Background:
Introduction to Numerical Methods
Overview – basic ingredients of the FEM
Comparison with alternative numerical methods
Basic Concepts of FEM – One-Dimensional Problems
Axial deformations of a bar or one-dimensional heat transfer
Strong and weak forms (variational and virtual work statements)
Primary and secondary variables of the formulation
Essential vs. natural boundary conditions
Methods of approximations (weak-form Galerkin method)
Finite element approximation functions (linear, quadratic, and cubic elements)
Assembly of element equations
Illustrative examples and discussion of results in light of physical response
Extension to of FEM to Two-Dimensional Problems
Membrane and heat transfer-like problems in 2D
Elements types (triangular and quadrilateral elements)
Axisymmetric problems
Discussions of representative field problems to understanding modeling issues
Eigenvalue and Time-Depenedent Problems
Free vibration of elastic systems (natural frequencies, modal response, etc)
Transient Analysis
Time integration procedures
Explicit dynamic integration
Plane and 3D Elasticity
Governing equations of plane elasticity problems
Elements types (triangular and quadrilateral elements)
Incompatible modes
3-D Elasticity problems
Types of 3-D Finite elements (interpolation functions)
Discussion of example problems to bring out modeling issues |
Composite Materials-An Introduction
An Introduction to Fiber-Reinforced Composite Materials
Equations of Anisotropic Elasticity
Introduction to Composite Materials
Constitutive Equations of a Lamina
Introduction to Non-Linear Problems
Geometric and material non-linearity
Nonlinear formulation of a 2-D Model problem
Solution algorithms for the solution of non-linear algebraic equations
Derivation of tangent stiffness coefficients
Convergence criteria
Nonlinear Bending of Beams
Euler-Bernoulli beam theory
Nonlinear finite element formulation of Euler-Bernoulli beam theory
Tangent stiffness calculations
Membrane locking
Timsohenko beam theory and its finite element model
Shear locking
Numerical examples
Nonlinear Bending of Plates
Nonlinear finite element formulation of the first-order shear deformation
(Mindlin) plate theory
Tangent matrix coefficients
Shear and membrane locking
Numerical examples
Composite Plates and Shells
Classical and First-Order Theories of Laminated Composite Plates
The First-Order Laminated Plate Theory
Laminate Stiffnesses for Selected Laminates
Linear Finite Element Analysis of Composite Plates and Shells
Nonlinear Analysis of Composite Plates and Shells
Third-Order Theory of Laminated Composite Plates and Shells
Layerwise Theory and Variable Kinematic Models
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