# Finite Element Analysis: Theory, Applications, and Practice

The finite element method (FEM) is a numerical technique to obtain approximate solutions to a wide variety of engineering problems. The FEM equations are solved by means of algebraic, differential, and integral equations. FEM models engineering problems from simple cantilever beams to blood vessel mechanics. CAD and CAE use finite element analysis (FEA) methods to solve and model the entire spectrum of engineering design. Finite element programs, such as ANSYS and NASTRAN, provide an interface to develop either quick strength stress calculations or complex assemblies analysis for interacting components.

##### Complete Details

This course includes extensive examples from simple beam theory to the soft tissue analysis using continuum mechanics to illustrate the concepts, and provide understanding and practice for CAE design modeling. Simple 1D, 2D, and 3D examples are easy to construct and match with closed-form solution to classical Timoshenko problems. Participants learn simple modeling techniques and methods to tackle advanced FE problems, allowing them to understand how to model structures quickly. Energy and direct matrix solution methods are compared. Theoretical concept discussions involve both lecture and in-class problem solution.

The course satisfies experience levels that include both engineering and manufacturing. Both the design drafter and design team manager learn the basic knowledge of FE methods. CAE models reduce the necessary prototype testing during the iterative design process. The modeling process improves velocity for design to manufacturing and production.

##### Course Materials

Participants receive a copy of the lecture notes. These notes are for participants only and are not for sale.

##### Coordinator and Lecturer

**Ertugrul Taciroglu, Ph. D.,** Professor, Civil and Environmental Engineering, Henry Samueli School of Engineering and Applied Science. Dr. Taciroglu earned a B.S. degree in 1993 from Istanbul Technical University, and M.S. and Ph.D. degrees from the University of Illinois at Urbana-Champaign (UIUC) in 1995, and 1998, respectively. After a stint at the Center for Simulation of Advanced Rockets (UIUC) as a postdoctoral researcher, he joined the Civil & Environmental Engineering Department at UCLA in 2001. His research activities span the disciplines of theoretical & applied mechanics and structural & geotechnical earthquake engineering. He is currently working on projects on soil‑structure interaction, system identification, performance based engineering, and simulation of structural response under extreme loads. Dr. Taciroglu is a 2006 recipient of the U.S. National Science Foundation CAREER award, and the 2011 Walter Huber Prize of the American Society of Civil Engineers (ASCE). In 2015, he was elected as a Fellow of the Engineering Mechanics Institute of the American Society of Civil Engineers (ASCE). He is the Managing Editor of the ASCE Journal of Structural Engineering, and serves on the Editorial Boards of ASCE Journal of Engineering Mechanics, EERI Earthquake Spectra, and Int. J. of Structural Control and Health Monitoring.

##### Daily Schedule

*Day 1*

**General FEA Modeling, Techniques, and Theory**

- Introduction, course outline, and requests
- Discussion of professional and personal software options
- Introduction to direct and energy methods FEA theory
- Mathematical background with linear algebra
- Introduction to 1D structural and heat transfer models
- Simple axis-symmetric models
- One-dimensional FEA
- Variational functions, element types (Truss, Beam, Shell, and Plates)
- Simple nonlinear problems and solution methods like Rayleigh Ritz
- Interpolation or shape functions

**Detailed Examples of FE Problems and Solutions**

- Build and solve FE model using preprocessor, solver, and postprocessor
- Introduction to stiffness matrix
- One-dimensional structural and heat transfer examples
- Simple vibrations analysis and modeling
- Discussions of variational mechanics and energy methods using virtual work
- Three cornerstones: equilibrium, boundary conditions, compatibility
- Geometry, material data, boundary conditions, solver choices, results and validation
- Validating and model checks by strength of materials

*Day 2*

**General Model Creation for Practical Problems and Theory**

- Two-dimensional finite elements
- Boundary and initial value problems
- Global and local coordinate systems
- Elasticity theory and variational mechanics theory
- Virtual work and equilibrium
- Element type introductions: triangle, square, beam, and frames
- Governing differential equations and simple beam theory
- Beam analysis using displacements and beam FE elements
- Matrix transformations

**Detailed Example of FE Problems and Solutions**

- Participant request problems
- Problems creating mesh structure for complex geometry
- Element type discussions: tetrahedral, plate, bricks
- Solving differential equations by direction solution
- Solving differential equations by energy methods
- — Virtual work-energy or variational mechanics with ref. equilibrium
- Simple model checking and use of elements for structural modeling
- Solution problems for complex models
- FE mathematics, stiffness matrix, interpolation functions
- Solutions without meaning (pseudo-elastic solutions)
- Global and local coordinate systems

*Day 3*

**General Nonlinear Structural Engineering Methods**

- Nonlinear modeling introduction
- Variational principles approximate solutions to FE
- Galerkin approximation
- Coupled partial differential equations and solvers
- Isoparametric finite elements
- Displacement-based elements
- Numerical integration methods for nonlinear problems
- More details on interpolations and shape functions
- Axisymmetric formulations
- Higher-order FEA elements ProMechanica
- Plate finite elements

**Detailed Examples for Nonlinear Modeling**

- Detailed examples for calculating creep and plasticity
- Options for creep and plasticity in ANSYS or MARC
- Buckling problems and solutions
- Modal and vibrations analysis modeling
- Problems in creep, plasticity, and hyperelasticity
- Material nonlinear problems: large or small strain
- Convergence problems and solution methods
- Computational needs and systems decisions
- Large FE models with 200 k to 1*10ˆ 6 elements
- Parallel processing and submitting to batch servers

**For more information contact the Short Course Program Office: **

shortcourses@uclaextension.edu | (310) 825-3344 | fax (310) 206-2815