Analysis of Structures on Elastic Foundation: Incorporating the Spectral Method of Boundary Elements

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
About the author
Preface
Introduction
1 Boundary equations and boundary element methods: Literature review, problem statement. The goals and objectives of the study
	1.1 Development of methods of potential
	1.2 Method of boundary elements
	1.3 Contact dynamic problems of the theory of elasticity
	1.4 Boundary equations in structural mechanics
	1.5 Research goals and objectives
	Note
	References
2 The guiding philosophy of boundary element methods and boundary value problems
	2.1 General concepts
	2.2 Methods of boundary equations in problems calculating structures on elastic foundation
	References
3 Boundary element method (BEM) in one-dimensional problems
	3.1 General approaches to constructing boundary equations
	3.2 The generalized functions in structural mechanics
	3.3 The generalized method of integral transformation and its relation to the method of boundary equations
	3.4 Constructing boundary equations with delta-transform technique
	3.5 Standardized form of boundary value problems
	3.6 The relationship of Green’s function with homogeneous solutions of the method of initial parameters
	References
4 Boundary element methods (BEM) in the multidimensional problems
	4.1 The integral equations of boundary element methods
	4.2 The construction of boundary equations by the delta-transformation technique
	4.3 The equivalence of direct and indirect BEM
	References
5 Spectral method of boundary elements (SMBE)
	5.1 SMBE in one-dimensional problems
	5.2 The spectral method of boundary element (SMBE) in multidimensional problems
	References
6 Structures on elastic foundation
	6.1 Overview and background
	6.2 The problems described by the integro-differential system of equations
	6.3 The application of the spectral method of boundary element to the oscillation of the plates on elastic foundation
	6.4 Application of integral transformations with exponential-trigonometric kernels for calculating structures on elastic foundation
	Notes
	References
7 Generalized model of elastic foundation
	7.1 The kernel of the generalized model of elastic foundation
	7.2 The determination of the characteristics of the generalized model of the elastic foundation (base)
	7.3 Contact problem for the rigid die, lying on the generalized elastic base
	7.4 On one method of calculation of structures on elastic foundation
	References
8 The application of SMBE to the design structure on elastic foundation
	8.1 The calculation of the membrane of arbitrary shape on an elastic foundation
	8.2 The calculation of the non-isolated beams and plates, lying on an elastic foundation, described by the generalized model
	8.3 The forced oscillations of a rectangular plate on an elastic foundation
	References
9 The special features of solution of dynamic problems by the method of boundary equations
	9.1 Accounting of (for) internal friction in the problems of analysis (calculating) of structures on an elastic foundation
	9.2 Construction of Green’s function for bases having frequency-dependent internal friction
	9.3 The Green’s functions of systems with the frequency-independent internal friction
	9.4 The Construction of the green’s function of the dynamic stationary problem for the elasto-viscous half-plane
	9.5 The numerical realization of boundary element method
	9.6 The influence (effect) of internal friction on harmonic oscillations of the rigid die lying on an inertial half-space
	9.7 A frequency-independent relative damping model
	9.8 Oscillations of beams lying on an elastic base with frequency-independent relative damping
	References
10 Interaction of structures with the ground under seismic impacts
	10.1 The propagation of seismic waves in the laminar inhomogeneous medium
	10.2 Solution of a plane problem of elasticity theory for a layer
		10.2.1 Solution of a plane problem of the theory of elasticity for an inhomogeneous layer in height
		10.2.2 Solution to the problem on wave propagation in homogeneous layer by the method of initial functions
		10.2.3 Interaction of structures with the ground under seismic impact
	References
Appendix A
Appendix B
Appendix C
Appendix D
Index