Instructor

Dr. Murthy Guddati

Civil, Construction, and Environmental Engineering

Phone: 919-515-7699
Fax: 919-515-7908
Email: mnguddat@ncsu.edu
Instructor Website
Research Website

# CE 526 Finite Element Methods in Structural Engineering

3 Credit Hours

Review of direct stiffness method; degrees of freedom; stiffness; assembly; transformation; analysis of solids through principle of virtual work; approximate stiffness through finite element shape functions; study of various finite elements including constant strain triangle and bilinear rectangle, their limitations and convergence issues; higher order elements, incompatible elements; isoparametric formulation and distorted elements; application of finite element analysis for solids and structures; modeling considerations and software use.

## Prerequisites

Graduate Introduction to Solid Mechanics (CE 515 or equivalent) and knowledge of undergraduate level advanced engineering mathematics.

## Course Objectives

Students will be able to use the finite element method in an informed manner to analyze solids and structures accurately and reliably, while recognizing the limitations of their analysis in relation to real physical problems. The course focuses on linear static analysis, but students will also be able to read literature and extend their knowledge related to dynamic and nonlinear finite element analysis.

## Course Topics

Topics will be selected from:

Analysis of Discrete Systems: degrees of freedom; bar, beam and frame elements; element stiffness matrix; assembly; global stiffness matrix and its properties.

Equations governing the deformation of 2-D solid continuum: equilibrium equations; strain-displacement relations; stress-strain relations; boundary conditions; principle of virtual work.

FEA of 2-D solids with simple elements: need for approximation; interpolation of displacements; stiffness matrices and consistent load vectors; bar and beam elements revisited; constant strain triangle; stiffening effect of approximation; quadratic triangle; bilinear rectangle; quadratic rectangles; inter-element compatibility; improved rectangular elements for bending deformation; stress calculation; overview of isoparametric elements.

Modeling Considerations: sources of errors; discretization errors and their estimation; convergence considerations; stress smoothing; solution checking; good and bad practices.

Isoparametric formulation: bar element; bilinear quadrilateral element; gauss quadrature; higher order elements; selective reduced integration; convergence considerations; stress calculation.

## Textbook

Textbook to be decided.

Homework 40 %
Mid-term 25 %
Final Exam 35 %

## Computer and Software Requirements

Please review minimum computer specifications recommended by NC State University and Engineering Online.

Some of the homework and the project will require the use of finite element analysis software. For this purpose a finite element software will be available remotely on the Eos system at NCSU. Students may choose to use other software, but access will be their responsibility.