Lecture meets 2 times per week for 75 minutes per meeting for 15 weeks
Specific course information
Catalog description: Fundamentals of theory of elasticity; variational principles; one-, two-, and three-dimensional elasticity finite elements; interpolation methods; numerical integration; convergence criteria; stress interpretation.
Prerequisites: CCE 47400 or equivalent, or graduate standing
Course status: Elective course
Specific goals for the course
Student learning outcomes - Upon successful completion of this course the student shall be able to:
have a good command of 3D elasticity governing equations
estimate stresses and strains in three-dimensional bodies
set-up weighted residual forms of governing equations for problems in linear elasticity
have a fundamental understanding of finite element technology in 1D, 2D, and 3D
find numerical solutions for elasticity problems
identify numerical issues (locking, spurious energy modes)
assess accuracy and convergence of finite element solutions
interpret and assess stress estimates
write Matlab programs for numerical analysis of elasticity problems
use commercial finite element software (ABAQUS)
communicate analysis methods and discuss results in technical papers
Relationship of course to program outcomes
Outcome 1: An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
Outcome 3: An ability to communicate effectively with a range of audiences.
Outcome 5: An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
Topics
REVIEW OF 3D LINEAR ELASTICITY
Stresses and strains in 3D, equilibrium, constitutive equations, boundary value problems
2D ELASTICITY
Plane stress and plane strain conditions, constitutive equations in 2D
VARIATIONAL FORMULATIONS
Weighted residuals for 1-D, 2-D and 3-D elasticity, divergence theorem, virtual work statement, essential and natural boundary conditions, the Fundamental Theorem of the Calculus of Variations
DISCRETIZATION VIA THE RITZ METHOD
The Ritz method of approximation, discretized governing equations, error and convergence, Lagrangian shape functions, finite element approximations
FINITE ELEMENTS IN 1D ELASTCITY
Finite element approximation, error and convergence
NUMERICAL IMPLEMENTATION
Assembly procedure, boundary conditions, solution of systems of linear equations, numerical integration using the Gauss quadrature
FINITE ELEMENTS IN 2D/3D ELASTCITY
Element technology in 2D (T3, T6, Q4, Q8, Q9, ..), and 3D
