A Ouazar, D Cheng, AHD Univ Pau LMA FRE2570 CNRSIPRA F-64000 Pau France Univ Abdelmalek Essaadi MASE Fac Sci & Tech Tangier Morocco Univ Mohammed 5 Ecole Mohammadia Ingn LASH Rabat Morocco Univ Mississippi Dept Civil Engn University MS 38677 USA

In this paper the optimization of ground-water pumping in coastal aquifers under the threat of saltwater intrusion is investigated. The aquifer is inhomogeneous and contains several hydraulic conductivities zones. The aquifer data such as the hydraulic conductivities are uncertain, but with their expected mean and standard deviation values given. A stochastic boundary element method based on the perturbation technique is employed as the simulation tool. The stochastic optimization is handled by the chance-constrained programming. Genetic algorithm is selected as the optimization tool. Numerical examples of deterministic and stochastic problems are provided to demonstrate the feasibility of the proposed schemes.

关键词： saltwater intrusion optimization uncertainty modeling boundary element method stochastic boundary element method genetic algorithm chance-constrained programming

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Dynamic response of tunnels in stochastic soils by the boundary element method

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ENGINEERING ANALYSIS WITH boundary elementS 2002年第8期26卷 667-680页

作者： Karakostas, CZ Manolis, GD Inst Engn Seismol & Earthquake Engn ITSAK GR-55102 Thessaloniki Greece Aristotle Univ Thessaloniki Dept Civil Engn GR-54006 Thessaloniki Greece

A stochastic boundary element method (SBEM) is developed in this work for evaluating the dynamic response of underground openings excited by seismically induced, horizontally polarized shear waves under steady-state conditions. The surrounding geological medium is viewed as an elastic continuum exhibiting large randomness in its mechanical properties, which implies that the wave number of the propagating signal is a function of a random variable. Suitable Green's functions are proposed and used within the context of the SBEM formulation. More specifically, a series expansion for the Green's functions is employed, where the basis functions are orthogonal polynomials of a random argument (polynomial chaos). These are subsequently incorporated in the SBEM formulation, which employs the usual quadratic, isoparametric line elements for modeling the surfaces of the problem in question. Finally, this formulation is used for the solution of a few problems of engineering interest involving buried cavities (tunnels). We note that the present approach departs from earlier boundary element derivations based on perturbations, which are valid for 'small' amounts of randomness in the elastic continuum. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： polynomial chaos random media SH waves soil dynamics stochastic boundary element method underground structures wave motion

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boundary element method for isotropic media with random shear moduli

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JOURNAL OF COMPUTATIONAL ACOUSTICS 2005年第1期13卷 229-258页

作者： Waubke, H Austrian Acad Sci Acoust Res Inst A-1010 Vienna Austria

Green's functions for elastic solids with random properties are usually derived by means of the perturbation method. This paper deals with a new approach that has the potential to deal with a large variability of random shear modulus based on the transformation of a polynomial chaos. The deterministic Green's functions for stresses and displacements and the principal values in the boundary integrals caused by a pressure load on the surface axe nonlinear transformations of the random variables. A series of transformations of the polynomial chaos is used to transform significant parts of the equation. The first operation is a projection of the log normal distributed shear modulus to a series of Hermite's polynomials based on a Gaussian variable. The second operation is the determination of an arbitrary potential of the wave velocity. The last operation, similar to the first one, consists in the determination of an exponential function depending on the inverse of the wave velocity. These operations, together with multiplications and summations, transform the complete relation from the random shear modulus to Green's functions and principal values. The inversion of the system matrix is already derived for the random finite element approach. The operations are independent of the specific problem and can be applied to almost all acoustic media and similar nonli near problems.

关键词： stochastic boundary element method polynomial chaos

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stochastic boundary element method FOR RELIABILITY ANALYSIS OF PLATE AND BEAMS COMPOSITE STRUCTURES

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Applied Mathematics and Mechanics(English Edition) 1997年第5期18卷 483-491页

作者：张妃二袁鸿 Department of Civil Engineering Guangdong University of Technology Guangzhou PR China

In this paper, the reliability of orthotropic plate and beams composite structures, which is under the actions of the stochastic loading and stochastic boundary conditions, have been analyzed by stochastic boundary element method. First, the boundary integral equation of orthotropic plate and beams composite structures is given in this paper, and then based on the stochastic boundary element method, the method for reliability analysis of stochastic structures is establishes and formulas for computation of reliability index of orthotropic plate and beams composite structures are obtained. The computed examples show the efficient of the method used in this paper.

关键词： stochastic boundary element method stochastic loading plate and beams composite structures reliability index

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