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ENME E3332: This coarse is intended for junior and senior level undergraduate students in science and engineering. The text material evolved from over 50 years of combined teaching experience of the authors in undergraduate finite element courses. The course deals with a formulation and application of the finite element method and it differs from the related finite element courses in the following three respects:


  1. It is introductory and self-contained. Only a modest background covered by most engineering and science curricula in the first two years is required. The relevant topics in mathematics, such as matrix algebra, differential and integral equations, and in physics, such as conservation laws and constitutive equations, are reinforced.

  2. It is generic. While most introductory finite element courses are application specific, such as being based on energy principles for linear elasticity, the finite element method in this course is formulated as a general purpose numerical procedure for solving partial differential equations. Consequently, students from various engineering and science disciplines will benefit equally from the exposition of the subject.

  3. It is a hands-on experience. The course integrates finite element theory, finite element code development and application of commercial software packages. Finite element code development is introduced through MATLAB exercises and a MATLAB program, whereas ABAQUS is chosen for demonstrating the use of the finite element method in the commercial arena.

Prerequisites: modest background in mathematics and physics, elementary computer programming, linear algebra, senior standing.

ENME E4363: The course covers fundamental modelling techniques aimed at bridging diverse temporal and spatial scales ranging from the atomic level to a full-scale product level. It focuses on practical multiscale methods that account for fine-scale (material) details but do not require their precise resolution. 

This course comprehensively covers theory and implementation, providing a detailed exposition of the state-of-the-art multiscale theories and their insertion into conventional (single-scale) finite element code architecture. The robustness and design aspects of multiscale methods are also emphasised, which is accomplished via four building blocks: upscaling of information, systematic reduction of information, characterization of information utilizing experimental data, and material optimization. 

Key features of the course are:

  • Combines fundamental theory and practical methods of multiscale modelling

  • Covers the state-of-the-art multiscale theories and examines their practical usability in design

  • Covers applications of multiscale methods

The course is intended for graduate students studying multiscale science and engineering. It is also a must-have reference for government laboratories, researchers and practitioners in civil, aerospace, pharmaceutical, electronics, and automotive industries, and commercial software vendors.

Prerequisites: Introductory courses in Finite Element method or equivalent are required.


Focus on formulation and finite element solution of nonlinear continuum mechanics problems. The course covers the following six  topics: (i) introduction to nonlinear continuum mechanics including tensor calculus, particles, configurations, deformation and motion, material derivative, deformation gradients, polar decomposition, velocity gradient, rate of deformation and spin, deformation of surface and volume elements, Lagrangian and Eulerian stress and strain, objectivity and frame invariance, and objective stress rate measures; (ii) formulation of nonlinear material models including  nonlinear elasticity, hyperelasticity, rate independent and dependent plasticity and damage; (iii) formulation of geometric nonlinearities including Lagrangian, Updated Lagrangian and Corotational formulations; (iv) formulation of discrete  finite element equations for nonlinear systems including stress update procedures and consistent linearization; (v) solution strategies for nonlinear problems (incrementation, iteration), and computational procedures for large systems of nonlinear algebraic equations including Newton method, local and global convergence of Newton method, line search, continuation methods, secant method for system of nonlinear equations and BFGS method; and (vi) special topics including formulation of contact problems (nonlinear boundary conditions), follower forces (deformation dependent forces) and nonlinear dynamics.

The course is aimed at exposing graduate students and practitioners from Civil, Mechanical, Aerospace, Chemical Engineering, Applied Mathematics, Physics and Materials with computational methods for nonlinear PDEs with emphasis on continuum mechanics.

Prerequisites: Introductory courses in Finite Element method or equivalent are required.

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