Linear and Nonlinear Analysis of Laminated Plates using Small and Large Deflection Theory

Inhaltsverzeichnis (Table of Contents)

• Introduction
  • Scope of the Work
  • Objectives and Motivation
  • Literature Review
• Theoretical Formulation
  • Mindlin Plate Theory
  • Stress-Strain Relations
  • Equilibrium Equations
  • Boundary Conditions
• Numerical Solution Technique
  • Dynamic Relaxation (DR) Method
  • Discretization and Finite Difference Scheme
  • Solution Procedure
  • Convergence Criteria
• Numerical Results and Discussion
  • Validation of the DR Solution
  • Effect of Shear Deformation
  • Effect of Material Anisotropy
  • Effect of Fiber Orientation
  • Effect of Coupling between Bending and Stretching

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

The main objective of this work is to develop a numerical method for analyzing the nonlinear behavior of rectangular laminated plates subjected to transverse loads. The study employs the Mindlin plate theory, which accounts for shear deformation, and utilizes the Dynamic Relaxation (DR) method for solving the governing equations.

• Nonlinear behavior of laminated plates
• Shear deformation effects
• Material anisotropy
• Fiber orientation influence
• Coupling between bending and stretching

Zusammenfassung der Kapitel (Chapter Summaries)

• Introduction: This chapter introduces the scope and objectives of the research, providing a background on the importance of understanding the nonlinear behavior of laminated plates. It also outlines the key themes and motivations behind the study.
• Theoretical Formulation: This chapter presents the theoretical foundation of the analysis, including the Mindlin plate theory, stress-strain relations, equilibrium equations, and boundary conditions. It lays the groundwork for the numerical solution method.
• Numerical Solution Technique: This chapter focuses on the Dynamic Relaxation (DR) method, a numerical technique used to solve the governing equations. It describes the discretization process, finite difference scheme, solution procedure, and convergence criteria.
• Numerical Results and Discussion: This chapter presents the results obtained using the DR method, demonstrating the validity of the solution by comparing it with existing analytical and numerical solutions. It then analyzes the effects of shear deformation, material anisotropy, fiber orientation, and coupling between bending and stretching on the plate's behavior.

Schlüsselwörter (Keywords)

The main keywords and focus topics of this work are: laminated plates, nonlinear analysis, Mindlin plate theory, Dynamic Relaxation (DR) method, shear deformation, material anisotropy, fiber orientation, bending-stretching coupling, numerical modeling.