Analysis of Structures on Elastic Foundation: Incorporating the Spectral Method of Boundary Elements By Levon Gregory Petrosian
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Analysis of Structures on Elastic Foundation: Incorporating the Spectral Method of Boundary Elements By Levon Gregory Petrosian

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571
File size
18.15 MB
Format
Digital PDF
Category
eBook[PDF]
About this ebook
Analysis of Structures on Elastic Foundation: Incorporating the Spectral Method of Boundary Elements" by Levon Gregory Petrosian presents advanced mathematical methods for solving static and dynamic problems in structural and soil mechanics. [1, 2]
Core Topics Covered
  • The Spectral Method of Boundary Elements (SMBE): Development of the SMBE framework utilizing integral transforms paired with an orthogonal kernel inside an extended domain. [1]
  • Boundary Equations Philosophy: Conceptual foundation of boundary element methods (BEM) applied specifically to boundary-value problems in engineering. [1]
  • Integral Transforms Theory: A unified engineering approach to integral transforms built upon the spectral theory of linear differential operators. [1]
  • A New Versatile Foundation Model: Presentation of a novel subgrade model providing distinct mathematical and practical advantages over classical Winkler or ground-based baselines. [1]
  • Generalized Functions (Distribution Theory): Deep mathematical integration of generalized functions to describe complex structural loads, boundary impacts, and classical method simplifications. [1, 2]
  • Static and Dynamic Calculations: Practical formulation and mathematical solution examples of both static loads and dynamic vibrations/oscillations. [1, 2]
  • Structural Elements Applications: Customized transforms and calculations tailored to standard architectural elements, including:
    • Bars
    • Beams
    • Plates (including rectangular and arbitrary forms on Winklerian bases)
    • Shells [1, 2, 3]
  • Soil-Structure Interaction: Modeling boundary-value interfaces linking structural loads directly with supporting soil mechanics. [1]
Overview of Key Technical Methodologies
Methodology Primary Function in Book
SMBE Resolves static and dynamic boundary-value problems across arbitrary structural boundaries.
Orthogonal Kernels Powers integral transforms across extended domains to solve differential structural equations.
Generalized Functions Simplifies structural math by consistently mapping discontinuous loads and irregular structural impacts.

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Topics

9781000585698 9781000585711 9781003273837 9781032227108 9781032227139 A New Versatile Foundation Model: Presentation of a novel subgrade model Boundary Equations Philosophy: Conceptual foundation of boundary element methods (BEM) Development of the SMBE framework Generalized Functions (Distribution Theory): Deep mathematical integration of generalized functions Generalized Functions Simplifies structural math by consistently mapping discontinuous loads and irregular structural impacts Integral Transforms Theory: A unified engineering approach to integral transforms Orthogonal Kernels Powers integral transforms across extended domains to solve differential structural equations. SMBE Resolves static and dynamic boundary-value problems across arbitrary structural boundaries. Soil-Structure Interaction: Modeling boundary-value interfaces linking structural loads Static and Dynamic Calculations: Practical formulation and mathematical solution examples Structural Elements Applications: Customized transforms and calculations The Spectral Method of Boundary Elements (SMBE)
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