CE 720


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, 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. 3 credit hours.

Prerequisite		Undergraduate solid mechanics Engineering mathematics (standard undergraduate curriculum) Matrix Structural Analysis (CE 425 / 594A or equivalent)

Course Objectives		At the end of the course, you will be able to use finite element method in an informed manner to analyze solids and structures accurately and reliably, while recognizing any limitations of your analysis in relation to real physical problem. The course focuses on linear static analysis. You will also be able to read literature and extend your knowledge related to dynamic and nonlinear finite element analysis.

Course Topics		Review of Matrix Structural Analysis: degrees of freedom; bar, beam and frame elements; element stiffness matrix and consistent load vectors; stiffness of rotated elements; assembly; global stiffness matrix and its properties; modeling and verification. 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.

Course Requirements		Homework 30 % Comprehensive modeling project: 20 % Mid-term 25 % Final Exam 25 %

Required Text		Concepts and Applications of Finite Element Analysis, R.D. Cook, D.S. Malkus, M.E. Plesha and R.J. Witt, 4th edition, John Wiley and Sons, 2002. ISBN: 0471356050

Computer and Internet Requirements		NCSU has recommended minimum specifications for computers used for classes. Depending on your computer needs, we recommend your computer meet or exceed the following minimum specifications below. PCs must have an Intel-compatible 800 MHz processor, 256 MB RAM, 8 GB hard drive with 1 GB free space available, 256 Color Display, CD-ROM drive, 800x600 (min.) video adapter, sound card, and speakers. The operating system should be Windows 2000 or XP. Real One Player Basic (available free online) and high speed Internet connection such as cable, DSL, T1 or LAN will be required for EOL courses. MAC users must have a G3 processor with firewire and USB factory built-in, 256 MB RAM, 10 GB with 1GB free space available, 256 Color Display, CD-ROM drive, 800x600 (min) video adapter, sound card, and speakers. The operating system must be MacOS 10.3 (minimum) along with the above RealOne and Internet specifications above. For more detailed information on computer specifications and recommendations, please refer to our website at: http://engineeringonline.ncsu.edu/currentstudents/computeraccess.htm

Software Requirements		Some of the homework and the final modeling project would be performed using the finite element analysis software ANSYS, which is available remotely on the Eos system at NCSU.

Instructor		Murthy N. Guddati, Assistant Professor Department of Civil, Construction and Environmental Engineering North Carolina State University 312 Mann Hall Raleigh, NC 27695 Phone: (919) 515-7699 Fax: (919) 515-7908 E-mail: mnguddat@eos.ncsu.edu Website: http://www4.ncsu.edu/~mnguddat/