Theory and Analysis of Elastic Plates and Shells, Second Edition
This text presents a complete treatment of the theory and analysis of elastic plates. It provides detailed coverage of classic and shear deformation plate theories and their solutions by analytical as well as numerical methods for bending, buckling and natural vibrations. Analytical solutions are based on the Navier and Levy solution method, and numerical solutions are based on the Rayleigh-Ritz methods and finite element method. The author address a range of topics, including basic equations of elasticity, virtual work and energy principles, cylindrical bending of plates, rectangular plates and an introduction to the finite element method with applications to plates.
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Energy Principles and Variational Methods
References for Additional Reading
Analysis of Plate Strips
Bending of Simply Supported Rectangular Plates
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3-D elasticity approximation functions bending moments boundary conditions circular plate clamped classical plate theory coefficients components compression constants constitutive equations coordinate system cosh critical buckling load cylindrical coordinate system deflections and bending deformation theory denotes derivatives determine distributed transverse load dx dx dx dy dxdy elastic foundation Euler-Lagrange equations Figure finite element model FSDT Galerkin method given by Eq integration isotropic plates linear matrix maximum deflection mode shape natural vibration Navier nodes nondimensionalized obtain orthotropic plates plate aspect ratio plate strip point load polynomials principle of virtual problem Rayleigh-Ritz method Rayleigh-Ritz solution rectangular plates Reddy rotary inertia shear deformation shear stress simply supported plate sinh square plates strains Table tensor thermal total potential energy transverse deflection uniformly distributed load values variables variational vector virtual displacements zero
Mesh Free Methods: Moving Beyond the Finite Element Method
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Analytical Methods in Anisotropic Elasticity: with Symbolic Computational Tools
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