The Fundamentals of Boundary Element Methods / Olena Sierikova, editor.

Format:

Book

Contributor:

Sierikova, Olena, editor.

Series:

Mathematics research developments series.

Mathematics Research Developments Series

Language:

English

Subjects (All):

Boundary element methods.

Physical Description:

1 online resource (159 pages)

Edition:

First edition.

Place of Publication:

New York : Nova Science Publishers, Inc., [2024]

Summary:

"The boundary element method is one of the most popular methods of numerical modeling the various problems in mechanics and physics. A huge achievement that attracts scientists from all over the world is the possibility to consider not the region itself, in which the problem needs to be solved, but its border. The boundary element method allows to significantly simplify the decision process, increasing the accuracy and reliability of the results. There are a large number of practical issues that formulated as the boundary value problems of mathematical physics or mechanics of deformed solids. Recently, a number of issues have been clarified about the interaction of different continuous media. Such problems include analyzing strength-strain states of hydroturbine equipment elements blades, hydroturbine covers, finding blade optimal parameters of powerful air installations and airplane wings, research in problems of flooding urban areas, estimations of liquid oscillation frequencies in tanks and reservoirs"-- Provided by publisher.

Contents:

Intro

Contents

Preface

Chapter 1

Boundary Element Methods for Liquid Hydrocarbon Reservoirs' Vibration Analysis

Abstract

Introduction

Technogenic Impact on Soils

Technogenic Impact on the Groundwaters

Atmospheric Air Pollution

The Effect of Oil on Vegetation

Construction of Scenarios for the Occurrence and Development of Emergency Situations Leading to the Death of People

Literature Review

Research Methods

Discussion

Outcomes

References

Chapter 2

Boundary and Finite Element Methods in Nanocomposites Effective Elastic Characteristics Estimation

Methodology

Basic Relations

Classical and Nonclassical Boundary Conditions

Boundary Element Method Implementation

Numerical Results and Discussion

Conclusion and Further Research

Acknowledgment

Chapter 3

Boundary Element Methods in One-Dimensional Singular Integral Equations

Benchmark Equation for Boundary Element Methods in 2D Problems

Boundary Elements with Constant Density

Linear Boundary Elements

Quadratic Boundary Elements

Cubic Boundary Elements

Conclusions and Further Research

Chapter 4

Boundary Element Methods for Hypersingular Integral Equations Over Circular Domains

Problem Statement

One-Dimensional Hypersingular Integral Equations

Two-Dimensional Hypersingular Integral Equations

Reducing Two-Dimensional Hypersingular Integral Equation to One-Dimensional for Circles

Chapter 5

Boundary Element Method Testing for Axially-Symmetrical Problems

Introduction.

Methodology

Determination of Vibrations Frequencies and Modes of a Rotation Shell in Vacuum

Determination of Liquid Pressure on the Shell

Because the S1 Is the Shell of Rotation, Then the Function W Will Be Represented As

Results and Discussion

Chapter 6

Construction of Fundamental Solution of {1,2}-Approximation Static Equations of Momentless Stress State for Transversely-Isotropic Plates

Purpose and Study Objectives

Materials and Methods

Basic Correlations and Mathematical Formulation of the Problem

Research Method Statement

Research Results and Discussion

Chapter 7

Boundary Element Method in Hydroelastic Interaction Problems of Structural Elements

Testing the Deterministic Method

Computer Simulation of Structure Forced Oscillations under the Condition of Vague Assignment of Load Parameters

Index

Blank Page.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes index.

Other Format:

Print version: Sierikova, Olena The Fundamentals of Boundary Element Methods

ISBN:

9798891138469