This course describes, besides the physical and mathematical background of the finite element method, special discretization techniques and algorithms which have to be applied for nonlinear problems of solid mechanics.
The course will describe the theory and computer implementation of nonlinear finite element method. The implementation will be carried out on simple heat transfer and solid mechanics problems.
The focus is on geometric nonlinearities; however some material nonlinearity will also be discussed. Both static and transient (timedependent) problems will be studied.
The main textbook of the course is the book “An Introduction to nonlinear finite element analysis” by J.N. Reddy. The book is suitable as a text book for a first course as nonlinear finite elements in mechanical, civil, aerospace engineering departments.
Syllabus
 Introduction
 A review of finite element method
 1D problems
 2D problems
 Library of 2D finite elements
 Numerical Integration
 Computer Implementation
 1D heat transfer problems
 Governing differential equation
 Weak formulation
 Finite element model
 Solution procedure
 Computer implementation
 EulerBernouli beams
 Timoshenko beams
 Model equation
 Weak form
 Finite element method
 Solution procedure
 Computer implementation
 Classical plate theory (CPT)
 Variational formulation of CPT
 Finite element models of CPT
 Computer Implementation of CPT

 Time approximation
 Stability and accuracy
 Transient analysis of nonlinear problems
 Computer implementation
 Numerical examples
 2D Continuum Elements
 Introduction
 Strain and stress measures
 Strain and stress measures between configurations
 Constitutive equations
 Total and updated Lagrangian formulations
 Finite element methods of 2D continua
 Nonlinear elastic problems
 Small deformation theory of plasticity
 Numerical examples
 Nonlinear bending of beams
 2D heat transfer problems
 Nonlinear bending of elastic plates
 Nonlinear analysis of 2D problems
 Finite element formulation of solid continua
 Material nonlinearity

Prerequisites:
 Finite Element I
 Continuum Mechanics